UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO
POSGRADO EN CIENCIAS (FÍSICA)
INSTITUTO DE FÍSICA
SEARCH FOR DARK MATTER, REACTOR AND SUPERNOVA
NEUTRINOS USING NOBLE LIQUID AND GERMANIUM
DETECTORS
TESIS
QUE PARA OPTAR POR EL GRADO DE
DOCTOR EN CIENCIAS
PRESENTA:
MARIO ANDRÉS ALPÍZAR VENEGAS
TUTOR PRINCIPAL
DR. ERIC VÁZQUEZ JÁUREGUI
INSTITUTO DE FÍSICA, UNAM
COMITÉ TUTOR
DR. EDUARDO PEINADO RODRÍGUEZ
INSTITUTO DE FÍSICA, UNAM
DRA. MYRIAM MONDRAGÓN CEBALLOS
INSTITUTO DE FÍSICA, UNAM
CIUDAD DE MÉXICO, ABRIL 2025
 
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PROTESTA UNIVERSITARIA DE INTEGRIDAD Y
HONESTIDAD ACADÉMICA PROFESIONAL
(Graduación con trabajo escrito)
De conformidad con lo dispuesto en los art́ıculos 87, fracción V del Estatuto General, 68,
primer párrafo, del Reglamento General de Estudios Universitarios y 26, fracción I, y 35 del
Reglamento General de Exámenes, me comprometo en todo tiempo a honrar a la Institución
y cumplir con los principios establecidos en el Código de Ética de la Universidad Nacional
Autónoma de México, especialmente con los de integridad y honestidad académica.
De acuerdo con lo anterior, manifiesto que el trabajo escrito titulado:
SEARCH FOR DARK MATTER, REACTOR AND SUPERNOVA NEUTRINOS USING
NOBLE LIQUID AND GERMANIUM DETECTORS
que presenté para obtener el grado de Doctorado es original, de mi autoŕıa y lo realicé con
el rigor metodológico exigido por mi programa de posgrado, citando las fuentes de ideas,
textos, gráficos u otro tipo de obras empleadas para su desarrollo.
En consecuencia, acepto que la falta de cumplimento de las disposiciones reglamentarias y
normativas de la Universidad, en particular las ya referidas en el Código de Ética, llevará a
la nulidad de los actos de carácter académico administrativo del proceso de graduación.
Atentamente
Mario Andrés Alṕızar Venegas
520462236
(Nombre, firma y Número de cuenta de la persona alumna)
11 
V¡O¡I'/UKn.>.D H.rqoro¡ ... l 
A'I!~U: 
''', 
COORDINACiÓN GENERAL DE ESTUDIOS DE POSGRADO 
CARTA AVAL PARA DAR INICIO A LOS TRÁMITES DE GRADUACiÓN 
Universidad Nacional Autónoma de México 
Secretaria General 
Coordinación General de Estudios de Posgrado 
Dr. Alberto Güijosa Hidalgo 
Programa de Posgrado en Ciencias Físicas 
Presente 
Quien suscribe, Dr. Eric Vázquez Jáuregui , tutor(a) 
principal de Mario Andrés Alpízar Venegas , con 
número de cuenta 520462236 , integrante del alumnado 
de Doctorado en Ciencias (Física) de ese programa, manifiesto 
bajo protesta de decir verdad que conozco el trabajo escrito de graduación 
elaborado por dicha persona, cuyo título es: 
SEARCH FOR DARK MATTER, REACTOR AND SUPERNOVA 
NEUTRINOS USING NOBLE L/QUID AND GERMAN/UM DETECTORS 
, así como el reporte que contiene el resultado emitido por la herramienta 
tecnológica de identificación de coincidencias y similitudes con la que se 
analizó ese trabajo, para la prevención de faltas de integridad académica. 
De esta manera, con fundamento en lo previsto por los artículos 96, 
fracción 111 del Estatuto General de la UNAM; 21 , primero y segundo 
párrafos, 32, 33 Y 34 del Reglamento General de Exámenes y; 22, 49, 
primer párrafo y 52, fracción II del Reglamento General de Estudios de 
Posgrado, AVALO que el trabajo de graduación presentado se envíe al 
jurado para su revisión y emisión de votos , por considerar que cumple con 
las exigencias de rigurosidad académica previstas en la legislación 
universitaria. 
Protesto lo necesario, 
Ciudad Universitaria, Cd. Mx., a 11 de c8,aT .'. 
Dr. Eric Vá ; q~ez Jáuregui 
abril de 202 5 
Tutor(a) principal 
Resumen
Esta tesis se centra en dos temas principales: la búsqueda de materia oscura usando el de-
tector DEAP-3600 y el estudio de la dispersión elástica coherente neutrino-núcleo (CEνNS),
incluyendo análisis con datos experimentales de CONUS+ y simulaciones de señales de su-
pernovas.
Primero, se presentan las evidencias principales que respaldan la existencia de la materia
oscura, describiendo las part́ıculas débilmente interactuantes (WIMPs), los axiones y los
neutrinos estériles como candidatos destacados, aśı como los métodos de detección.
Seguidamente, se describe en detalle el detector DEAP-3600. Se desarrolló un modelo
exhaustivo del fondo de neutrones radiogénicos usando el marco estad́ıstico de razón de
verosimilitud perfilada, construyendo y optimizando múltiples funciones de densidad de prob-
abilidad. Además, se exploró un enfoque basado en aprendizaje automático para identificar
retrocesos nucleares múltiples en interacciones de neutrones, un desaf́ıo para el cual no existe
una solución actualmente. Un clasificador tipo árbol de decisión potenciado mostró resulta-
dos prometedores para mitigar este fondo en futuros análisis. También se mejoró el modelo
de fondo gamma en la búsqueda de axiones solares al incluir emisiones gamma por captura
de neutrones en molibdeno y cobalto, incrementando significativamente el valor-p para la
hipótesis de sólo ruido de fondo, de 0.5±0.3% a 25±1%. Las búsquedas de WIMPs y axiones
solares continúan activamente en la colaboración DEAP.
Los resultados del experimento CONUS+ fueron empleados para para restringir parámetros
del Modelo Estándar (SM) y teoŕıas más allá del Modelo Estándar (BSM) mediante análisis
de optimización con χ2. Este trabajo produjo el primer ĺımite del ángulo de mezcla débil
obtenido de interacciones CEνNS con antineutrinos electrónicos de reactor provenientes de
una medición con significancia mayor a 3σ: sin2 θW = 0.268 ± 0.047. Adicionalmente, se
impuso un ĺımite superior al 90% de confianza para el momento magnético del neutrino:
µν ≤ 5.6 × 10−10µB. También se impusieron restricciones sobre interacciones no estándar
(NSI), con contornos en el plano ϵuVee –ϵ
dV
ee comparables a los de COHERENT. Estos resul-
tados confirman el potencial de CEνNS para estudiar parámetros electrodébiles como θW y
µν , y explorar escenarios BSM como las NSI.
De manera complementaria, se simularon señales de CEνNS producidas por el colapso
gravitacional de una supernova (SN) usando el software de código abierto EstrellaNueva.
Las capacidades de detección de DEAP-3600 y LUX-ZEPLIN (LZ) fueron evaluadas para
una SN de 15 M⊙, a distancias de 0.196, 10.0 y 20.0 kpc. DEAP se limita a eventos cercanos,
mientras que LZ puede detectar señales en todo el disco galáctico. Por consiguiente, se con-
struyeron cotas superiores e inferiores en los conteos de eventos para optimización mediante
χ2, obteniendo ĺımites para θW y µν , y analizando el efecto de la distancia. Además, se pro-
puso un método para aproximar la composición en sabores del haz de neutrinos, permitiendo
estudiar las NSI considerando tanto la jerarqúıa normal (NH) como la invertida (IH). Estos
resultados destacan el potencial de detectores de ĺıquidos nobles para explorar propiedades
fundamentales del neutrino, estableciendo una base sólida para futuras búsquedas con señales
de CEνNS provenientes de supernovas.
iv
Abstract
This thesis focuses on two main topics: the search for dark matter using the DEAP-
3600 detector, and the study of coherent elastic neutrino-nucleus scattering (CEνNS). The
latter includes analyses based on experimental data from the CONUS+ collaboration and
simulations of supernova neutrino signals.
To begin with, the main lines of evidence supporting the existence of dark matter are
presented. Weakly interacting massive particles (WIMPs), axions, and sterile neutrinos are
described as some of the most prominent candidates. The primary detection methods are
also outlined in this work.
Subsequently, the DEAP-3600 dark matter detector is described in detail. A comprehen-
sive background model for radiogenic neutrons was developed within the Profile Likelihood
Ratio statistical framework. Numerous probability density functions were constructed and
optimized to characterize this background. Additionally, a machine learning approach was
explored to identify multiple nuclear recoils from neutron interactions—a challenge for which
no current solution exists. A Boosted Decision Tree classifier achieved promising perfor-
mance, demonstrating the potential of machine learning techniques for neutron background
suppression in future analyses. The gamma background model for the solar axion search
was also improved by incorporating neutron capture gamma emissions from molybdenum
and cobalt isotopes, significantly increasing the background-only p-value from 0.5±0.3% to
25±1%. Both the WIMP and solar axion searches are ongoing efforts within the DEAP
collaboration.
Results from the CONUS+ experiment were used to constrain parameters from the Stan-
dard Model (SM) and beyond (BSM) using a χ2-based optimization analysis. This work pro-
duced the first CEνNS-derived limit on the weak mixing angle for reactor electron antineutri-
nos, from a measurement with a significance greater than 3σ: sin2 θW = 0.268± 0.047, along
with a 90% confidence upper limit on the neutrino magnetic moment: µν ≤ 5.6× 10−10µB.
Limits on Non-Standard Interactions (NSI) were also obtained, with contours in the ϵuVee –ϵ
dV
ee
plane comparable to those reported by COHERENT. These results show that CEνNS is a
powerful tool for probing electroweak parameters such as θW and µν , and for exploring BSM
scenarios such as NSI.
As part of the CEνNS investigation, signals from core-collapse supernovae (SNe) were sim-
ulated using the open-source software EstrellaNueva. The detection capabilities of DEAP-
3600 and LUX-ZEPLIN (LZ) were evaluated for a SN originating from a 15 M⊙ progenitor
star at distances of 0.196, 10.0, and 20.0 kpc. While DEAP is limited to nearby events,
LZ could detect SN signals across the entire galactic disk. Upper and lower bounds on the
expected event counts were established to enable χ2 optimization. Limits on θW and µν were
derived, and the effect of SN distance on these constraints was analyzed. Additionally, a
method was proposed to approximate the flavor composition of the neutrino burst, enabling
the study of NSI for all neutrino flavors considering both the normal (NH) and inverted (IH)
hierarchies. The results from this investigation demonstrate the potential of noble liquid
detectors to explore fundamental neutrino properties and lay the groundwork for future SNe
CEνNS-based searches.
v
Agradecimientos
Agradezco a mis papás, Mario y Eney, por su apoyo incondicional durante todos estos
años. Gracias por motivarme a perseguir mis sueños y por haberme criado para ser una
persona sincera y trabajadora, como ustedes. A mis hermanos, Meli y Jose, gracias por
visitarme y mantenerme cerca a través de sus mensajes; sent́ı su cariño a la distancia. A
mi abuelito Mario, gracias por habernos dejado un legado de generosidad y cariño. A Tita,
gracias por ser mi segunda mamá; este logro también fue posible gracias a tus enseñanzas
de vida.
Gracias, profe Eric, por tu esfuerzo y dedicación durante estos seis años de mentoŕıa en
la maestŕıa y el doctorado. Tu trabajo siempre fue hecho a conciencia, y priorizando el lado
humano de las personas. Gracias, profes Eduardo y Myriam. Valoro mucho las clases que
tuve con ambos y les agradezco también por completar mi comité tutor all-star. Extiendo
mi agradecimiento a otros profesores de la UNAM que me dieron excelentes cursos y que
fueron fundamentales en mi doctorado, especialmente a los profes Alexis Aguilar y Alberto
Mart́ın. También agradezco a los profes de la UCR, en especial a Blai Garolera y Alejandro
Jenkins: este largo proceso comenzó junto a ustedes. A Alberto Ángeles, gracias por la
terapia brindada con tanta dedicación; fue indispensable para sacar esto adelante.
A Alice: gracias por tu compañ́ıa en este arduo camino. Tu apoyo, paciencia y amor han
sido una gran inspiración durante todo este tiempo.
A mis hermanos no de sangre, Alfredo y Marco, gracias por creer en mı́ durante todos estos
años. Gracias por las visitas, y las charlas a distancia; sin ustedes esto no habŕıa sido posible.
A PalcoVIP: Mauricio, Favián y Pedro, gracias; su compañ́ıa ha estado muy presente a través
de nuestras charlas de fútbol y demás asuntos dignos de ser considerados en nuestro foro de
discusión. A mi hermana catalana, Nat, gracias por la motivación, los consejos tan atinados,
y los ánimos en los momentos cuesta arriba del doctorado. Tu determinación me sirvió de
ejemplo para seguir adelante. A Kattia, gracias por estar presente tanto en los tiempos de la
UCR como de la UNAM; tu amistad, que se ha mantenido durante los años y la distancia,
ha significado mucho para mı́. Hago una mención especial a Rigo, mi gato, por su valioso
aporte en demostraciones y tareas de f́ısica. A mis demás amigos, de f́ısica, música, artes
marciales, roomies y otras facetas de la vida: gracias. Su amistad fue un aliento a lo largo
de este proceso.
Este trabajo de tesis fue realizado gracias al Programa UNAM-PAPIIT IN105923.
vi
Contents
1 Introduction 1
2 Evidence for Dark Matter 3
2.1 Galaxy Velocities in Clusters and Galaxy Rotation Curves . . . . . . . . . . 3
2.2 Anisotropy of the Cosmic Microwave Background Temperature . . . . . . . . 6
2.3 Gravitational Lensing in Galaxy Clusters . . . . . . . . . . . . . . . . . . . . 10
3 Dark Matter Candidates and
Methods of Detection 13
3.1 Weakly Interacting Massive Particles . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Axions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 Sterile Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Methods of Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4.1 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.4.2 Direct Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4.3 Indirect Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 The DEAP-3600 Detector 21
4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Scintillation from Nuclear Recoils in Liquid Argon . . . . . . . . . . . . . . . 23
4.3 Pulse Shape Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4 Background Sources and Region of Interest . . . . . . . . . . . . . . . . . . . 25
4.4.1 Electrons and Gamma Rays . . . . . . . . . . . . . . . . . . . . . . . 26
4.4.2 Alpha Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.3 Neutrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.4 Region of Interest and Background Estimates . . . . . . . . . . . . . 28
5 Neutron Background in DEAP-3600 31
5.1 The Profile Likelihood Ratio Method . . . . . . . . . . . . . . . . . . . . . . 31
5.2 Radiogenic Neutron Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.3 PDFs for the Radiogenic Neutrons . . . . . . . . . . . . . . . . . . . . . . . 35
5.3.1 NSCBayes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.3.2 Fprompt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.3.3 MblikelihoodR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.4 Neutron Discrimination Using Machine Learning . . . . . . . . . . . . . . . . 47
vii
viii CONTENTS
5.5 Formulation as a Machine Learning Problem . . . . . . . . . . . . . . . . . . 48
5.6 Data Collecting and Processing . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.7 Model Training and Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.7.1 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.7.2 Evaluation Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.7.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.7.4 Additional Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.8 Findings and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6 Gamma Background for the Search of 5.5 MeV Solar Axions 61
6.1 Production Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.2 Interactions with the Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.1 Compton Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.2 Decay to 2γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.3 Inverse Primakoff Effect . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.4 Axioelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.3 Signal and its dependence on axion mass . . . . . . . . . . . . . . . . . . . . 63
6.4 Region of Interest for Axion Search . . . . . . . . . . . . . . . . . . . . . . . 63
6.5 Background Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.5.1 γ-rays from Neutron Capture . . . . . . . . . . . . . . . . . . . . . . 65
6.5.2 γ-rays from 208Tl Decay . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.6 Simulations for the Neutron Capture γ-ray Background . . . . . . . . . . . . 66
7 Exploration of Neutrinos in the Standard Model and Beyond 73
7.1 General Aspects about Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . 73
7.2 Coherent Elastic Neutrino-Nucleus Scattering . . . . . . . . . . . . . . . . . 78
7.3 CEνNS Measurement by the CONUS+
Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7.3.1 Description of the CONUS+ Detector . . . . . . . . . . . . . . . . . . 79
7.3.2 Results of the CEνNS Measurement by CONUS+ . . . . . . . . . . . 82
7.4 Study of Scenarios in the SM and Beyond . . . . . . . . . . . . . . . . . . . 84
7.4.1 Calculation of the Number of events . . . . . . . . . . . . . . . . . . 85
7.4.2 Weak Mixing Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.4.3 Magnetic Moment of the Neutrino . . . . . . . . . . . . . . . . . . . . 90
7.4.4 Non-Standard Interactions . . . . . . . . . . . . . . . . . . . . . . . . 95
7.5 Neutrino Production in Core-Collapse Supernovae . . . . . . . . . . . . . . . 99
7.6 CEνNS Simulations for DEAP-3600 and LUX-ZEPLIN with EstrellaNueva . 103
7.7 SN Neutrino Parameter Analysis: SM and Beyond . . . . . . . . . . . . . . . 109
7.7.1 Results for the Weak Mixing Angle . . . . . . . . . . . . . . . . . . . 111
7.7.2 Findings for the Neutrino Magnetic Moment . . . . . . . . . . . . . . 112
7.7.3 Implications for Non-Standard Interactions . . . . . . . . . . . . . . . 118
7.8 Conclusions from the Parameter Analysis with SN Neutrinos . . . . . . . . . 120
8 Conclusions 123
CONTENTS ix
Appendix A Acronyms and Abbreviations Used 127
Appendix B Supplementary Plots for the CEνNS Studies 131
Bibliography 137
x CONTENTS
List of Figures
2.1 Rotation curves of 21 galaxies studied by Vera Rubin. . . . . . . . . . . . . . 4
2.2 Rotation curve with the contributions of its main components. . . . . . . . . 5
2.3 Dipole anisotropy of the CMB. . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Multipole anisotropy of the CMB temperature. . . . . . . . . . . . . . . . . . 7
2.5 CMB power spectrum with a fit for the ΛCDM model. . . . . . . . . . . . . 8
2.6 Relation of the peaks in the CMB power spectrum to the cosmological pa-
rameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.7 Diagram of light deflection by a massive object. . . . . . . . . . . . . . . . . 10
2.8 Gravitational lensing in Galaxy Cluster CL0024+17. . . . . . . . . . . . . . 11
2.9 Galaxy Cluster 1E 0657–56, known as the “Bullet Cluster”. . . . . . . . . . . 11
2.10 Galaxy clusters as evidence for dark matter: MACS J0025, Abell 520, Abell
2744, and ZwCl 1358+62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1 Mass range for various dark matter candidates. . . . . . . . . . . . . . . . . 13
3.2 Comparison of WIMP and dark matter relic densities as a function of WIMP
mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Axion mass range with constraints. . . . . . . . . . . . . . . . . . . . . . . . 15
3.4 Methods of detection for dark matter. . . . . . . . . . . . . . . . . . . . . . . 17
3.5 LZ spin independet WIMP-nucleon upper limit. . . . . . . . . . . . . . . . . 19
3.6 SM products from the annihilation of WIMPs. . . . . . . . . . . . . . . . . . 20
4.1 Outer structure of the DEAP-3600 detector . . . . . . . . . . . . . . . . . . 22
4.2 Acrylic vessel and inner structure. . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Nuclear recoil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4 Scintillation signal comparison of ER and NR. . . . . . . . . . . . . . . . . . 25
4.5 NR and ER bands in Fprompt and PE. . . . . . . . . . . . . . . . . . . . . . . 26
4.6 WIMP search region of interest . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.1 Comparison of statistical methods for limit setting. . . . . . . . . . . . . . . 34
5.2 PLR Region of Interest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.3 Representation of the radiogenic neutron simulations in two stages. . . . . . 35
5.4 Flowchart of the datasets in the neutron simulations. . . . . . . . . . . . . . 37
5.5 Normalized PIFGAR histogram. . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.6 NSC fit for the PIF2 tpbUP dataset. . . . . . . . . . . . . . . . . . . . . . . 39
5.7 RPR fit for the PIF2 rfrUP distribution, in the 90-150 PE bin. . . . . . . . . 41
xi
xii LIST OF FIGURES
5.8 RPR N and µ parameter fits for the nominal PIF3 and nominal PIF2 datasets. 43
5.9 RPR λ and σ parameter fits for the rfrUP PIF2 and rfrUP PIF3 datasets. . 44
5.10 MBR fit for the PIF2 tpbUP distribution, in the 120-150 PE bin. . . . . . . 45
5.11 MBR N and θ parameter fits for the rfrUP PIF2 and tpbDOWN PIF3 datasets. 46
5.12 Confusion matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.13 Definition of an ROC curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.14 Individual vs boosted decision tree. . . . . . . . . . . . . . . . . . . . . . . . 53
5.15 Confusion matrix for the boosted decision tree in the validation phase. . . . 54
5.16 ROC curve for the BDT in the validation phase. . . . . . . . . . . . . . . . . 55
5.17 Confusion matrix for the boosted decision tree in the testing phase. . . . . . 56
5.18 ROC curve for the BDT in the testing phase. . . . . . . . . . . . . . . . . . 57
5.19 Predicted multiple recoils for the AmBe dataset. . . . . . . . . . . . . . . . . 59
6.1 Feynman Diagrams of the Four Axion-Detector Interactions . . . . . . . . . 63
6.2 Signal of the four axion interactions . . . . . . . . . . . . . . . . . . . . . . . 64
6.3 Total energy deposited in the detector for Compton Conversion and 2γ Decay
for different axion masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.4 Mechanism of γ-ray production by neutron capture . . . . . . . . . . . . . . 65
6.5 Spectrum generated for γ-rays produced in the decay of 208Tl . . . . . . . . . 66
6.6 Comparison of background models before and after gamma rays from neutron
captures in 59Co and Mo isotopes were added. . . . . . . . . . . . . . . . . . 67
6.7 Simulated gamma rays from the steel casing and neck of the detector . . . . 68
6.8 Energy deposited in liquid argon by gammas emitted due to neutron capture
in 59Co and 95Mo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.9 Acceptance for radial cut at 750 mm for simulated neutrons from the acrylic
container. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.10 Preliminary background model for the axion search after blind analysis . . . 70
6.11 Preliminary exclusion curves for gAe . . . . . . . . . . . . . . . . . . . . . . . 70
7.1 Neutrino sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.2 Neutrino mass hierarchies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.3 Feynman diagram for neutrinoless double beta decay. . . . . . . . . . . . . . 77
7.4 Feynman diagram for CEνNS. . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7.5 Representation of CEνNS and enhanced cross-section. . . . . . . . . . . . . . 79
7.6 Use of CEνNS events for probing the neutrino magnetic moment and non-
standard interactions parameters. . . . . . . . . . . . . . . . . . . . . . . . . 80
7.7 Setup of the CONUS+ experiment. . . . . . . . . . . . . . . . . . . . . . . . 81
7.8 Production of reactor antineutrinos. . . . . . . . . . . . . . . . . . . . . . . . 81
7.9 HPGe diodes in CONUS+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.10 CONUS+ CEνNS signal prediction and data. . . . . . . . . . . . . . . . . . 83
7.11 Trigger efficiency of the CONUS+ diodes. . . . . . . . . . . . . . . . . . . . 86
7.12 Germanium total CEνNS cross sections. . . . . . . . . . . . . . . . . . . . . 87
7.13 Event rates for CONUS+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.14 Weak mixing angle fit for CONUS+. . . . . . . . . . . . . . . . . . . . . . . 91
7.15 Neutrino Magnetic moment χ2 profile for CONUS+. . . . . . . . . . . . . . . 92
LIST OF FIGURES xiii
7.16 Neutrino magnetic moment 90% CL. upper limit for CONUS+. . . . . . . . 94
7.17 NSI parameter limits for CONUS+. . . . . . . . . . . . . . . . . . . . . . . . 98
7.18 Diagram of the Supernova stages. . . . . . . . . . . . . . . . . . . . . . . . . 101
7.19 Neutrino Fluences with MSW Effect. . . . . . . . . . . . . . . . . . . . . . . 102
7.20 Diagram of the LZ detector structure. . . . . . . . . . . . . . . . . . . . . . . 104
7.21 Variable neutrino fluxes during a SN. . . . . . . . . . . . . . . . . . . . . . . 105
7.22 Xe and Ar total CEνNS cross sections. . . . . . . . . . . . . . . . . . . . . . 106
7.23 Simulated neutrino fluences by flavor and distances. . . . . . . . . . . . . . . 108
7.24 DEAP-3600 and LZ detection efficiencies. . . . . . . . . . . . . . . . . . . . . 109
7.25 Event rates for LZ and DEAP at various SN distances. . . . . . . . . . . . . 110
7.26 Results for sin2 θW as a function of SN distance. . . . . . . . . . . . . . . . . 113
7.27 SN Results for sin2 θW compared to measurements from other experiments. . 114
7.28 90% CL. upper limits for µν as a function of SN distance. . . . . . . . . . . . 116
7.29 SN results for µν compared to measurements from other experiments. . . . . 117
7.30 NSI parameters 95% CL. contour comparison for DEAP-3600, LZ and CONUS+.121
B.1 Helm form factors for germanium. . . . . . . . . . . . . . . . . . . . . . . . . 131
B.2 Event rates for individual CONUS+ detectors. . . . . . . . . . . . . . . . . . 132
B.3 Helm form factors for Xe and Ar. . . . . . . . . . . . . . . . . . . . . . . . . 133
B.4 DEAP-3600 event rates at 10.0 (left) and 20 kpc (right). . . . . . . . . . . . 133
B.5 NSI parameter 95% CL. contours for DEAP-3600 and LZ at 0.196 kpc (NH). 134
B.6 NSI parameter 95% CL. contours for DEAP-3600 and LZ at 0.196 kpc (IH). 135
B.7 NSI parameter contours, NH vs IH, for LZ and DEAP-3600 at 0.196 kpc. . . 136
xiv LIST OF FIGURES
List of Tables
2.1 Current physical densities as cosmological parameters of the ΛCDM model. . 9
4.1 Background Estimates for the latest published WIMP search. . . . . . . . . 29
5.1 PMT array mass, purity and neutron yield used in the simulations. . . . . . 36
5.2 Count of multiple and single nuclear recoils from the PMT neutron dataset. 49
5.3 Metric scores for the BDT in the validation phase. . . . . . . . . . . . . . . . 55
5.4 Metric scores for the BDT in testing. . . . . . . . . . . . . . . . . . . . . . . 57
6.1 Number of events generated per molybdenum isotope. . . . . . . . . . . . . . 69
7.1 Detector data in the CONUS+ CEνNS measurement. . . . . . . . . . . . . . 84
7.2 Natural abundances of the germanium isotopes. . . . . . . . . . . . . . . . . 86
7.3 Events calculated for each detector. . . . . . . . . . . . . . . . . . . . . . . . 89
7.4 Natural abundances of the xenon isotopes. . . . . . . . . . . . . . . . . . . . 106
7.5 SN CEνNS simulated detections for LZ and DEAP-3600 at different distances. 107
7.6 SN CEνNS 1σ intervals for LZ and DEAP-3600 at different distances. . . . . 111
7.7 Results for sin2 θW for the SN study. . . . . . . . . . . . . . . . . . . . . . . 112
7.8 Neutrino magnetic moment upper limits for the SN study. . . . . . . . . . . 115
7.9 Flavor compositions of event counts for DEAP-3600 and LZ. . . . . . . . . . 119
xv
xvi LIST OF TABLES
1 Introduction
The field of particle physics has provided some of the most far-reaching insights in hu-
manity’s ongoing pursuit to understand more about the Universe. This pursuit is currently
focused on pushing beyond known territory, extending the boundaries of what is understood,
while also refining the knowledge we already possess.
One of the main driving forces in this pursuit is the effort to explain dark matter. The key
observations leading to the conclusion that dark matter must exist include galaxy rotation
curves, the anisotropy in the cosmic microwave background, and the matter distribution
inferred from gravitational lensing observed in numerous galaxy clusters. Together, these
unexplained phenomena point to the existence of a type of matter that must be massive,
stable, and non-interacting electromagnetically. This is the focus of discussion in Chapter 2.
A plethora of ideas have been proposed to account for these observations. Chapter 3 de-
scribes three of the leading candidates: weakly interacting massive particles (WIMPs), QCD
axions, and sterile neutrinos. The main detection methods (direct, indirect, and production)
are also reviewed.
One of the leading initiatives in direct detection is spearheaded by the DEAP-3600 exper-
iment. Its detection principles as a liquid argon scintillation detector are described in detail
in Chapter 4, along with its primary background sources, such as neutrons and gamma rays,
relevant to the search for different dark matter candidates.
Radiogenic neutron background is the focus of Chapter 5. The statistical methodology
by which background sources are modeled has a far-reaching impact on the sensitivity of
experiments seeking rare phenomena such as dark matter interactions. Starting in Section
5.1, the Profile Likelihood Ratio framework is introduced and applied to the characterization
of radiogenic neutrons, as part of an ongoing initiative by the DEAP collaboration.
Physics research often evolves in symbiosis with technological innovation: advances in
one often fuel progress in the other. One such case is the application of machine learning,
which has had a profound impact on particle physics. Section 5.4 begins the exploration of a
novel classification strategy for mitigating neutron background in nuclear recoil dark matter
searches. This technique exploits a currently underutilized discriminant: the difference in
scattering behavior between neutrons and nuclei, versus WIMPs and nuclei. The results of
this exploratory study are encouraging, and future directions are proposed that may prove
valuable for WIMP searches dealing with radiogenic neutrons as a considerable background
source.
In addition to QCD axions, related theoretical models propose the existence of new parti-
cles known as axion-like particles (ALPs), which could be produced in the Sun. DEAP also
contributes to the investigation of these models through an ongoing solar axion search. A
1
2 CHAPTER 1. INTRODUCTION
contribution to the background model for this effort is described in Chapter 6.
Neutrinos offer a unique window into new physics: their non-zero masses—revealed through
flavor oscillations—fall outside the explanatory scope of the Standard Model. Moreover, their
interactions provide a valuable means of probing and refining our understanding of elec-
troweak processes. Chapter 7 explores this potential by analyzing coherent elastic neutrino-
nucleus scattering (CEνNS) using reactor neutrinos from the CONUS+ experiment. This
analysis is used to probe the weak mixing angle, the magnetic moment of the neutrino, and
possible new physics trough Non-Standard Interactions (NSIs). The work presented here
forms the basis of the first peer-reviewed publication analyzing CONUS+ data.
The fascinating events of core-collapse supernovae also offer a powerful avenue for exploring
Standard Model physics and beyond, through CEνNS measurements. Beginning in Section
7.5, simulations are carried out to model signals at DEAP-3600 and LUX-ZEPLIN (LZ),
currently the largest operating dark matter detector. Constraints are obtained for the weak
mixing angle, the magnetic moment of the neutrino, and NSI parameters. A methodology
is proposed to guide future studies aiming to expand on this analysis.
This thesis represents a focused effort to contribute meaningfully to the rich tradition of
particle physics−striving to understand more about the Universe and expand the boundaries
of what is known.
2 Evidence for Dark Matter
The evidence supporting the existence of dark matter (DM) is substantial and spans mass
scales ranging from galaxies to large scale structures such as galaxy clusters and filaments.
While this evidence has been accumulated for decades, it is important to clarify that all
of it stems from gravitational interactions. However, this evidence arises from varied and
compelling sources, making DM the leading contender to explain these observations.
The following sections will review some of the most conclusive observations supporting the
existence of DM, including galaxy rotation curves, temperature anisotropies in the cosmic
microwave background, and gravitational lensing in galaxy clusters.
2.1 Galaxy Velocities in Clusters and Galaxy Rotation
Curves
The most compelling source of evidence in favor of the DM hypothesis comes from galaxy
velocities in a cluster and galaxy rotation curves. The velocities of galaxies in a galaxy
cluster are correlated to the amount of matter in the cluster, and can be used to infer its
density. Rotation curves are constructed by measuring the rotational velocity of the stars in
a galaxy as a function of their distance to the galactic center. As shall be seen, this method
can provide an insight into the galactic mass and how it is spatially distributed.
Fritz Zwicky conducted an early example of these studies in 1933 [1, 2]. He measured the
velocities of the galaxies in the Coma cluster by using the Doppler red-shift in their spectra,
and found that there was a higher dispersion than expected in these velocities. Zwicky
determined this dispersion by taking into account the well known cosmological red-shift,
this meant that these galaxies were moving faster than expected. He related these velocities
to the cluster’s mass via the Virial theorem, and found that the density of the cluster should
be approximately 400 times greater than what could be accounted for by its luminous matter,
otherwise the galaxies in the cluster would disperse. Zwicky hypothesized that there must
be a non luminous but massive form of matter providing the necessary density to hold the
cluster together, which he referred to as dunkle materie (dark matter).
The next significant hint pointing in the direction of DM comes from studying rotational
curves of individual galaxies. This is also achieved by examining the Doppler shifted spectra.
When looking at the galaxy edge-on, the Doppler effect will produce a more significant red-
shift on the end of the galaxy that spins away from the observer, while the opposite will
occur on the other end.
By using Newtonian mechanics, the rotational velocity of the stars in a galaxy v(r) can be
3
4 CHAPTER 2. EVIDENCE FOR DARK MATTER
determined as a function of their distance to the galactic center. Equating the centripetal
force to the gravitational force and rearranging, produces the following relation:
v(r) =
√
GM(r)
r
, (2.1)
where r is the distance of an arbitrary point to the galactic center, M(r) is the galaxy’s
mass as a function of r and G is Newton’s gravitational constant. At the outer regions of the
galaxy, the mass density due to the stars in the galaxy is approximately constant. Assuming
that stars are the dominant component of the galactic mass results in this proportionality
relation:
v(r) ∝ r−1/2. (2.2)
According to (2.2), the rotational velocities of the stars in a galaxy as a function of their
distance to the galactic center should vary as r−1/2, however, this is not what was observed
by the American astronomer Vera Rubin in 1980 [3] 1. She, along with her colleagues Kent
Ford and Norbert Thonnard, measured the rotational curves of 21 spiral galaxies of type
Sc, which have an easily identifiable galactic center, and found that v(r) is approximately
constant for the outer regions of the galaxies.
Figure 2.1: Rotation curves of the 21 Sc type galaxies studied by Vera Rubin [3].
In order to explain the approximately constant rotation curves seen in 2.1, the term M(r)
in Equation 2.2 would have to increase linearly proportional to r. If the majority of the mass
in galaxy were due to the stars in it, this would mean that the density of stars would increase
as the distance from the galactic center also increases, this contradicts the observations made
by Rubin.
One possible explanation to this conundrum derives from extending Zwicky’s hypothesis,
and proposing that DM exists not only in the scale of galaxy clusters, but also around
individual galaxies. This would provide a source of mass that could explain the rotation
curves while also accounting for the insufficient amount of luminous matter needed to explain
1Prior to this, Rubin and Ford reported flat rotation curves in observations of the Andromeda galaxy [4].
2.1. GALAXY VELOCITIES IN CLUSTERS AND GALAXY ROTATION CURVES 5
this phenomenon. Following this idea and imposing the proportionality between M(r) and
r, the M(r) term in Equation 2.2 takes the form:
M(r) =
∫
V (r)
ρ(r′)dV ′ = 4π
∫ r
0
ρ(r′)r′2dr′ ∝ r. (2.3)
where spherical symmetry has been made use of, which is consistent with Rubin’s observa-
tions. In order for the proportionality relation in Equation 2.3 to hold, the mass density
term ρ(r′) must be proportional to r′−2:
M(r) = 4π
∫ r
0
ρ(r′)r′2dr′ ∝
∫ r
0
r′2
r′2
dr′ ∝ r. (2.4)
By proposing that the majority of the mass in a galaxy is not due to its stars, but instead
to DM distributed in a halo around it as outlined in Equation 2.4, the rotation curves can
be explained. This massive DM halo is the main contributor to a galaxy’s rotation curve, as
can be seen in Figure 2.2 for the galaxy NGC 6503.
Figure 2.2: Rotation curve of the galaxy NGC 6503, with the contributions of its main
components: non luminous gas, the galactic disk, and the dark matter halo. [5].
As an example, for our Milky Way galaxy it is estimated that its total mass within a
radius of 20 kpc is 1.91+0.18
−0.17 ×1011 solar masses, while the DM halo within that same radius
accounts for 1.37+0.18
−0.17 ×1011 of those solar masses [6]. From this, it is derived that the local
DM density in the solar system is approximately ρ0 = 0.3 GeV/cm3 [5].
It is important to note that DM is not the only possible explanation for the rotation
curves. An alternative approach is given by Milgrom [7], in which he proposes that instead
6 CHAPTER 2. EVIDENCE FOR DARK MATTER
of adding a new form of matter, changing the behavior of gravity can also be used to explain
the observations. This idea receives the name of Modified Newtonian Dynamics (MoND),
and has been considered as DM’s most prominent rival hypothesis. However, recent studies
have shown that DM is an overall better fit for rotation curves [8], and that MoND makes
some predictions that contradict observations in wide binary star systems [9].
Currently, the hypothesis that galaxies are contained in a halo of massive matter that does
not interact with light, DM, is the most favored explanation for the galaxy rotation curves.
2.2 Anisotropy of the Cosmic Microwave Background
Temperature
The cosmic microwave background (CMB) is a relic radiation that began propagating
freely approximately 370 thousand years after the Big Bang [10]. Approximately 10−10
seconds after the Big Bang, the universe was composed of a quark-gluon plasma, as well
as electrons and positrons. As the universe expanded and cooled, these quarks eventually
formed protons and neutrons in a process known as baryogenesis, while the electrons and
positrons annihilated each other, producing photons. This led to a period during which these
photons did not propagate freely, as they scattered off the charged particles they encountered:
the protons and electrons that survived annihilation. As the temperature of the universe
dropped, these protons, neutrons, and electrons reached energies low enough to form helium
and hydrogen atoms, which are neutral in electrical charge, making them transparent to the
photons. It was then, approximately 370 thousand years after the Big Bang, during a period
known as recombination, that these photons decoupled from the thermal equilibrium they
were in with the electrons and positrons and began to propagate freely.
When emitted, these photons were in the infrared region, but the expansion of the universe
has caused them to be redshifted to wavelengths in the microwave part of the spectrum, hence
the name given to this radiation [11]. The existence of the CMB was proposed in 1948 by
Georgiy Gamow [12], and it was confirmed by Arno Penzias and Robert Wilson through an
accidental detection in 1965 [13].
During the initial years after its observation, it was believed that the CMB temperature
was isotropic, meaning that the temperature of these photons was the same in every direction.
However, this was found not to be true in 1991 when the COBE satellite detected fluctuations
in the temperature with respect to the mean of 2.7 K [14]. The largest of these fluctuations
is due to the Doppler effect caused by the relative motion of the Earth with respect to the
CMB rest frame, this is known as the dipole CMB anisotropy [15] (see Figure 2.3).
When looked at with a more precise angular resolution, smaller scale fluctuations become
apparent. The variation in temperature can be written as a function of the angular position
as seen from Earth, θ and ϕ, in the following manner:
∆T
T
=
∞
∑
l=0
l
∑
m=−l
almYlm(θ, ϕ). (2.5)
In Equation 2.5, the l index determines the order of the angular resolution, which increases
with l according to the relation:
2.2. ANISOTROPYOF THE COSMICMICROWAVE BACKGROUND TEMPERATURE7
Figure 2.3: Dipole anisotropy of the CMB produced by the Doppler effect due to the relative
motion between the Earth and the CMB rest frame. It produces a variation in temperature
with respect to the mean of 2.7 K, represented in color scale [16].
∆θ =
180◦
l
. (2.6)
The smaller scale fluctuations seen in Figure 2.4 are originated by the phenomenon of
baryon acoustic oscillations in the proton, neutron and electron plasma [10]. The acoustic
waves are a product of small scale density variations in the plasma, which can be traced
back to curvature fluctuations originated in the inflationary period. In regions where the
plasma density was slightly higher, the temperature was also higher, due to the effect of
the gravitational compression. As a consequence of this compression, more photon radiation
was emitted in those regions, which in turn caused the plasma particles to disperse and the
density to decrease. When the density decreased, the particles were drawn together again
by gravity and the cycle of rarefaction and compression started over, producing oscillations
in the plasma.
Figure 2.4: Anisotropy of the CMB temperature up to order l ≈ 2500, the dipole term has
been removed for clarity [17].
The speed of propagation of these acoustic oscillations in the plasma, also known as the
8 CHAPTER 2. EVIDENCE FOR DARK MATTER
speed of sound (cs), is given by [10]:
c2s =
δp
δρ
=
c2
3
1
1 + 3ρB/4ργ
, (2.7)
where p is the pressure of the plasma, ρB and ργ are the baryon and photon density in the
medium respectively, and c is the speed of light in a vacuum. When the photons propagated,
at the moment of the recombination, they carried this information about the oscillation
parameters in their temperature anisotropy.
The temperature anisotropy can be studied by examining the power spectrum of the CMB
with high angular resolution. This allows for comparison with theoretical models to evaluate
how well they explain the observations. Such an approach is demonstrated by the results
obtained by Planck [18] in Figure 2.5, which include an expansion up to multipole orders of
l ≈ 2500.
Figure 2.5: Power spectrum of the CMB temperature obtained by the Planck satellite.
Multipolar expansion up to the order l ≈ 2500. In blue, the best fit curve, based in the
ΛCDM cosmological model [18].
The power spectrum shows the angular scale, as seen from Earth, of the regions with
fluctuations in temperature. The odd peaks correspond to regions of the plasma that were
at maximal compression at the moment of recombination, while the even peaks are regions
at maximal rarefactions. Measuring the diameter of compression regions in the CMB, cor-
responding to the highest peak in Figure 2.5 allows us to verify that the universe is flat.
This verification, in turn, makes it possible to estimate the total mass-energy content of
the universe, since it must coincide with the critical density required for a flat space. The
second peak from left to right, corresponds to regions of maximum rarefaction; comparing its
2.2. ANISOTROPYOF THE COSMICMICROWAVE BACKGROUND TEMPERATURE9
height to that of the first peak allows an estimation of the fraction of the total mass-energy
content comprised by baryonic matter [19]. The heights of the remaining peaks give insights
on when the radiation epoch of the early universe gave way to the matter dominated epoch.
The matter that dominated the mass-energy density of the universe at that time could not
have been baryonic matter, or it would have resulted in a higher second peak, making DM
an ideal explanation for those peaks. The data points from the CMB spectra are fitted with
great precision using the ΛCDM cosmological model, where Λ represents the cosmological
constant responsible for the acceleration of the universes expansion, and CDM stands for cold
DM. The term cold refers to the DM being non-relativistic, capable of forming structures
such as galactic halos. These findings are summarized in Figure 2.6, and the estimated pa-
rameter values are shown in Table 2.1. This shows that DM is approximately five times more
abundant than baryonic matter, highlighting the importance of studying a form of matter
that constitutes such a significant portion of the matter-energy density of the universe.
Figure 2.6: Power spectrum of the CMB and relation of its peaks with the cosmological
parameters [20].
Parameter Value Contribution to the total
mass-energy density (%)
ΩΛh
2 (Dark Energy) 0.3107± 0.0082 68.5 ± 3.20
Ωmh
2(Total Matter) 0.143± 0.001 31.5 ± 0.859
Ωch
2 (Cold Dark Matter) 0.120± 0.001 26.5 ± 0.757
Ωbh
2 (Baryonic Matter) 0.0224± 0.0001 4.94 ± 0.122
Table 2.1: Current physical densities (Ωih
2) as cosmological parameters of the ΛCDM model,
in terms of the dimensionless Hubble parameter h = 0.674± 0.005 = H0
100kms−1Mpc−1 [18].
10 CHAPTER 2. EVIDENCE FOR DARK MATTER
2.3 Gravitational Lensing in Galaxy Clusters
A consequence of general relativity is that the path followed by light curves significantly
near massive objects. This is observed as a deflection of the light received by the observer
relative to that emitted from the source and as a magnification of the received image [21].
Detecting these deflected and magnified images indicates the presence of a nearby massive
object; however, in some cases, this massive object does not interact electromagnetically.
The deflection angle α depends on the mass M of the object and the radial distance d
between the light beam and the object, also known as the impact parameter [22], as shown
in Figure 2.7. The relationship between these quantities is:
α =
4GM
c2d
. (2.8)
In Equation (2.8), G is Newton’s gravitational constant, and c is the speed of light in a
vacuum. From this relationship, it can be seen that the deflection effect will be greater as
the object’s mass increases and as the light beam passes closer to the object.
Figure 2.7: Light beam deflected by an angle α by an object of mass M , with an impact
parameter d [23].
Considering the magnification effect, the study of gravitational lensing is divided into
strong and weak lensing regimes. By studying images taken by the Hubble Space Telescope,
among others, strong gravitational lensing has been found on numerous occasions in regions
where there is not enough baryonic matter to account for it [24], such as in the galaxy cluster
CL0024+17 [25–27] (see Figure 2.8). Similarly, evidence of DM has been discovered through
the study of weak gravitational lensing [24, 28, 29].
A case of particular interest is the cluster 1E 0657–56, known as the “Bullet Cluster”. This
cluster is actually the collision of two galaxy clusters, observed using optical methods to study
the gravitational lensing effect present [31], as well as by the Chandra X-ray observatory
satellite [32]. The gravitational lensing study found where most of the mass is concentrated
in this cluster, while X-ray observations identified where the highest density of baryonic
matter is located. These results were compared (see Figure 2.9), revealing that the region
where the gravitational lensing effect is most pronounced does not coincide with the region
containing the baryonic matter. This implies that in the Bullet Cluster, most of the mass does
not correspond to baryonic matter but rather to a type of matter that exerts a gravitational
lensing effect but does not interact electromagnetically, as expected for DM.
Although the Bullet Cluster is the most well-known example, other galaxy cluster collisions
showing a similar disparity between the gravitational lensing effect and the observed amount
of baryonic matter have also been discovered. Notable examples include MACS J0025 (the
2.3. GRAVITATIONAL LENSING IN GALAXY CLUSTERS 11
Figure 2.8: Galaxy Cluster CL0024+17. On the left, magnified and distorted images due
to strong gravitational lensing are visible. On the right, in blue, is a reconstruction of the
regions where DM is likely located [30].
Figure 2.9: Galaxy Cluster 1E 0657–56, known as the “Bullet Cluster”. In pink, the regions
with high baryonic matter density are shown, and in blue, the regions where the gravitational
lensing effect is strongest, possibly due to dark matter [33].
“Baby Bullet”) [24], Abell 520 (the “Train Wreck Cluster”) [34], Abell 2744 (the “Pandora
Cluster”) [35], and ZwCl 1358+62 [36] (see Figure 2.10).
The observations presented in this chapter represent some of the most compelling evidence
suggesting the existence of DM. Although all are gravitational in nature, they arise from a
diverse set of measurements involving physical processes across a wide range of scales and
cosmic epochs. Theoretical models of DM candidates, along with methods of detection, are
described in the following chapter.
12 CHAPTER 2. EVIDENCE FOR DARK MATTER
Figure 2.10: Galaxy clusters as evidence for dark matter. Upper left: ZwCl 1358+62, the
dark matter map is shown in blue, in pink the ordinary matter [36]. Upper right: Abell 520,
hot gas is shown in green, dark matter in blue [37]. Lower left: MACS J0025, showing dark
matter in blue and ordinary matter in pink [38]. Lower right: Abell 2744, dark matter is
shown in blue, hot gas in red [39].
3 Dark Matter Candidates and
Methods of Detection
In order to explain the observations outlined in Chapter 2, any particle that constitutes
dark matter (DM) must have the following characteristics:
• It must be electrically neutral to avoid any electromagnetic interaction.
• It must be massive and non-relativistic to form cosmological structures.
• It has to be stable, with a lifetime equal to, or greater than, the age of the universe in
order to produce acoustic oscillations in the CMB.
No particle in the Standard Model (SM) meets all of these criteria: electrons, muons, taus,
quarks, and W± are electrically charged; photons are massless; neutrinos are not massive
enough and could not form galactic halos and other structures attributed to DM due to being
ultrarelativistic; the Higgs and Z bosons, and the gluons are all ruled out by the stability
requirement. It becomes clear that DM must be a gateway to physics beyond the SM.
Figure 3.1: Mass range for various dark matter candidates [40].
A wide variety of ideas have been proposed, originating from different theoretical frame-
works and addressing various problems. As shown in Figure 3.1, DM candidates cover an
extensive range of masses: from 10−6 eV QCD axions, to primordial black holes an order
of magnitude more massive than our Sun. In this chapter, the defining properties of some
of the most studied candidates will be presented. Specifically, weakly interacting massive
particles, axions, and sterile neutrinos, all of which play an important role in the research
presented in this work.
13
14 CHAPTER 3. DARK MATTER CANDIDATES AND METHODS OF DETECTION
3.1 Weakly Interacting Massive Particles
The most extensively studied DM candidates are the Weakly Interacting Massive Particles
(WIMPs). These hypothetical particles are expected to interact gravitationally and, at most,
via the weak nuclear force. WIMPs naturally satisfy the conditions required for DM, making
them a common subject of theoretical and experimental research [41–44].
A widely studied mechanism by which WIMPs may have been produced is known as
thermal freeze-out [45]. In the early universe, when temperatures were much higher than
the WIMP rest mass, WIMPs were in thermal equilibrium with the plasma. They were
produced and annihilated at equal rates through interactions with SM particles.
As the universe expanded and cooled, the temperature of the plasma dropped below
the WIMP mass threshold. This caused annihilation interactions to dominate. Once the
interaction rate dropped below the Hubble expansion rate, WIMPs decoupled from the
thermal equilibrium, and their abundance effectively “froze out”, resulting in a WIMP relic
density. This would have occurred approximately 10−10 seconds after the Big Bang, during
the electroweak era.
For a WIMP mass in the range of 100 GeV - 1 TeV, the predicted relic density matches
the currently observed DM density (see Figure 3.2). This coincidence is often referred to
as the WIMP “miracle”, and it has served as strong motivation for WIMP-focused DM
investigations.
As discussed in Section 2.2, DM left observable evidence of its existence in the baryon
acoustic oscillations of the CMB. These anisotropies indicate that DM already existed well
before recombination. This is consistent with thermal freeze-out as the proposed produc-
tion mechanism for WIMPs, and further supports the ongoing theoretical and experimental
interest in WIMPs as viable DM candidates.
Figure 3.2: Comparison of WIMP and dark matter relic densities (ΩX and ΩDM respectively)
as a function of WIMP mass (mX). Both densities coincide for WIMP masses in the range
100 GeV - 1 TeV [41].
3.2. AXIONS 15
3.2 Axions
Axions1 were not originally proposed as DM candidates. Instead, they arise from a possible
solution to the strong CP problem: the question of why CP (conjugation of charge and
parity) symmetry violation is not observed in strong interactions. The CP-violating term
in the QCD Lagrangian is proportional to Θ, known as the strong CP phase, which can
take values between 0 and 2π. In order to avoid observable CP violation, such as a large
neutron electric dipole moment, Θ must be tuned to extremely small values of the order
of Θ < 10−10 [46]. Therefore, the strong CP problem is formulated as a naturalness, or
fine-tuning, problem related to the value of Θ.
The solution proposed by Roberto Peccei and Helen Quinn [47] involves introducing a new
global symmetry to the SM, known as the Peccei-Quinn (PQ) symmetry, U(1)PQ. When
spontaneously broken, this symmetry produces a pseudo-Goldstone boson, known as the
axion. The axion field dynamically relaxes the CP violating phase Θ to zero, thus eliminating
the need for fine-tuning.
The mass of the axion (ma) is given by [48]:
ma = (5.70± 0.07)µeV
(
1012GeV
fa
)
, (3.1)
where fa is the axion decay constant. As shown in Figure 3.3, the axion mass is limited by
cosmological and astrophysical observations to a range of 10−11 < ma[eV ] < 10−2 [49].
Axions require additional considerations related to the breaking of the Peccei–Quinn (PQ)
symmetry [50], specifically regarding whether the symmetry is spontaneously broken during
inflation and whether it remains broken afterward. Regardless of whether both conditions
are met or at least one is violated, axions can still account for all or a significant fraction
of the currently observed DM. This motivates their study and experimental search as one of
the leading DM candidates.
Figure 3.3: Masses below 10−22 eV, above 10−2 eV, and within the shaded region are ex-
cluded. [49]. Constraints from fuzzy dark matter and black hole spins assume negligible
axion self-interactions. The SN 1987A limit applies only to QCD axions. Regions beyond
“The QCD axion” correspond to axion-like particles (ALPs) discussed in Chapter 6.
1The viable dark matter candidate axions described here are often referred to as QCD axions, due to
their role as part of a proposed explanation to the strong CP problem.
16 CHAPTER 3. DARK MATTER CANDIDATES AND METHODS OF DETECTION
3.3 Sterile Neutrinos
Neutrino oscillation between the flavor states (e, µ, τ) provides unequivocal evidence of
neutrino masses (discussed in Section 7.1). There is no explanation within the SM for
the mechanism by which neutrinos acquire mass; representing one of the most compelling
indications for the need of new physics. One possible explanation for neutrino masses is the
see-saw mechanism [51–53]. In this framework, right-handed neutrinos are introduced; they
must be neutral under both electric and weak interactions, which is why they are referred
to as sterile neutrinos.
The most general renormalizable mass terms in the lepton sector, including the sterile
neutrinos, consist of a Dirac mass term that couples left and right-handed states, and a Ma-
jorana mass term for the right-handed neutrinos. When the electroweak symmetry breaking
occurs, the Higgs field acquires a vacuum expectation value of ⟨H⟩ ≈ 247 GeV, and neutrinos
propagate as mass eigenstates that diagonalize the mass matrix. Consider, for simplicity,
one generation:
mν(1gen) =
(
0 m
m M
)
, (3.2)
where m represents the Dirac term mass, and M the Majorana mass. This matrix is diago-
nalized by the physical masses expressed as:
mν(1gen)1,2 =
√
m2 +
1
4
M2 ± 1
2
M. (3.3)
In the limit where M >> m, the solutions can be approximated by mheavy >> mlight as:
mheavy ≈ M, mlight ≈
m2
M
≈ m2
mheavy
. (3.4)
Equation 3.4 shows an inversely proportional relation between mheavy and mlight, which is
the reason for the name of the see-saw mechanism.
By assuming a Yukawa coupling in the range of 10−8 − 10−5 and taking the light neutrino
mass as mlight ≈ 0.05 eV (inferred from atmospheric neutrino oscillations [54]), the corre-
sponding heavy neutrino masses, mheavy, are estimated to lie between 1 keV and 1 TeV,
approximately in the electroweak scale.
Sterile neutrinos are compelling DM candidates due to their minimal interactions with
SM particles, potential masses and stability. Additionally, sterile neutrinos could play a role
in leptogenesis [55–57], potentially providing insights into the matter-antimatter asymmetry
observed in the universe. These characteristics make sterile neutrinos an interesting subject
in the search for DM and physics beyond the SM.
3.4 Methods of Detection
The DM candidates discussed in the previous sections are well-motivated by theoretical
arguments. However, like all proposals for new physics, their existence must ultimately be
3.4. METHODS OF DETECTION 17
confirmed through experimental detection. Figure 3.4 illustrates the possible interactions
between SM particles and DM involved in the three main detection strategies: production,
direct detection, and indirect detection. These methods are outlined in this section.
Figure 3.4: Methods of detection for dark matter. SM denotes a Standard Model particle, χ
a dark matter particle. Production: SM+ SM → χ+ χ+ SM. Direct detection: χ+ SM →
χ+ SM. Indirect detection: χ+ χ → SM + SM.
3.4.1 Production
The production approach aims to detect DM by creating it through interactions between
SM particles. Such processes could occur through interactions of the following form:
SM + SM → χ+ χ+ SM. (3.5)
In collider experiments, DM particles (χ) are hypothesized to be produced through inter-
actions among SM particles. These DM particles, being weakly interacting, would not be
detected directly. Instead, their presence would be inferred from the detection of SM particles
resulting from subsequent decay processes, alongside a measurable imbalance in transverse
momentum, referred to as missing transverse momentum, which corresponds to the unde-
tected χ particles.
The main effort in DM production is carried out by the European Council for Nuclear
Research (CERN) at the Large Hadron Collider (LHC) in Geneva, Switzerland. These
searches are led by the ATLAS and CMS collaborations. So far, no conclusive evidence of
any deviation from the SM has been observed in proton-proton collisions at a center-of-mass
energy of
√
s = 13 TeV [58, 59]. Although no DM particles have been detected, these searches
18 CHAPTER 3. DARK MATTER CANDIDATES AND METHODS OF DETECTION
have set increasingly stringent limits on various theoretical models. Proposed colliders such
as the Future Circular Collider (FCC) [60], and the Circular Electron Positron Collider
(CEPC) [61] are expected to lead the next generation of DM production experiments.
3.4.2 Direct Detection
Direct detection of DM occurs when it interacts with ordinary matter and the products of
that interaction include both DM and detectable SM particles. Direct detection differs from
indirect detection in that the interactions occur within the detector itself, whereas indirect
detection involves observing the byproducts of interactions that take place elsewhere. Direct
detection of DM is a central focus of this work, investigated in Chapters 4, 5 and 6. In
direct detection experiments, DM particles are hypothesized to interact with SM particles
through scattering processes. The primary types of scattering are elastic and inelastic. In
elastic scattering, the total kinetic energy of the system is conserved, meaning the particles
involved emerge from the interaction without any change in their internal states. This process
can be represented as:
χ+ SM → χ+ SM. (3.6)
Ongoing direct detection experiments employ a variety of detection media and techniques.
The main detectors currently in operation include:
• DEAP-3600: a 3.6 tonne liquid argon detector located in SNOLAB, Canada [62]. A
detailed description is provided in Chapter 4.
• LUX-ZEPLIN: a 7 tonne liquid xenon detector, located at the Sanford Underground
Research Facility (SURF) in South Dakota, USA [63]. Studied in Section 7.6.
• XENONnT: a 5.9 tonne liquid xenon detector [64]. Located at the Gran Sasso National
Laboratory (LNGS) in Italy, it is an upgrade of the XENON1T experiment [65].
• PandaX-4T: a liquid xenon detector with a sensitive target mass of 3.7 tonne [66],
situated at the China Jinping Underground Laboratory (CJPL) in Sichuan, China.
• SuperCDMS: also located at SNOLAB, this experiment uses germanium and silicon
crystals to search for DM [67].
• ADMX: an axion direct detection experiment [68] sited at the Center for Experimental
Nuclear Physics and Astrophysics (CENPA) at the University of Washington. ADMX
uses a magnetic field to convert axions into detectable microwave photons.
• CRESST: also sited at Gran Sasso, this experiment utilizes calcium tungstate (CaWO4)
crystals for DM detection [69].
• PICO-40L: a bubble chamber detector hosted at SNOLAB, it uses C3F8 as its target
fluid to detect dark matter particles [70].
3.4. METHODS OF DETECTION 19
There is currently no significant evidence of DM from direct detection experiments. How-
ever, these results have allowed researchers to place increasingly stringent upper limits on
the interaction cross section between WIMPs and the nucleons of the noble elements used
in detectors. The most stringent limit on the spin-independent WIMP-nucleon cross section
is presently held by LUX-ZEPLIN (shown in Figure 3.5).
Figure 3.5: 90% CL. upper limits on the spin-independent WIMP-nucleon cross section set
by LUX-ZEPLIN [71].
3.4.3 Indirect Detection
Indirect detection searches involve detecting SM products resulting from the interaction
between two or more DM candidates. These interactions are commonly modeled as annihi-
lation or decay processes:
χ+ χ → SM + SM. (3.7)
While indirect detection does not allow for the direct observation of DM itself, it can
distinguish between various candidates based on the products that would result from anni-
hilation processes. For WIMPs, the detectable products of annihilation include gamma rays,
neutrinos, antiprotons, and antideuterons, as illustrated in Figure 3.6.
20 CHAPTER 3. DARK MATTER CANDIDATES AND METHODS OF DETECTION
Figure 3.6: Annihilation of WIMPs at a center-of-mass energy of 100 GeV, and their Stan-
dard Model products [72].
Examples of experiments that search for DM through indirect detection include: Fermi
space telescope [72], IceCube Neutrino Observatory [73], the VERITAS telescope array in
Arizona [74], HAWC Cherenkov Detector [75], Super-Kamiokande Neutrino Observatory
[76], and the Pierre Auger Observatory [77]. Indirect detection experiments have not yet
provided conclusive evidence of DM annihilation or decay. However, these experiments have
been crucial in constraining interaction cross sections and decay rates, providing valuable
information for theoretical models.
A distinct approach from the previously described detection methods is taken by beam-
dump experiments, which combine both production and direct detection mechanisms. In
these experiments, DM is both produced and detected within the same setup. A proton
beam is directed onto a target, where interactions are expected to produce DM particles
with masses in the MeV to a few GeV range. These particles are then searched for via direct
detection. One example is the MiniBooNE-DM experiment, which consists of a spherical
detector filled with 818 tons of mineral oil [78].
In the following chapters, various contributions to the DEAP-3600 direct DM detection
effort are presented. Chapter 5 focuses on the radiogenic neutron background, presenting
a framework for its characterization and exploring a machine learning–based approach to
neutron discrimination. The gamma background is refined for a solar axion-like particle
search in Chapter 6. Lastly, in Chapter 7, DEAP-3600 and LUX-ZEPLIN are the subject of
a SM and beyond analysis, using a simulated neutrino signal.
4 The DEAP-3600 Detector
4.1 Description
DEAP-3600 is a DM detector, located in SNOLAB, Ontario, Canada. It is kept 2 km
underground to provide shielding from muons and other backgrounds, and is operated by
the DEAP collaboration [62]. It is mainly used in the search for weakly interacting massive
particles (WIMPs) [79–81], however, there are also published results and ongoing efforts to:
restrict the non-relativistic effective field theory interactions between WIMPs and argon [82],
search for Planck-scale multiple interacting massive particles [83] and neutrinos [84], measure
the specific activity of 39Ar in atmospheric argon [85] and measure the scintillation quenching
factor of alpha particles in liquid argon [86]. The main principle by which DEAP-3600 can
be used for particle detection is scintillation light emission from nuclear recoil interactions
in liquid argon, this process will be explained in detail in Section 4.2.
The outer structure of the detector (see Figure 4.1) consists of a cylindrical tank of 7.8 m
of diameter and height, filled with water kept at a temperature of 12 ◦C [87]. Inside this tank
there is a 3.4 m diameter spherical steel shell, which is refrigerated using liquid nitrogen.
The spherical shell is supported by a 30 cm diameter tube which holds it from the top of the
outer cylinder. This shell is equipped with 48 Hammamatsu photo-multiplier tubes (PMT)
used for filtering out muons by their Cherenkov radiation emitted in the water tank.
Inside the spherical shell (see Figure 4.2) is an acrylic vessel, which is a sphere of an inner
and outer radii of 85 and 90 cm respectively. The liquid argon is kept in this vessel, at a
pressure of approximately 1 atmosphere and a temperature between 87 and 85 K.
The inner surface of the acrylic vessel is coated with a layer of tetraphenyl-butadiene (TPB)
which acts as a wavelength shifter for the scintillation emitted by the argon, shifting it from
UV to visible light. In addition to the muon veto PMTs, inside the spherical shell there are
255 Hamamatsu R5912 tubes, which amplify the signal generated by the scintillation light
after it has been shifted by the TPB layer, with a typical gain factor of 8.0× 105.
21
22 CHAPTER 4. THE DEAP-3600 DETECTOR
Figure 4.1: Outer structure of the DEAP-3600 detector [87].
Figure 4.2: Acrylic vessel and inner structure [81].
4.2. SCINTILLATION FROM NUCLEAR RECOILS IN LIQUID ARGON 23
4.2 Scintillation from Nuclear Recoils in Liquid Argon
As mentioned in Section 4.1, the principle by which DEAP-3600 can be used for DM
detection is when a nuclear recoil occurs. This could happen if a WIMP from the DM
halo scatters elastically with an argon nucleus in the detector (see Figure 4.3), this is called
a nuclear recoil (NR). In this interaction, the WIMP could deposit energy in the nucleus
according to Equation 4.1, where µ is the reduced mass of the nucleus and the WIMP, v is
the relative velocity between both in the center of mass frame and mN is the mass of the
nucleus [88]. For a 100 GeV WIMP, the energy deposited in an argon nucleus via elastic
scattering is low, of the order of a few tenths of keV [43].
Figure 4.3: Nuclear recoil produced by a WIMP scattering elastically on a target nucleus
[89].
ER =
µ2v2(1− cosθR)
mN
. (4.1)
When an argon atom gains energy via elastic scattering, it is left in an excited state
(Ar∗) [90]. This excited atom, called exciton, might then combine with another argon atom,
resulting in the formation of an excimer (Ar2), a short-lived bound state. The excimer
subsequently separates, emitting scintillation light in the ultraviolet part of the spectrum,
which peaks at 128 nm [91]. This process is outlined in Equation 4.2. The energy of the
scintillation UV light corresponds to 9.8 eV, which is lower than the energy required to excite
the ground state electrons in an argon atom to the first excited state, approximately 12 eV
[92], meaning that liquid argon is transparent to its own scintillation light. This light is
then shifted to the visible part of the spectrum by the TPB layer in the inner surface of the
acrylic vessel and its signal is amplified by the multiplier tubes, which allows for the nuclear
recoil to be detected.
Ar + energy → Ar∗
Ar∗ +Ar → Ar2
Ar2 → Ar + Ar + γ(128nm) (4.2)
4.3 Pulse Shape Discrimination
The scintillation process described in Section 4.2 can also be triggered by scattering in-
teractions with the electron cloud, which can occur between the electrons in the argon atom
24 CHAPTER 4. THE DEAP-3600 DETECTOR
and other electrons, or gamma rays. In this case the process is called electron recoil (ER).
An ER results in scintillation light with the same peak wavelength, making it difficult to
differentiate from an NR.
There is, however, one key difference between NR and ER that allows for discrimination
between both: a significant fraction of the scintillation light from an NR is emitted in a
shorter time duration than in an ER. This is explained by the fact that NR interactions are
more prone to form excimers in the singlet spin coupling state, while ERs form triplet spin
state excimers with a higher probability. The singlet has an approximate lifetime of 7 ns,
and the triplet one of 1600 ns [93].
This difference is exploited in a method called pulse shape discrimination (PSD), by defin-
ing an appropriate time span during which to register the fraction of the light captured by
the PMTs and comparing that to the approximate duration of the event. Following this idea,
a ratio can be defined in which the resulting fraction has a large enough difference between
nuclear recoils and electron recoils that allows for reliable discrimination between both. This
ratio receives the name Fprompt, and Equation 4.3 shows how it is defined mathematically
[81]. The shorter (prompt) time window has a duration of approximately 88 ns, while the
longer one lasts for over 10 µs. Fprompt is a ratio of the voltage gathered by the PMTs during
these time windows; it takes a typical value of ≈ 0.7 for nuclear recoils, and ≈ 0.3 for electron
recoils (see Figure 4.4). This way, nuclear and electron recoil processes can be differentiated
from each other.
Fprompt =
∑60ns
t=−28ns PE(t)
∑10µs
t=−28ns PE(t)
. (4.3)
The parameter space formed by Fprompt and PE, the amount of photoelectrons captured by
the PMTs that account for the voltage in the signal, allows for a clear visual representation
of NRs and ERs in two separate bands (see Figure 4.5). If the expected signal is a nuclear
recoil, the electron recoil band can be discarded as background, and vice-versa. An additional
feature of the Fprompt-PE parameter space is allowing for background mitigation based on
the energy of the interaction, because processes with higher energies will produce a higher
value of PE. The methods by which backgrounds are mitigated are discussed more in detail
in Section 4.4.
4.4. BACKGROUND SOURCES AND REGION OF INTEREST 25
Figure 4.4: Scintillation signal comparison of electron recoils (up) and nuclear recoils (down).
The Y axis represents the voltage of the signal captured by the PMTs, the X axis is the time
during which the signal was detected. The prompt time duration is represented in yellow,
while the longer duration is in the light blue area. The nuclear recoils have a higher fraction
of their total signal in the yellow-to-blue ratio than the electron recoils [94].
4.4 Background Sources and Region of Interest
As was discussed in Section 4.2, the energy deposited by a WIMP in a nuclear recoil is low,
of the order of a few tens of keV, this means that minimizing background interactions is of
paramount importance for a DM direct detection experiment. The main background sources
that can trigger a scintillation process in liquid argon are: electrons, gamma rays, alpha
particles and neutrons. Not all of these backgrounds will trigger a nuclear recoil, making
PSD an effective method in mitigating the backgrounds that produce electron recoils (see
Section 4.3 for a detailed discussion of PSD). In this section, a description of each of the
main background sources, and the physical processes from which they arise, will be made,
accompanied with an argument on how each source can be mitigated to possibilitate a WIMP
search.
26 CHAPTER 4. THE DEAP-3600 DETECTOR
Figure 4.5: NR and ER bands in the Fprompt and PE space [95].
4.4.1 Electrons and Gamma Rays
The dominant source of electrons are the β-decays occurring in the 39Ar isotope present
in the LAr. Electrons also originate from 42Ar and its daughter 39K, which have a lower
activity but dominate the background spectrum for energies higher than 2.6 MeV [96]. These
isotopes are of cosmogenical origin, and are present in any argon sample extracted from the
atmosphere.
The gamma rays mainly originate from decays of 232Th, 238U and 40K, all of which are
present in the structural components of the detector. Gammas can also be produced as emis-
sions from neutron captures, which can arise from (α, n) and spontaneous fission reactions
in other components of the detector that act as neutron sources, such as the borosilicate
glass in the PMTs.
Both gamma rays and electrons can result in scintillation light emission if they interact
with the 40Ar, however, these backgrounds do so via electron recoil. This means that the
scintillation emitted from these interactions will occur during a longer time, and thus, can
be reliably identified using the PSD method described in Section 4.3.
An additional electromagnetic background process induced by electrons and gamma ray
interactions is the Cherenkov radiation that can be emitted in the PMT glass and light
guides. This radiation has a significant UV component which can be detected by the PMTs
as scintillation light, resembling the light emitted from a nuclear recoil. PSD can also be
employed to mitigate these backgrounds, but in this case the prompt fraction of light in the
nuclear recoils is lower in comparison. Due to the fact that Cherenkov radiation emission
occurs in very short time frames, < 1 ns, these events have an Fprompt value of ≈ 0.9,
making it significantly higher than ≈ 0.7 for the NR band [81]. This allows for the successful
identification of these processes as not NR in origin.
4.4. BACKGROUND SOURCES AND REGION OF INTEREST 27
4.4.2 Alpha Particles
Alpha particles in DEAP-3600 originate mainly from decays of 222Rn, 220Rn y 210Po [95],
which are present in the outer components of the detector, such as the piping and the AV.
An example of one of the background alpha decays is illustrated in Equation 4.4, the isotope
222
84 Rn decays into 218
82 Po and an alpha particle represented by a helium nucleus.
222
84 Rn →218
82 Po +4
2 He (4.4)
Alpha particles interact with the LAr via NR [97], however, as can be seen in Figure 4.5,
the alphas produced in the decay of 222Rn, 210Po, 218Po and 214Po, although reconstructed in
the NR band, are registered at much higher energies than what an NR by a WIMP from the
galactic halo would produce. This allows for these alphas to be discriminated as background
even-though they also generate NR scintillation.
However, alpha particles that deposit only a fraction of their energy can produce detection
signals that overlap with the WIMP region of interest. This region is the part of the Fprompt
and PE parameter space designated for WIMP interactions, as described in Section 4.4.4.
Most of these alpha particles are emitted by decays that occur in the AV, the TPB coating
and the neck of the detector. These are all outer components (see Figure 4.2), and the
background effects of these alphas can be mitigated by reducing the fiducial volume of the
LAr used in the search. This is done in practice by imposing a radial cut at 750 mm and a
cut in the vertical direction (along the neck of the detector) at 550 mm, measured from the
geometrical center of the AV.
4.4.3 Neutrons
Neutrons can interact with argon atoms through NR, and this interaction may occur
within the same energy range as an NR caused by a WIMP. There are two main categories
of processes from which neutrons can originate as a background source: cosmogenic and
radiogenic. In the present Section both of these types of processes will be examined, and
the methods for their mitigation will be described.
Cosmogenic neutrons are induced by atmospheric muons in (µ, n) reactions. The con-
tribution of these neutrons as a background source is greatly reduced by the 2 km rock
shielding of the nickel mine at which DEAP-3600 is located, which is equivalent to 6 km of
water. An additional layer of mitigation is provided by the cylindrical water tank in which
the detector is submerged [87]. If any atmospheric muons penetrate to that depth, they can
still be mitigated by the Cherenkov radiation emitted in the water tank, which is detected
by the external PMTs (see Figure 4.1).
Radiogenic neutrons arise from the inherent radioactivity in the materials from which the
detector was built. The most significant contributions are those of (α, n) reactions and
spontaneous fission. Approximately 70% of the background interactions from radiogenic
neutrons are produced in (α, n) reactions from alpha decays of 238U and 232Th [98].
Isolating radiogenic neutrons is a difficult task, since they produce NR interactions that
overlap with the energy ranges at which WIMP recoils occur, and can’t be discriminated by
Cherenkov light like the cosmogenic variant of neutrons. The focus for this background source
shifts to estimating its contribution and subtracting the estimated value from the events
28 CHAPTER 4. THE DEAP-3600 DETECTOR
detected. This is achieved with the use of Monte Carlo simulations, which are performed
using software such as Reactor Analysis Tool (RAT [99]) and NeuCBOT [100], which are
widely used tools for simulations and analysis at the DEAP collaboration.
4.4.4 Region of Interest and Background Estimates
The Fprompt and PE parameter space is used to define a region of interest (ROI) in which
the WIMP interactions can be identified after mitigating the background sources described in
the previous sections (see Figure 4.6). The main criteria for defining the ROI is restricting it
to the NR band and the energy range at which WIMPs can be reliably singled out from all the
background sources. In the latest published WIMP search analysis [81], these criteria were
used to further refine the background mitigation in the ROI without significantly decreasing
the WIMP acceptance:
• In the range of 95-160 PE, the curve is defined such that the number of expected
electron recoil events is less than 0.05.
• The curve from 160-200 PE is defined for a constant 1% loss of nuclear recoil acceptance.
• The upper curve spanning the range 95-200 PE delineates a constant 30% loss of
nuclear recoil acceptance, ensuring that the expected number of alpha particle events
in the region of interest is less than 0.5.
• The upper limit for PE is given by the kinematics of the WIMP-argon nucleus inter-
action, for WIMPs in the mass range of 100 GeV. For higher PE values, the noise
produced by alpha particles and neutrons is expected to be greater, while the fraction
of expected WIMPs would not significantly increase.
In the same analysis, an estimated contribution of events in the ROI was made for each of
the background sources, which yielded the results shown in Table 4.1.
The DEAP-3600 detector plays a central role in this work. Its radiogenic neutron back-
ground is the subject of investigation in Chapter 5, where the neutron contribution to the
background model is characterized, and a novel mitigation approach involving machine learn-
ing is explored for future implementation. A contribution to the search for MeV-scale so-
lar axion-like particles using DEAP-3600 is presented in Chapter 6. Lastly, in Chapter 7,
DEAP-3600’s sensitivity to coherent elastic neutrino-nucleus scattering from supernovae is
examined, along with potential implications for the Standard Model and beyond.
4.4. BACKGROUND SOURCES AND REGION OF INTEREST 29
Figure 4.6: Region of interest (in black) defined for the WIMP search [81]. The Y axis
represents the Fprompt parameter and the X axis the photoelectrons, and its equivalent nuclear
recoil energy in keV.
Background Source NROI
ERs from βs and γs 0.03 ± 0.01
Cherenkov from βs and γs <0.14
Neutrons (Radiogenic) 0.10+0.10
−0.09
Neutrons (Cosmogenic) <0.1
Alphas from AV Surface <0.08
Alphas from AV Neck 0.49+0.27
−0.26
Total 0.62+0.31
−0.28
Table 4.1: Background Estimates for the latest published WIMP search, separated by each
source and the contribution to the ROI in number of events (NROI) [81].
30 CHAPTER 4. THE DEAP-3600 DETECTOR
5 Neutron Background in DEAP-3600
Dark matter direct detection experiments aim to observe very rare signal events, while
accounting for commonly occurring background events. This requires a background model
capable of providing sufficient sensitivity to establish upper limits or discovery contours,
depending on the case. The following chapter presents this work’s contribution to modeling
and mitigating the radiogenic neutron background in DEAP-3600. Radiogenic neutrons
constitute the most challenging background to reduce, as neutron-induced nuclear recoils
are indistinguishable from WIMP interactions when relying solely on PSD, as described in
Section 4.4.3.
The radiogenic neutron background is modeled within a Profile Likelihood Ratio frame-
work. By accurately characterizing the radiogenic neutron contribution, the analysis en-
hances the experiment’s ability to distinguish potential DM signals from background-induced
events. This contribution is part of the collaboration’s ongoing effort to perform a DM search
with a longer livetime than that of the most recently published WIMP search [81].
Additionally, beginning in Section 5.4, a machine learning method to further mitigate ra-
diogenic neutron backgrounds is introduced. This work constitutes an initial exploration into
distinguishing neutrons from WIMPs by leveraging differences in the likelihood of observing
multiple versus single nuclear recoils.
5.1 The Profile Likelihood Ratio Method
The Profile Likelihood Ratio (PLR) method is a statistical framework widely used in DM
detection experiments [54, 101]. It enables a simultaneous fit of signal and background events,
while allowing for systematic uncertainties to be parametrized as nuisance parameters.
As an example to illustrate the PLR method [102], consider a histogram measuring a
variable x, the expected value of the number of events in the ith bin of the histogram (E[ni])
is written as:
E[ni] = µsi + bi, (5.1)
where µ is a parameter that characterizes the signal strength. The quantities si and bi are
the mean number of signal and background events in the ith bin, which are written in terms
of a probability density function as:
si = stot
∫
i
fs(x,θ),
31
32 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
bi = btot
∫
i
fb(x,θ); (5.2)
where fs and fb are the probability density functions (PDFs) of the variable x for signal and
background events. The set of nuisance parameters characterizing the PDFs are given by
θ, stot and btot are the total number of signal and background events in the histogram, and
the integrals
∫
i
fs(x,θ) and
∫
i
fb(x,θ) are the probabilities that the signal and background
events are found in the ith bin.
The likelihood of observing a signal strength parameter µ, given a set of parameters θ, is
L(µ,θ), and the profile likelihood ratio is defined as:
λ(µ) =
L(µ, θ̃(µ))
L(µ̂, θ̂)
. (5.3)
The numerator in the PLR definition denotes the likelihood of observing µ given θ̃, the set
of parameters that maximizes L for that specific µ; that is, a conditional maximum of L.
The denominator represents the global maximum of L, where the likelihood is maximized
unconditionally for a signal parameter µ̂ and a set of nuisance parameters θ̂. The quantity
λ(µ) can take values between 0 and 1, where values close to 1 indicate a good agreement
between the measured data and the hypothesized value of µ 1.
A test statistic that depends only on the signal strength parameter µ can be constructed
from λ(µ) in Equation 5.3 for two different scenarios: imposing an upper limit (κµ), and
calculating the significance of a discovery (κ0). For the case of imposing an upper limit, µ̂
takes lower values than µ, and the exclusion test statistic is defined as follows:
κµ =



−2ln(λ) for µ̂ ≤ µ,
0 for µ̂ > µ.
(5.4)
Given that 0 ≤ λ ≤ 1, this implies that κµ ≥ 0. The minimum value, κµ = 0 corresponds to
µ̂ = µ, this is the case in which the data is the most compatible with the signal hypothesis.
As κµ increases, the data becomes more compatible with the background-only hypothesis.
For an observed test statistic κµ,obs, a signal p-value is defined to test Hµ, the signal
hypothesis, as follows:
pµ =
∫ ∞
κµ,obs
f(κµ|Hµ)dκµ, (5.5)
where f(κ|Hµ) denotes the PDF for κ assumingHµ. The p-value pµ represents the probability
of measuring data of equal or greater incompatibility with Hµ. The hypothesis Hµ is rejected
if pµ is below a certain threshold; for example: if pµ ≤ 5%, Hµ is rejected at 95% CL.
In the case of calculating the significance of a discovery, the discovery test statistic is
defined as:
1By Neyman-Pearson’s lemma [103], the PLR is the most powerful test statistic when testing a null and
alternate hypothesis, H0 and H1 respectively, in terms of observed data x that can reject H0. It can also be
written as λ = L(H1|x)
L(H0|x)
.
5.2. RADIOGENIC NEUTRON SIMULATIONS 33
κ0 =



−2ln(λ(0)) for µ̂ ≥ µ,
0 for µ̂ < µ,
(5.6)
where κ0 ≥ 0, and λ(0) is the PLR for the background-only hypothesis H0. The value of
most compatibility with H0 is κ0 = 0, while increasing values indicante less compatibility
with H0.
The null p-value, to test H0, is given by:
p0 =
∫ ∞
κ0,obs
f(κ0|H0)dκ0. (5.7)
f(κ|H0) is the PDF for κ given the background-only hypothesis H0. This p-value defines
the probability of observing a test statistic of greater incompatibility with H0. Analogous
to the first case, if p0 is below certain threshold, H0 is rejected with the complementary CL.
Due to its statistical advantages, the DEAP collaboration is actively working to implement
the Profile Likelihood Ratio (PLR) method [90]. One key reason this method has become
the standard across DM experiments is that, when the background model provides sufficient
sensitivity, it outperforms other statistical approaches — as illustrated in Figure 5.1. This
improved sensitivity enables the use of an expanded region of interest (ROI), as shown in
Figure 5.2. Compared to the ROI described in Section 4.4.4, the upper bound of the region
is a curve that extends up to values of 0.76 Fprompt, significantly expanding the area of the
parameter space analyzed. In the following sections, this work’s contribution to modeling
the radiogenic neutron background within the PLR framework is presented.
5.2 Radiogenic Neutron Simulations
The simulated neutrons were generated as a collaborative work using the C++ based
software Reactor Analysis Tool (RAT) [99], which combines features from Geant4 [106]
and ROOT [107]. RAT is widely used in the DEAP collaboration for data generation and
analysis. It allows for the simulation of physical processes ocurring in an accurate model of
the DEAP-3600 detector. The simulations were performed in clusters to which the DEAP
collaboration is granted access by the Canadian organization The Alliance [108].
The radiogenic neutrons simulated correspond to (α, n) reactions from decays in the lower
part of the 238U chain (from 226Ra to 206Pb). Two systematic uncertainties were taken into
account in these simulations: the scattering length of the TPB wavelength shifter and the
refractive index of the liquid argon (LAr) in the detector, both of which play a key role in
the propagation of scintillation light to the PMTs. A total of five datasets were generated:
one using the nominal detector settings, and four representing the upper and lower bounds
of variation for each of the two systematics.
In order to optimize the usage of computing resources, the simulations were divided into
two stages (illustrated in Figure 5.3):
1. A total of 9.96 × 108 nominal neutrons simulated isotropically from the borosilicate
glass in the PMT array. These neutrons were simulated without the optical physical
34 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
Figure 5.1: Comparison of exclusion curves for the median spin independent WIMP-nucleon
scattering cross section σmed as a function of WIMP mass, using the Poisson, Maximum Gap
[104], and PLR methods [105]. The limits were imposed with a simulated dataset consisting
of 10 background events and 1 signal event, as a function of different threshold energies.
Figure 5.2: Comparison of the ROI used in the most recent dark matter published search
[81] (described in Section 4.4.4), and the proposed ROI for the PLR analysis [90] .
5.3. PDFS FOR THE RADIOGENIC NEUTRONS 35
processes, such as scintillation light emission and recollection. The neutrons from this
stage that reach the outer AV radius (901.449 mm) are counted, and their energy and
momentum is captured to be used as input for stage 2.
2. An energy spectrum and angular distribution were obtained from the energies and
momenta of the stage 1 neutrons that reached the outer radius of the AV. Using these
distributions, five neutron datasets were generated at the outer AV radius: one corre-
sponding to the nominal configuration and four representing the systematic variations.
The number of simulated neutrons for each dataset (approximately 7.25×105) matched
the number of stage 1 neutrons that reached the outer AV radius. In this second stage,
optical processes were enabled, modeling the scintillation light collected by the detec-
tor.
Figure 5.3: Amplified view of the internal components of DEAP-3600 [81], showing the two
stages of the radiogenic neutron simulations. Stage 1 (blue): 9.96× 108 neutrons simulated
isotropically from the PMT borosilicate glass. Stage 2 (red): 7.25× 105 neutrons simulated
for each dataset (nominal and 4 systematics), from the outer AV radius (901.449 mm), with
the energy spectrum and momentum distribution captured from the stage 1 neutrons. This
is exemplified for 1 PMT, the simulations accounted for the entirety the PMT array.
Additional properties of the radiogenic neutrons generated in the PMT array are listed in
Table 5.1.
5.3 PDFs for the Radiogenic Neutrons
The goal of this analysis was to produce PDFs for the nominal and systematic radiogenic
neutron datasets using functions that accurately represent the histogram data, without being
more complex than necessary. The purpose of these PDFs was to characterize the neutron
36 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
PMT Array Parameter Value
Mass 188.96± 3.78 kg [109]
Purity (lower 238U) 175.64± 4.93 ppb [110]
Yield (lower 238U) (132.0± 26.4)× 10−12 neutrons
g×s×ppb
[111]
Table 5.1: PMT array mass, purity and neutron yield used in the simulations. The yield
for the lower part of the 238U chain was taken from existing data calculated using the
SOURCES4C software [111].
background distribution for the PLR analysis, analogous to fb(x,θ) in Equation 5.2. The
variables considered for describing the background sources in the PLR analysis were:
• NSCBayes (NSC): a measure of the energy captured from the interactions. It is mea-
sured in qPE (labeled as PE for simplicity), which correspond to the pulse charge of
an event collected by a PMT, divided by the average single-photoelectron charge in
the PMT.
• Pulse Index First Gaseous Argon (PIFGAR): the number of PMTs oriented toward
the LAr volume that registered light from an event before any PMTs in the gaseous
argon (GAr) region detected a signal.
• MblikelihoodR (MBR): reconstructed radial position of the event.
• Fprompt (RPR): a measure of the fraction of the scintillation light emitted during the
prompt window (described in Section 4.3). It is used to discriminate nuclear and
electron recoils. Referred to as Rprompt (RPR) in the most recent analyses.
These variables were used to construct histograms, and the PDFs were fitted to the his-
tograms (see Figure 5.4). The steps taken for constructing the PDFs are summarized as
follows:
1. After applying cuts focused on selecting regions of parameter space where radiogenic
neutrons reconstruct, the five datasets were divided in two subsets each according to
their value of pifgar. Events with PIFGAR ≤ 2 were grouped in the PIF2 set, while
all other events (PIFGAR > 2) were categorized as PIF3. The number of events in
each of these pifgar categories was approximately equal.
2. A histogram of NSC was constructed for each PIFGAR set, in the range of 90 ≤ PE ≤
990 which corresponds approximately to a nuclear recoil energy range of 52 ≤ keVnr ≤
570. These histograms were then fitted, resulting in 10 PDFs for NSC (two PIFGAR
subsets times 5 datasets of nominal + 4 systematics).
3. RPR and MBR histograms for each PIFGAR subset were subsequently fitted for spe-
cific PE bins. This resulted in 14× 2× 5 = 140 fits for RPR, and 23× 2× 5 = 230 fits
for RPR.
4. The parameters of the functions used for fitting the RPR and MBR histograms were
later fitted as a function of the PE bin occupied by each respective histogram.
5.3. PDFS FOR THE RADIOGENIC NEUTRONS 37
Figure 5.4: Flowchart of the datasets in the neutron simulations. Five datasets, account-
ing for nominal and the four systematic variations: the refractive index of the LAr (rfrUP
and rfrDOWN), and the scattering length of the TPB wavelength shifter (tpbUP and tpb-
DOWN). Each dataset was divided into two subsets: PIFGAR ≤ 2 and > 3 (labeled pif2
and pif3, respectively). The NSC PDFs were constructed for each of these two subsets. RPR
and MBR histograms were fitted on specific PE bins, and the parameters of these PDFs were
fitted as a function of the corresponding PE values, for all subsets.
Figure 5.5: Normalized PIFGAR histogram for the nominal settings. The dataset was
divided into two subsets: PIFGAR ≤ 2 and PIFGAR > 3.
38 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
A normalization convention was adopted by the collaborators studying the different back-
ground sources in this analysis. The convention is to normalize the histograms to 1 event
per liveday. For the radiogenic neutrons, the normalization weights (w) were obtained in the
following manner:
f = mPMT × pPMT × yPMT = 378.5 days−1,
teq = 9.96× 108/f = 2.63× 106 days,
w = 1/teq = 3.80× 10−7 days−1. (5.8)
where mPMT , pPMT and yPMT correspond respectively to: the mass, purity and yield of
the PMT array (shown in Table 5.1), and the time to which the simulations from stage 1
are equivalent to is teq. The corresponding PDFs and fitted parameters, refined through
several iterations, are evaluated using the reduced χ2 metric provided by the ROOT package
MINUIT [112], and are detailed in the following sections. The normalized histogram for
PIFGAR is presented in Figure 5.5.
5.3.1 NSCBayes
The NSC histograms as a function of qPE (labeled PE here for simplicity) were fitted with
a sigmoid function of the corresponding form:
f(PE) =
N
1 + exp
(
−PE−xs
ts
) · exp
(
−PE
θ
)
θ
. (5.9)
This function has four parameters:
• The norm factor N , adjusts the maximum value of the sigmoid.
• The midpoint of the sigmoid is characterized by xs.
• The parameter ts describes the steepness of the sigmoid curvature.
• The mean of the exponential term is described by θ.
Accounting for all five datasets and the two PIFGAR subdivisions, a total of 4 × 5 × 2 =
40 parameter values were produced for the NSC histograms. An example of one of these
histograms is presented in Figure 5.6.
5.3.2 Fprompt
The Fprompt (labeled as Rprompt in the most recent analysis) histograms were obtained
including the full 90-990 PE range, divided in 13 NSC bins of width 60 PE from 90 to 900
PE, and a final 90 PE bin to 990. This was motivated in obtaining sufficient statistics for
each PE bin, while providing enough data points for the parameter fits. The Fprompt values
considered are in the range 0.5-1.0, corresponding to the nuclear recoil band described in
Section 4.3.
5.3. PDFS FOR THE RADIOGENIC NEUTRONS 39
Figure 5.6: NSC fit for the stage 2 neutrons (AV) of the pif2 tpbUP dataset. The parameter
values are indicated in the legend, along with the reduced χ2 value. Fit status = 0 is an
indicator provided by Minuit of a successful fit convergence. As an additional check, the
histogram and the sigmoid area are seen to agree to within 0.5%.
40 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
The histograms resemble a gaussian distribution with a left skew. The function that
performed best achieving a satisfactory goodness of fit, while trying to use only as many
parameters as necessary, was a gaussian with an error function term, presented as follows:
f(x) =
N
σ
√
2π
· exp
(
−1
2
(
x− µ
σ
)2
)
·
(
1 + erf
(
λ(x− µ)
σ
√
2
))
. (5.10)
This function uses four parameters:
• The norm factor N .
• The mean of the gaussian distribution µ.
• The standard deviation σ.
• The λ parameter of the error function term. A negative λ results in a left skew, while a
positive λ produces a right skew. A value of λ = 0 recovers a gaussian curve depending
only on the three parameters described previously.
The Accounting for all five datasets, the two PIFGAR subdivisions, and the 14 PE bins, a
total of 4× 5× 2× 14 = 560 parameter values were produced for the RPR histograms. An
example of one of these fits is shown in Figure 5.7.
The four parameters in the curve defined in Equation 5.10 were plotted separately as a
function of the PE bin of their respective histogram. As an additional consistency check
for the RPR and MBR distributions, a second normalization factor was applied to each
histogram to ensure that its integral matched the integral of the corresponding PE bin in
the respective systematic and PIFGAR datasets.
The parameters N and µ were fitted using a six parameter three-part piecewise function:
a quadratic section, followed by a cubic portion, and ending with another quadratic. Conti-
nuity conditions on the function and its first derivative fully determine the cubic component.
This piecewise function is defined as follows:
f(x) =











A1(x−X1)
2 + Y1, for x < X1
ax3 + bx2 + cx+ d, for X1 ≤ x < X2
A2(x−X2)
2 + Y2, for x ≥ X2,
(5.11)
The points (X1, Y1) and (X2, Y2) are the coordinates for the transition points, which coincide
with the vertexes of the quadratic segments; A1 and A2 are additional parameters for the
quadratic terms. The coefficients a, b, c, and d are defined by the continuity conditions as
given below:
5.3. PDFS FOR THE RADIOGENIC NEUTRONS 41
Figure 5.7: RPR fit for the PIF2 rfrUP distribution, in the 90-150 PE bin. The best fit
parameter values are included, along with the reduced χ2 for goodness of fit evaluation. The
fit function, histogram and PE integrals are also shown. The histogram was normalized to
ensure coincidence with the PE bin integral.
42 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
a =
−2Y1 + 2Y2
X3
1 − 3X2
1X2 + 3X1X2
2 −X3
2
, (5.12)
b =
3X1Y1 − 3X1Y2 + 3X2Y1 − 3X2Y2
X3
1 − 3X2
1X2 + 3X1X2
2 −X3
2
, (5.13)
c =
−6X1X2Y1 + 6X1X2Y2
X3
1 − 3X2
1X2 + 3X1X2
2 −X3
2
, (5.14)
d =
X3
1Y2 − 3X2
1X2Y2 + 3X1X
2
2Y1 −X3
2Y1
X3
1 − 3X2
1X2 + 3X1X2
2 −X3
2
. (5.15)
Examples of parameter fits for N and µ are shown in Figure 5.8.
The remaining parameters, λ and σ, were fitted using a linear and a quadratic function,
respectively, and an example of these fits can be seen in Figure 5.9.
Accounting for the number of parameters, the 5 datasets and the PIFGAR subsets, a
total of 6 × 5 × 2 = 60 parameters were produced for N and µ, 2 × 5 × 2 = 20 for λ, and
3× 5× 2 = 30 for σ.
5.3.3 MblikelihoodR
The NSC range for the MBR histograms was reduced to 90-990 PE, and the radial positions
included were in the range 0-720 mm, this was decided to favor consistency in the fits without
compromising the integrity of the most relevant radial positions in the distributions. The
NSC range was distributed in 17 bins with a width of 30 PE from 90 to 600, followed by 5
bins of 60 PE up to 900, and one last 90 PE bin up to 990. The function used for the MBR
histograms is an exponential as written below:
f(x) =
N
θ
exp
(−x
θ
)
. (5.16)
This exponential function has two parameters:
• The norm parameter N .
• The mean, given by θ.
The total number of parameters produced for the MBR histogram fits is determined by the
parameters in the function, the nominal and systematics datasets, the PIFGAR subsets and
the number of PE bins, respectively: 2× 5× 2× 23 = 460. The MBR histogram fit for the
tpbUP PIF2 dataset in the 120-150 PE bin is presented in Figure 5.10.
The norm parameter N was fitted with a two segment piecewise function defined as:
f(x) =





A+ s
x−B
, for 0 < x < x0
m · x+
(
A+ s
x0−B
−m · x0
)
, for x ≥ x0.
(5.17)
5.3. PDFS FOR THE RADIOGENIC NEUTRONS 43
Figure 5.8: RPR N (top) and µ (bottom) parameter fits for the nominal PIF3 and nominal
PIF2 datasets, respectively. Both parameters were fitted using the piecewise function defined
in Equation 5.11. The best fit values and the reduced χ2 are shown in the legends. The blue
dashed lines denote the limits of the 90-990 PE range.
N Rprompt Para meter Fit nom (pif > 2) 
z 
0.004 e- quad-cube-<¡u.ad 
+1 
XI • 2.23 1e+02 ± J.898e_Ol 
se- '(1 • 3.277e-ú3 ± , .2 12e-04 
X2 . 7.464e+02 ± 4.64Be_Ol 
L '(2 . L248e-{)3 ± , .226e-04 
0.003 
'V -, 1 Al . -1.62Be-Ú8 ± 2.370e-0lI 
+T A2 . -7.S53e-Q9 ± 6.52Se-09 
sF-
\'" 
Chi21NDF _ 10.469 / 8 
Fit status . O 
0.00 
0.002 
0.00 2e-
0.001 Se- "- + 
0.00 'e- 1 ~ 
Se-
j 
0.000 
100 200 300 400 soo 600 700 BOO 900 1000 
PE 
mu Rprompt Parameter Fit nom (pif <= 2) 
2e- ~ 
, , 
Xl .2.'".-<l" " .. ' •• m 
Yl . 1._01 ' U250_()J 
. t-' X2 . 2.'''' • ..,''' ~._."" 
Y2 • 2.n50-«,l , 1 . ...,1 .. 0\l 
Al . 1 .0<&-01 ' 0.8' ''''07 
'e- A2 • -• . 0QCI0-09 ' 1." " , 0\l 
C"" , N Df " . >Se I ~ 
§ 
O., 
o., 
o. +1 
' e- 1+ 
'f-tt 
, 
9e- -~ 
0.7 
0.7 , e- -r-
0.7 7e-
0.7 Se-
100 200 300 400 soo 600 700 BOO 900 1000 
PE 
44 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
Figure 5.9: RPR λ (top) and σ (bottom) parameter fits for the rfrUP PIF2 and rfrUP PIF3
datasets, respectively. The parameter λ was fitted linearly, while a quadratic function was
used for σ. The best fit values and the reduced χ2 are shown in the legends.
sf-
of-
Sf-
of-
Sf-
-, of-
-, Sf-
• 0.09 E 
º' • 
0.08 
0.07 
0.06 
0.05 
0 .04 
0.03 
0.02 
lambda Rprompt Parameter Fit rfrUP (pif <= 2) 
-h -L 
~ 
, , 
Lineal F ~ 
pO • · 1.127 • • 00 ~ 3. 192.·0' 
p l ·· M ll . · 05~7 . r.oo. · ().I 
Chi2;N OF _ 16.376 113 
100 200 300 400 500 600 700 800 900 1000 
PE 
sigma Rprompt Parameter Fit rfrUP (pif > 2) 
d-
+ 
-- Polyoorn;aI Fit 
pO . 9.81Mf1-02 i 3.005&-03 
pi • -2033<1-04 i ' .B3I)e·05 
p2 • 1 .433f1-07 i L71l5e-08 
Chi2lNOF • 19000 / 11 
+ 
100 200 300 400 500 600 700 800 900 1000 
PE 
5.3. PDFS FOR THE RADIOGENIC NEUTRONS 45
Figure 5.10: MBR fit for the PIF2 tpbUP distribution, in the 120-150 PE bin. The best fit
parameter values are included, along with the reduced χ2 for goodness of fit evaluation. The
fit function, histogram and PE integrals are also shown. The histogram was normalized to
ensure coincidence with the PE bin integral.
46 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
Figure 5.11: MBR N (top) and θ (bottom) parameter fits for the rfrUP PIF2 and tpbDOWN
PIF3 datasets, respectively. The parameter N was fitted with the piecewise function defined
in Equation 5.17, while θ was fitted linearly. The best fit values and the reduced χ2 are
shown in the legends. The blue dotted lines represent the PE=90 lower bound of the NSC
region.
z O. " 
O. 2e-
De-
-O. 2e-
-O. ' e-
-O. 6e-
o 
- 2 De-
-4 De-
De-
- 8 De-
N mblikelihoodR Parameter Fit rfrUP (pif <= 2) 
~ , 
r 
200 400 600 
l 
Asymptotic t li near 
A = 6.92OO-08 ± 2.485e-08 
B = 5O.493 ± 5.783e-02 
s = -1 .63273e-05 ± 5.1 76e-05 
x_O = 231 .606 ± 2.OO2e+OO 
m = 6.5376ge-13 ± 8.084e-1 4 
Chi2INDF = 9,270 / 18 
Fit status = O 
BOO 1000 
PE 
Theta mblikelihoodR Parameter Fil tpbDOWN (pif > 2) 
Lineal Fit 
00 _ · 1.07&. 02 ~ • . 0820 _00 
o l .4 . 7060 · 0 2 ~ 3 .10 '0 · 1.r.l 
Chi2;N DF _ 3.3.687 130 
Fit . tatus _ o 
t 
-1-ht t 
f :: ttt t t - ~ - 10 
- 12 
- 14 De-
- 16 O 
200 300 400 500 600 700 BOO 900 
PE 
5.4. NEUTRON DISCRIMINATION USING MACHINE LEARNING 47
The segment to the left of the transition point x0 is an asymptotic function, with a horizontal
asymptote in A as x → ∞, and a vertical one in x = B. To the right of x0, the function
becomes linear, ensuring that the transition point is part of the line. The parameter θ was
fitted linearly. N and θ fits for the rfrUP PIF2 and tpbDOWN PIF3 datasets, respectively
can be seen in Figure 5.11.
The total number of parameters for the MBR parameter fits is given by: the number of
parameters in the function, the 5 datasets and the PIFGAR subsets, respectively, resulting
in 4× 5× 2 = 40 parameters for N , and 2× 5× 2 = 20 parameters for θ.
Taking all variables into account, the total number of parameters involved in the his-
togram fits is 40 + 560 + 460 = 1060, corresponding to NSC, RPR and MBR, respectively.
Additionally, the number of parameters from the parameter fits rises to 110+60 = 170 from
RPR and MBR. The best fit values from the parameter fits for all variables in the RPR
and MBR fits were written to a ROOT file, along with the values from the NSC fits and
the PIFGAR histogram shown in Figure 5.5. This ROOT file serves as input to the PLR
analysis framework, along with analogous files provided by collaborators working on other
primary background sources, including alpha decays originating in the detector neck, the AV
surface, and copper dust present in the LAr. This is an ongoing project within the DEAP
collaboration, aimed at conducting a WIMP search using the PLR method on a dataset with
a livetime of 388 days.
5.4 Neutron Discrimination Using Machine Learning
As discussed in 4.4, radiogenic neutrons cannot be filtered by using the PSD method
detailed in 4.3 because they also interact via nuclear recoil with the 40Ar nuclei. This means
that they will lie in the same Fprompt band that WIMPs would, at overlapping energies.
There is, however, one key difference between the interactions of WIMPs and neutrons
that might help in mitigating this background source: neutrons have a higher probability
of multiple interactions with the argon nuclei. This argument can be made in terms of the
mean distance traveled by a particle through matter without having an interaction, the mean
free path (λ), which is given by [113]:
λ =
1
nσ
(5.18)
where n is the density of target nuclei per unit volume and σ is the interaction cross section.
The numerical values for the atomic density of liquid argon at 87 K and 1 atm, taken
from [114], and the upper limit for the WIMP-nucleon scattering cross section for a 100 GeV
WIMP imposed by DEAP [81], yield the following approximate upper limit for the mean
free path of WIMPs in liquid argon:
λWIMP >
1
2.11× 1022 atoms
cm3 · 3.9× 10−45cm2
= 1.2× 1022cm = 1.3× 104ly. (5.19)
Doing a similar exercise for the neutrons, with the value for the scattering cross section
stated in [115], results in this mean free path:
48 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
λneutron =
1
2.11× 1022 atoms
cm3 · 4.21× 10−25cm2
= 1.13m. (5.20)
The difference is staggering, and given that the radius of the acrylic vessel in the DEAP 3600
detector is approximately 85 cm [87], it becomes evident that the probability of a WIMP
scattering more than once with an 40Ar nucleus can be reliably neglected when compared to
the same interaction for a neutron. This means that, in principle, recognizing interactions
with multiple nuclear recoils can be used as a reliable method for identifying neutrons in the
signal seen at the detector. Developing an additional method to mitigate this background
could potentially lead to more stringent limits or a higher probability of detecting new
phenomena, making this research topic of significant importance. Currently, no established
method exists for achieving this. This study aims to serve as an initial step for this purpose,
exploring one of the possible directions towards this goal.
5.5 Formulation as a Machine Learning Problem
In physical terms, the problem can be stated as finding a method for identifying multiple
nuclear recoils in the LAr volume of the detector, which, by the argument presented in Section
5.4, can be reliably discarded as candidates for WIMP-nucleus scattering interactions, being
identified instead as caused by background sources such as radiogenic neutrons.
Given that there is no straightforward way to determine if the light captured by the PMTs
comes from multiple nuclear recoils caused by a single neutron, this problem doesn’t have a
practical analytical solution. However, it can be addressed using machine learning methods,
which do not require an explicit analytical relationship between the independent and target
variables to be provided. Instead, these methods rely on extracting patterns and information
directly from the provided dataset, making them particularly suited to problems where no
practical analytical formulation exists.
Because real detector data cannot currently provide information on the number of nuclear
recoils caused by neutrons, the analysis relies on simulated data as its primary input source.
Simulations have been extensively used by the DEAP collaboration to estimate background
contributions in previous analyses [81, 95, 116]. These simulations, generated using the RAT
software [99], accurately model the detector’s geometry and the relevant physical processes,
making them a reliable source for this study.
An additional advantage of using simulations is that information on the physical trajectory
followed by the neutron is available, which makes it possible to count the number of scat-
terings between a given neutron and argon nuclei. This provides a ground truth for tagging
multiple nuclear recoil interactions produced by radiogenic neutrons, as well as additional
useful information such as the proportion of these neutrons that scatter with more than one
argon nucleus.
The fact that ground truth is accessible makes this problem well-suited for analysis with
supervised machine learning algorithms. Since the task can be reduced to determining
whether an interaction is either a single or a multiple nuclear recoil, a binary classification
supervised learning algorithm is the most appropriate choice. These algorithms are trained
5.6. DATA COLLECTING AND PROCESSING 49
on data labeled as either true or false in a binary target class, and can then be used to
classify unlabeled data into one of these two categories.
5.6 Data Collecting and Processing
The primary sources for this analysis were simulated radiogenic neutron datasets. The
dataset used for model training was a dataset of 100 million neutrons generated isotropically
from the PMT array; an additional dataset of 10 thousand neutrons generated from the
AV (see 4.1) was used for model evaluation. Both of these datasets consist of neutrons
emitted from radioactive decays in the lower part of the U238 decay chain, with the spectra
for their corresponding materials (borosilicate glass and acrylic, respectively). These Monte
Carlo datasets contain information about the trajectory, position, and physical processes
undergone by the neutrons. An additional dataset was used for model validation, consisting
of real data collected when an Americium-Beryllium (AmBe) neutron source was deployed.
A ROOT script was written that accesses the trajectories of the neutrons, identifies the
ones that have penetrated to the LAr volume, and counts the number of scattering interac-
tions with 40Ar nuclei. This allowed for the creation of a binary feature that assigned the
value of 1 to neutrons with more than 1 nuclear recoil, and 0 to those with exactly 1. Neu-
trons that did not produce any nuclear recoils were not used for this analysis, since ultimately
they wouldn’t be detected by the PMTs. This binary feature was used as the ground truth
that served as a flag for training various supervised machine learning algorithms. The other
features in the dataset contain information such as: the time interval between 2 events, the
reconstructed position of the events, Fprompt (see Section 4.3), the number of pulses registered
in a specific time window, and the pulse charge divided by the average single photo-electron
charge for each PMT for each event.
From this part of the analysis, it was derived that approximately 80% of the neutrons
that scatter with an argon nucleus do so multiple times (see Table 5.2). This finding fur-
ther highlights the reach of accurately identifying multiple nuclear recoils, since this could
potentially be related to 80% of the neutrons that are detected in the PMTs.
Number of Neutrons Percentage of Total
Multiple Nuclear Recoils 7754 80.43
Single Nuclear Recoil 1887 19.57
Table 5.2: Count of multiple and single nuclear recoils from the PMT neutron dataset.
An imbalanced training dataset, such as the one used here, where the classes are approx-
imately in an 80-20 distribution, can introduce significant biases in the model and make
predictions unreliable [117, 118]. There are two main methods for addressing class imbal-
ance: oversampling and undersampling [119]. Oversampling involves increasing the number
of instances in the minority class, while undersampling reduces the number of samples in the
majority class. Both methods were applied and compared in this study.
Oversampling was performed using the method of Synthetic Minority Oversampling Tech-
nique (SMOTE) from the imbalanced-learn Python library [120], which generates synthetic
50 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
samples for the minority class in order to balance the dataset. Undersampling was imple-
mented by randomly selecting an equal number of multiple recoil samples to match the
number of single recoil samples. The best results were achieved with the dataset balanced
through undersampling; consequently, all the results presented in this chapter were generated
using this dataset.
5.7 Model Training and Evaluation
5.7.1 Training
The dataset outlined in Section 5.6 was used to train and evaluate several binary classi-
fication algorithms, using an 80-20 train-validation split. This process consists of splitting
the dataset into 2 subsets by random sampling; one containing 80% of the samples, used for
training the different classification algorithms, and a second one with the remaining 20%,
used for validating and comparing the models. The splits are performed several times, in
order to produce an average of the validation metrics for all the splits. This is called cross-
validation [121], and it is done to ensure that the results obtained are not the product of a
specific train-validation split, but rather an actual feature of the data.
The multiple recoil flag was removed from the training dataset before the different models
were trained, and then these were evaluated by using them to make predictions on the
validation dataset, and comparing these predictions with the flags containing the ground
truth for this dataset. The models trained and evaluated with this method include: decision
tree, support vector classifier, random forest, boosted decision tree, and fully connected
neural network.
5.7.2 Evaluation Metrics
The primary evaluation metrics for a classification algorithm are the counts of correctly
and incorrectly classified samples [122]. For the case of binary classification, the classes are
referred to as positive and negative. The count of samples predicted correctly as positive
is called true positive (TP), while the count of samples incorrectly classified as positive is
referred to as false positive (FP). The same logic applies to the negative labeled samples, in
which the count of correctly classified negative samples is called true negative (TN), and the
samples incorrectly classified as negative are called false negative (FN). These metrics can
be visualized in a confusion matrix (see Figure 5.12).
A variety of additional model evaluation metrics are derived from the confusion matrix
[123]. The most relevant for this analysis are listed below.
• Accuracy:
Accuracy =
TP + TN
TP + TN + FP + FN
(5.21)
Accuracy is the fraction of the correctly labeled samples out of the totality of the
dataset. The best possible accuracy value is 1, the worst possible is 0.
5.7. MODEL TRAINING AND EVALUATION 51
Figure 5.12: Binary classification metrics true positive (TP), false positive (FP), true neg-
ative (TN) and false negative (FN) visualized in a confusion matrix. The true values are
arranged in rows, while the predicted labels are represented in the columns of the matrix.
• Precision:
Precision =
TP
TP + FP
(5.22)
The precision metric quantifies how many of the positive predictions made by the
model were correct. The best precision score attainable by a model is 1, while the
worst possible is 0.
• True positive rate (TPR), also known as recall or acceptance:
TPR =
TP
TP + FN
(5.23)
TPR represents the fraction of samples correctly labeled as positive out of all the
positive instances in the dataset. The best possible TPR is 1, the worst is 0.
• False positive rate (FPR):
FPR =
FP
FP + TN
(5.24)
FPR is the fraction of incorrectly classified negatives out of all the negatives in the
dataset. The best possible FPR is 0, the worst is 1.
• Specificity, also known as background rejection rate (BRR):
BRR =
TN
FP + TN
= 1− FPR (5.25)
52 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
BRR measures the performance of the model in minimizing the incorrect classification
of instances as positive. The extreme values of this metric are 1 (best possible) and 0
(worst possible).
• F1 score (F1):
F1 = 2× Precision× Recall
Precision + Recall
=
2TP
2TP + FP + FN
(5.26)
F1 is the harmonic mean between precision and recall. It measures how precise the
model is in classifying instances as positive, while still being able to correctly classify
as many positive instances as possible. The best F1 score is 1, the worst is 0.
• Receiver operating characteristic (ROC) curve, and area under the curve (AUC):
Classification models predict a probability of a sample belonging to the positive class,
usually the threshold for labeling a sample as positive is a probability greater than 1/2.
The ROC curve evaluates the model’s performance across all possible thresholds by
plotting the TPR against the FPR. A quickly increasing ROC curve that approaches
the top left corner of the plot indicates a strongly performing classification model that
maximizes TPR while minimizing FPR. The model’s performance is compared with a
baseline that represents a classifier that predicts either class with equal probability. The
area under the ROC curve (AUC) provides additional information on the effectiveness
of the classifier: an AUC of 1 indicates perfect classification, an AUC of 1/2 is that
of the random classifier, and values below that indicate a model that systematically
misclassifies. The ROC curve and the AUC are illustrated in figure 5.13.
5.7.3 Validation
The best performance with the validation dataset was achieved by the boosted decision
tree (BDT) model from the Python library scikit-learn [124]. Decision trees split data itera-
tively based on specific variables to create a tree-like structure of decisions, classifying data
into distinct groups. Starting from a root node, data is divided into branches using rules
that optimize separation between categories, ultimately ending in leaves that represent the
final predictions. BDTs enhance the basic decision tree by using an ensemble of trees to
improve accuracy [125]. Boosting combines multiple individual trees, called weak learners,
sequentially, one after the other, into a more accurate model (see Figure 5.14). By assigning
more weight to misclassified data in each iteration, boosting algorithms minimize classifica-
tion errors. The model was trained with the following hyperparameters: n estimators (the
number of trees) set to 100, and learning rate (which controls each tree’s contribution to
the final prediction) set to 0.12. BDTs have been used previously by the DEAP collaboration
[126], as well as by other highly renowned experiments such as the Large Hadron Collider
(LHC) [127–129], the Jiangmen Underground Neutrino Observatory (JUNO) [130] and the
Mini Booster Neutrino Experiment (MiniBooNE) at Fermilab [131].
5.7. MODEL TRAINING AND EVALUATION 53
Figure 5.13: The ROC curve [123] is constructed by calculating the TPR and FPR for all
classification thresholds. The green curve represents a good performance, the red one a
classification model that consistently misclassifies. The black diagonal line in the middle
serves as a baseline and it represents a model that randomly predicts classes with equal
probability. The AUC of a robust model is close to 1, while that of the random classifier
represented by the diagonal line is 1/2.
Figure 5.14: An individual decision tree (left), blue rectangles represent nodes that split
into branches and end in green circles representing leaves. A boosted decision tree (right),
a sequence of individual decision trees in which each tree is trained on the misclassified
instances of the previous tree, creating a more accurate model.
54 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
The best performing BDT developed in this work achieved the results shown in the con-
fusion matrix in Figure 5.15. The following evaluation value counts were obtained:
• TP = 265.
• FN = 97.
• FP = 77.
• TN = 316.
Figure 5.15: Confusion matrix achieved with the BDT in the validation stage of its evalua-
tion.
From the confusion matrix, it can be seen that the false negative and positive counts
are significantly lower than the true counts; this means that the BDT favors the correct
classification of multiple and single recoil events. The scores obtained for the metrics derived
from the confusion matrix are listed in Table 5.3. The ROC curve for this model is shown
in Figure 5.16, with an achieved AUC value of 0.85, significantly higher than the baseline
value of 1/2 attainable by random guessing.
5.7. MODEL TRAINING AND EVALUATION 55
Metric Score
Accuracy 0.77
Precision 0.78
True Positive Rate 0.73
False Positive Rate 0.20
Specificity 0.80
F1 0.75
Table 5.3: Metric scores derived from the confusion matrix for the BDT in the validation
phase.
Figure 5.16: ROC curve for the BDT in the validation phase. The diagonal line ascending
from left to right represents the performance of a random classifier that predicts each class
with equal probability, with an AUC of 1/2. The AUC value achieved by the BDT is 0.85.
5.7.4 Additional Tests
The model was subject to testing with two additional datasets: the first one consists of an
MC dataset of radiogenic neutrons generated from the AV of the detector, the second one
was gathered from real data taken during runs when a neutron source was deployed. The
results presented in this section are color coded by dataset: the figures plotted in purple
correspond to the AV neutrons MC dataset, and the image in orange to the neutron source
runs.
For the first test, the trained BDT did predictions on the AV simulated neutrons dataset.
This dataset also has information on trajectories and interactions, making it possible to
56 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
compare with the true values for multiple and single nuclear recoils. The results obtained by
the BDT for this dataset are shown in the confusion matrix in image 5.17. The evaluation
counts obtained in the testing stage are:
• TP = 950.
• FN = 383.
• FP = 106.
• TN = 291.
Comparing this confusion matrix with the one achieved in the validation phase reveals a
preference for false negatives rather than true negatives. It also shows a vast majority of
multiple recoils correctly classified.
Figure 5.17: Confusion matrix achieved with the BDT in the testing stage of its evaluation.
The metrics derived from the confusion matrix are shown in Table 5.4. These show a
minor decrease in accuracy, true positive rate, specificity, and F1 score, while maintaining
a favorable evaluation overall. There is a significant increase in precision, which can be
attributed to the large number of true positives compared to the false positives shown in the
confusion matrix.
The ROC curve for the AV dataset, shown in Figure 5.18, shows a performance that
is significantly better than the random guessing represented by the diagonal dashed line.
5.7. MODEL TRAINING AND EVALUATION 57
Metric Score
Accuracy 0.72
Precision 0.90
True Positive Rate 0.71
False Positive Rate 0.27
Specificity 0.73
F1 0.80
Table 5.4: Metric scores derived from the confusion matrix for the BDT in the testing phase.
The AUC has a value of 0.80, a minor decrease with respect to the result obtained in the
validation phase of 0.85. This can be traced back to a slower growth in TPR for low values
of FPR.
Figure 5.18: ROC curve for the BDT in the testing phase with the AV neutrons MC dataset.
The diagonal line ascending from left to right represents the performance of a random clas-
sifier that predicts each class with equal probability, with an AUC of 1/2. The AUC value
achieved by the BDT is 0.80.
The last test done on the BDT had the purpose of simulating a realistic application
scenario, in which predictions made on real data taken by the detector will be the subject
of evaluation. To this end, the dataset used for this test consists of six runs of data taken
when an Americium-Beryllium (AmBe) neutron source was deployed, resulting in a livetime
of 4 days, 6 hours, and 14 minutes. The AmBe source has a neutron emission rate of 4.8
kHz [87], which allows for the assumption that all events recorded in these runs originate
58 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
from neutrons emitted by the calibration source.
As previously mentioned, it is currently not possible to distinguish between multiple and
single nuclear recoils in real data. This makes truth labels unattainable, rendering the use
of a confusion matrix for evaluation impossible. To overcome this obstacle, an estimation
of the expected number of multiple recoils can be obtained by assuming that approximately
80% of neutrons that produce a recoil do so multiple times. By taking into account the
assumption that all events registered in this runs are neutrons emitted by the AmBe source,
a number of multiple recoils can be estimated as 80% of the total events.
In order to better emulate a realistic scenario, the events from the AmBe runs were selected
by reconstructing inside the PLR ROI (see Section 5.1); no additional cuts were applied to
the data. This would be a case in which being able to identify multiple recoils would be a
helpful way of mitigating a background source in the ROI.
The predictions for this dataset are shown in Figure 5.19. The points correspond to the
location in the Fprompt - qPE parameter space of the events classified as multiple recoils by
the BDT. An expected number of multiple recoils is shown, making the assumption that this
will correspond to approximately 80% of all events registered. The prediction of 104+14
−12 is
fairly lower than the expected 263 multiple recoils; however, being able to filter a significant
fraction of the events is still helpful in the mitigation of radiogenic neutrons as a background
source.
5.8 Findings and Conclusions
This study was conducted as an initial step toward developing a new mechanism for
mitigating radiogenic neutron backgrounds through multiple recoil discrimination. This is a
complex problem for which a reliable solution has not yet been established. As discussed in
Section 5.4, taking advantage of the high probability of neutrons causing multiple nuclear
recoils could considerably improve background rejection in DM searches, thereby increasing
the sensitivity of detectors like DEAP-3600 to potential WIMP signals.
While Boosted Decision Trees (BDTs) implemented at the production level in other appli-
cations have achieved higher evaluation results than those obtained in this study [126, 127],
this work provides a promising foundation towards the possibility of reaching similar levels
of reliability in multiple nuclear recoil identification. The classification results obtained were
significantly better than random guessing, and an evaluation in a realistic scenario of appli-
cation demonstrated the successful identification of a significant fraction of events expected
to be multiple recoils (see Figure 5.19).
Future efforts in this direction could benefit significantly from incorporating algorithms
that leverage spatial information from interaction positions recorded by the detector, rather
than relying solely on a variable-based approach. One promising avenue is the use of Graph
Neural Networks (GNNs), which are a specialized type of artificial neural network designed
to process graph-structured data, where nodes represent entities and edges define their re-
lationships [132]. GNNs have been widely used for particle tracking and identification in
particle physics experiments such as IceCube [133–135], and the LHC [136, 137]. Their
ability to model complex spatial dependencies suggests they could enhance multiple recoil
discrimination, potentially improving classification performance in future studies. Continu-
5.8. FINDINGS AND CONCLUSIONS 59
Figure 5.19: The orange points represent the central value of predicted multiple recoils for
the AmBe dataset in the PLR region of interest. The expected number of multiple recoils
is an approximation based on the assumption that the total number of events corresponds
solely of neutrons from the AmBe calibration source. The uncertainties were calculated by
determining a standard deviation of the probabilities predicted by the BDT, and then adding
and subtracting that deviation from the probabilities, and applying the threshold of 50% for
a positive prediction of a multiple recoil.
ing this research may yield valuable results for experiments conducting WIMP searches that
must address radiogenic neutrons as a significant background source.
60 CHAPTER 5. NEUTRON BACKGROUND IN DEAP-3600
6 Gamma Background for the Search
of 5.5 MeV Solar Axions
In addition to WIMPs, DEAP-3600 is sensitive to other new physics models. Among
these are axion-like particles (ALPs), pseudoscalar bosons that arise from the spontaneous
breaking of global U(1) symmetries. While for the QCD axion described in Section 3.2 the
product of its photon coupling and mass is essentially fixed through QCD dynamics, ALPs
constitute a broader class in which the coupling and mass can vary independently as free
parameters [138]. ALPs would interact through electron recoils within the LAr volume in the
detector. This chapter describes the potential mechanism for solar ALP production, outlines
the interactions that DEAP-3600 could detect, and presents a contribution to refining the
gamma-ray background model relevant for the ALP search.
6.1 Production Mechanism
In addition to the QCD axions described in Section 3.2, there are other mechanisms
through which ALPs would be produced. One such mechanism is the proton-proton fusion
chain that occurs in the Sun [139]:
p+ p → d+ e+ + νe
d+ p →3 He + γ (5.5MeV), (6.1)
where the 3He initially remains in an excited state and can emit a 5.5 MeV photon. If solar
ALPs exist, the same excited 3He nucleus can instead emit an ALP of the same energy [140].
The reaction is written as follows, where the ALP is denoted by a:
d+ p →3 He + a (5.5MeV). (6.2)
Unlike the axions described in Section 3.2, ALPs in the MeV mass range would be too
short-lived to be viable DM candidates, but can still have a connection to a rich dark sector
[141]. Additionally, MeV ALPs might contribute to the anomalous magnetic moment of the
electron, and have not been ruled out by the (g − 2)e results [142].
61
62CHAPTER 6. GAMMABACKGROUND FOR THE SEARCHOF 5.5 MEV SOLAR AXIONS
6.2 Interactions with the Detector
The DEAP-3600 detector is sensitive to ALPs through the process of electron recoil with
the electron cloud of 40Ar atoms. Electron recoils can be generated by ALPs through four
interactions: Compton conversion, decay to 2 γs, inverse Primakoff effect, and axioelectric
effect. A description of each mechanism will be provided next.
6.2.1 Compton Conversion
Compton Conversion, see Figure 6.1 upper left corner, occurs when an axion and a free
electron interact, producing an electron and a photon:
a+ e− → γ + e−. (6.3)
The signal produced by this interaction would be an electron and a photon with a combined
energy of 5.5 MeV.
6.2.2 Decay to 2γ
The decay of an axion into two photons, see Figure 6.1 upper right, is described by the
equation:
a → γγ. (6.4)
The signal observed in this decay would be two photons, each with momentum equal to
half of the axion’s mass, in the rest frame of the axion.
6.2.3 Inverse Primakoff Effect
In the Inverse Primakoff Effect, see Figure 6.1 lower left, an axion interacts with an electron
bound to an atom, producing a photon. Unlike in Compton Conversion, the electron remains
bound to the atom:
a+ Z → γ + Z. (6.5)
In this interaction, a photon with an energy of 5.5 MeV would be observed.
6.2.4 Axioelectric Effect
The axioelectric effect, see Figure 6.1 lower right, is analogous to the photoelectric effect.
In this interaction, the axion deposits its energy on a bound electron causing it to be ejected:
a+ e− + Z → e− + Z. (6.6)
In the axioelectric effect, an electron with a kinetic energy of 5.5 MeV would be the
observed signal.
6.3. SIGNAL AND ITS DEPENDENCE ON AXION MASS 63
Figure 6.1: Feynman diagrams for the four interactions to which DEAP-3600 could be
sensitive in the search for 5.5 MeV solar axions. Time is on the horizontal axis, a represents
an axion, e an electron or positron, and Z an atom. The wavy lines represent a photon, and
the solid lines without a label can represent a quark, electron, or positron. The label eb is
used to denote an electron bound to an atom [143].
6.3 Signal and its dependence on axion mass
The signal that would be observed in the detector, in case of axion detection, was modeled
using Monte Carlo simulations of each of the 4 interactions to which DEAP-3600 is sensitive.
For these simulations, the GEANT4.9.6 software was used within the RAT framework [143].
For each of the four interactions, the energy deposited in the liquid argon was plotted, as
shown in Figure 6.2. The Compton Conversion and 2γ Decay interactions are dependent
on the axion mass. The spectrum produced by both interactions does not vary significantly
for different axion masses, except when the axion mass approaches 5.5 MeV and enters the
non-relativistic regime, as shown in Figure 6.3.
6.4 Region of Interest for Axion Search
The region of interest for the axion search in DEAP-3600 is defined by the energy range
between 5.26 MeV and 5.71 MeV. These correspond to 36000 qPE and 39000 qPE, respec-
64CHAPTER 6. GAMMABACKGROUND FOR THE SEARCHOF 5.5 MEV SOLAR AXIONS
Energy (MeV)
0 1 2 3 4 5 6E
ve
nt
s 
pe
r 
0.
03
 M
eV
 B
in
 / 
T
ot
al
 E
ve
nt
s
5−10
4−10
3−10
2−10
1−10
1 Compton Conversion γAxion Decay to 2
Inverse Primakov Axio-Electric
Figure 6.2: Total energy deposited in the detector by each of the four interactions that
DEAP-3600 is sensitive to. The axion mass used for Compton Conversion and 2γ Decay is
49 keV [143].
Energy (MeV)
0 1 2 3 4 5 6
P
ro
ba
bi
lit
y 
pe
r 
0.
03
 M
eV
5−10
4−10
3−10
2−10
1−10
1  = 10 keVAm  = 23 keVAm
 = 36 keVAm  = 49 keVAm
 = 62 keVAm  = 75 keVAm
 = 100 keVAm  = 1000 keVAm
 = 3000 keVAm  = 5000 keVAm
 = 5480 keVAm
Energy (MeV)
0 1 2 3 4 5 6
P
ro
ba
bi
lit
y 
pe
r 
0.
03
 M
eV
3−10
2−10
1−10
 = 10 keVAm  = 23 keVAm
 = 36 keVAm  = 49 keVAm
 = 62 keVAm  = 75 keVAm
 = 100 keVAm  = 1000 keVAm
 = 3000 keVAm  = 5000 keVAm
 = 5480 keVAm
Figure 6.3: Total energy deposited in the detector for Compton Conversion (left) and 2γ
Decay (right). Both produce two primary particles, an electron and a photon for Compton
Conversion, and two photons for Decay. The spectrum produced by axions of different
masses is shown. For both interactions, the spectrum remains unchanged until the axion
mass approaches 5.5 MeV, at which point it becomes non-relativistic [143].
tively, where the qPE variable corresponds to the charge of the recorded pulse divided by
the average charge of a photoelectron for each photo-multiplier tube [144].
6.5 Background Sources
Other physical processes that produce electronic recoils in liquid argon, depositing 5.5
MeV of energy, are background sources for the axion search in DEAP-3600. The two main
processes that constitute background sources are: γ-rays emitted from neutron capture and
6.5. BACKGROUND SOURCES 65
γ-rays produced by the radioactive decay of 208Tl.
6.5.1 γ-rays from Neutron Capture
The main background source for this search is γ-rays emitted from neutron capture. This
process occurs when a neutron emitted by a component of the detector, through either
(α, n) reactions or spontaneous fission, is later captured by a nearby nucleus, which emits a
gamma-ray that deposits its energy in the liquid argon, causing an electron recoil (see Figure
6.4).
To mitigate this background source, Monte Carlo simulations of γ-rays emitted from neu-
tron capture are carried out, and these are then subtracted from the measured events (see
Section 6.6).
Figure 6.4: Example of the mechanism for γ-ray production via neutron capture. In this case,
a radiogenic neutron emitted by an (α, n) reaction from the glass of the PMTs is captured
by a nucleus in the acrylic, which subsequently emits a γ-ray that deposits its energy in the
liquid argon. This is the primary background source for the search of 5.5 MeV solar axions
[143].
6.5.2 γ-rays from 208Tl Decay
208Tl is present in some components of the detector, it can produce γ-rays through various
decays [145]. To determine whether this is a significant background source, Monte Carlo
simulations of this process were carried out for decays occurring in the acrylic container and
the liquid argon, the two components from which the largest number of electronic recoils
could be generated. It was found that not enough γ-rays with energies near 5.5 MeV are
produced by this mechanism to be considered a significant background source in the axion
search (see Figure 6.5).
66CHAPTER 6. GAMMABACKGROUND FOR THE SEARCHOF 5.5 MEV SOLAR AXIONS
Energy Deposited in LAr (MeV)
0 1 2 3 4 5
ev
en
ts
 p
er
 5
5 
ke
V
 b
in
 / 
M
C
 d
at
as
et
7−10
6−10
5−10
4−10
3−10
2−10
1−10
Tl in the AV208
Tl in the LAr208
Figure 6.5: Spectrum generated by Monte Carlo for γ-rays emitted by the decay of 208Tl,
for decays occurring in the acrylic container (black) and liquid argon (green) [143].
6.6 Simulations for the Neutron Capture γ-ray Back-
ground
The main contribution presented in this work to the axion search project is focused on the
background model caused by gamma rays from neutron capture, detailed in Section 6.5.1.
Initially, the background model for the axion search showed a significant deficit compared to
the background observed in the data for energy values close to the region of interest specified
in Section 6.4 (see upper Figure 6.6).
An extensive search was conducted to determine which background sources had not yet
been accounted for and might be causing this excess in relation to the model. It was de-
termined that the steel, from which the casing surrounding the acrylic container is made,
contains significant amounts of 59Co and molybdenum isotopes 92, 94, 95, 96, 97, 98, and
100 in their natural abundance. Since cobalt and molybdenum are present in the steel,
simulations were conducted of the gamma rays emitted with the neutron capture spectrum
for these isotopes obtained from the International Atomic Energy Agency (IAEA) database
[146]. These simulations were carried out using the RAT software [99], specifying that the
gamma rays were emitted from the steel present in the spherical shell and the neck of the
detector (see Figure 6.7). It was determined that these isotopes could capture neutrons that
emit gamma rays with energies in the region of interest for the search, as shown in Figure
6.8.
To complete the background model, similar simulations were carried out for 59Co and all
molybdenum isotopes. The distribution of simulated events for these was based on their
6.6. SIMULATIONS FOR THE NEUTRON CAPTURE γ-RAY BACKGROUND 67
Figure 6.6: Background model before neutron capture gamma rays in 59Co and Mo isotopes
were added (top), with a p-value of 0.5 ± 0.3%. After 59Co and Mo isotopes were added
(bottom), the model shows a significant improvement around the region of interest, which
covers values between 5.26 MeV (36,000 qPE) and 5.71 MeV (39,000 qPE). The p-value
increases to 25± 1% [147].
neutron capture cross-section and their natural relative abundance (see Table 6.1). The
total number of events generated, after 1,000 simulation iterations, was 97,165,000.
68CHAPTER 6. GAMMABACKGROUND FOR THE SEARCHOF 5.5 MEV SOLAR AXIONS
Figure 6.7: Projection of the spatial distribution for the gamma rays simulated from the
steel casing and neck of the detector. The spatial distribution from which the gammas were
emitted for neutron capture in 95Mo is used as an example.
Figure 6.8: Energy deposited in liquid argon by gammas emitted due to neutron capture in
59Co (right) and 95Mo (left), as an example of the isotopes included for Mo. In both cases,
these isotopes deposit energy in the region of interest for the axion search, around 5.5 MeV.
Subsequently, the simulated data was included in the background model for the axion
search. By including gammas from neutron capture in Mo isotopes and 59Co, the background
model improved significantly. The unexplained background near the region of interest was
reduced, and the model’s p-value increased significantly from 0.5 ± 0.3% to 25 ± 1% (see
Figure 6.6). This allowed the analysis process for the axion search to continue.
Additionally, a study of event acceptance for the radial fiducial cut used in the axion
search was carried out. This cut was set at 750 mm measured from the center of the acrylic
container. To conduct the study, the acceptance was calculated at different radial cuts in
terms of energy deposited in the argon, both for simulated data and data obtained from
the AmBe calibration source. It was found that the value used for the radial cut provides
satisfactory event acceptance while reducing background sources (see Figure 6.9).
6.6. SIMULATIONS FOR THE NEUTRON CAPTURE γ-RAY BACKGROUND 69
Molybdenum Isotope (A) Events per Iteration
92 920
94 1311
95 71443
96 7968
97 9389
98 4880
100 1254
Total 97165
Table 6.1: Number of events generated per iteration for each molybdenum isotope, consider-
ing relative abundance and neutron capture cross-section. A total of 1,000 iterations of data
generation were performed with this event distribution, resulting in a total of 97,165,000
events.
2 4 6 8 10
mc_edep (MeV)
0.0
0.2
0.4
0.6
0.8
1.0
Ac
ce
pt
an
ce
Acceptance for mc_edep with cut on mbR at 750 mm
Fits for mc_edep in 1.26 - 9.95 MeV
y = 0.6149, p = 0.187
y = 0.0113x +0.5517, p = 0.2216
PMT neutrons MC nominal
Figure 6.9: Acceptance for the radial fiducial cut at 750 mm from the center of the acrylic
container, calculated in terms of energy deposited in liquid argon for neutrons simulated
from the photo-multiplier tubes.
A blind analysis was performed by a collaborator with the background model obtained
after the inclusion of 59Co and Mo isotopes. No excess of events relative to the null hypothesis
was found in the region of interest (see Figure 6.10). This allowed exclusion curves to be
set for the axion-electron coupling constant gAe, the axion-photon coupling constant gAγ,
and the product of the axion-electron coupling constant and the isovector component of the
axion-nucleon coupling constant |gAe × g3AN |.
The preliminary exclusion curves obtained by the collaboration are more restrictive than
those from the BGO experiment [148] and are an order of magnitude above those obtained
by Borexino [149]. Figure 6.11 shows the exclusion curve obtained for the axion-electron
coupling constant gae, with the Axioelectric Effect and Compton Conversion processes.
70CHAPTER 6. GAMMABACKGROUND FOR THE SEARCHOF 5.5 MEV SOLAR AXIONS
Energy (MeV)
5 6 7 8 9 10
C
ou
nt
s 
/ 6
0.
9 
ke
V
 / 
D
at
as
et
1
10
210 Data Null Hypothesis Total Model
Ar (n,*) Fe (n,*) Cr (n,*)
Ni (n,*) Mn (n,*) Cl (n,*)
Mo (n,*) )γC (n, βTl 208LAr 
)γCo (n,59 5.5 MeV Solar Axion
DEAP
0063Preliminary
Energy (MeV)
5 6 7 8 9 10
(d
at
a 
- 
M
C
) 
/ M
C
1.0−
0.8−
0.6−
0.4−
0.2−
0.0
0.2
0.4
0.6
0.8
1.0
68.2% 95.4% 99.7%
Figure 6.10: Preliminary background model for the axion search, following the blind search
process. It shows no significant excess of events in the region of interest from 5.26 to 5.71
MeV [147]. An earlier version of these results is available in [143].
 [MeV]Am
5−10 4−10 3−10 2−10 1−10 1 10
A
e
g
13−10
12−10
11−10
10−10
9−10
8−10
7−10
6−10
5−10
4−10
DEAP
0063
BGO AEDEAP AE
DEAP CC
Borexino CC
Figure 6.11: Preliminary exclusion curves obtained for the axion-electron coupling constant
gAe in the hadronic axion model, for the Axioelectric Effect (AE) and Compton Conversion
(CC) processes [147]. An earlier version of these results is available in [143].
6.6. SIMULATIONS FOR THE NEUTRON CAPTURE γ-RAY BACKGROUND 71
A draft of the Axion Search article with the preliminary results shown here was written
and submitted for internal review by the committee overseeing this analysis. The review
process continues, with contributions from various collaborators.
72CHAPTER 6. GAMMABACKGROUND FOR THE SEARCHOF 5.5 MEV SOLAR AXIONS
7 Exploration of Neutrinos in the Stan-
dard Model and Beyond
7.1 General Aspects about Neutrinos
In the early 1900s, it was believed that the process of β decay violated the conservation of
energy and momentum. This conclusion was drawn from the observation that the spectrum of
the resulting electron, inferred from Equation 7.1, was continuous. If energy were accounted
for by only the resulting nucleus and electron, the electron spectrum would have been mono-
energetic [150].
(A,Z) → (A,Z± 1) + e∓ +missing energy and momentum. (7.1)
To solve this problem, in 1930 Wolfgang Pauli proposed the existence of a spin 1/2 particle
with a neutral electrical charge and a small mass, that would carry the unaccounted for
energy and momentum [151]. In 1933 Fermi developed an explanation for β decay using this
particle, which he named neutrino [152]. The neutrino was conclusively discovered in 1956
using a scintillation detector at a reactor in the Savannah River nuclear plant [153].
Neutrino interactions are chiral in nature; only left-handed neutrinos and right-handed
antineutrinos participate in weak interactions [138]. This chiral property is intrinsic to the
Standard Model (SM) and applies to neutrinos in their leptonic flavor states: electron (νe),
muon (νµ), and tau (ντ ). These flavors arise from the different processes that produce the
neutrinos and antineutrinos, for example:
n → p+ e− + ν̄e, (7.2)
π+ → µ+ + νµ, (7.3)
and
τ− → µ− + ν̄µ + ντ . (7.4)
Neutrinos can be produced in several sources such as the Sun, nuclear reactors, and particle
accelerators. The different neutrino sources, as well as their energy and flux, are visualized
in Figure 7.1.
However, neutrinos do not propagate as pure flavor states. Instead, each flavor eigenstate
is a quantum superposition of three mass eigenstates, labeled simply as 1, 2, and 3 [155]. This
73
74CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
Figure 7.1: Flux vs neutrino energy for different sources for neutrinos [154].
became evident when attempts were made to measure solar neutrinos. Electron neutrinos
are produced in various steps of the pp chain that occurs in the sun, which starts with the
fusion of two protons and results in the production of two alpha particles [156]. The results of
the first experiment to measure solar neutrinos were reported in 1968 [157]. The experiment
used chlorine to detect νe via the interaction:
νe +
37 Cl →37Ar + e−, (7.5)
but was only able to account for approximately 1/3 of the expected neutrinos. This discrep-
ancy became known as the solar neutrino problem.
The resolution of this problem came about when it was considered that neutrinos oscillate
between three different flavor states, two of which could not be detected by inverse beta decay
in chlorine. The confirmation of solar neutrino oscillations was achieved at the Sudbury
Neutrino Observatory (SNO) in 2001 [158], when a detection mechanism using heavy water
was able to detect all three flavors. This mechanism consisted of the following processes:
νe + d → p+ p+ e−, (7.6)
ν + d → n+ p+ ν, (7.7)
and
ν + e → ν + e, (7.8)
where ν represents a neutrino of any flavor, and d the deuterium present in heavy water.
When combining their results with those reported previously by Super-Kamiokande [159],
7.1. GENERAL ASPECTS ABOUT NEUTRINOS 75
SNO was able to account for 100% of the expected solar neutrino flux, concluding that 35%
consists of νe, while the remaining 65% is made up of νµ or ντ .
The probability of neutrino oscillation can be obtained by studying a description of this
phenomenon in terms of the superposition of quantum states [156]. Assuming, for simplicity,
only two different flavors (νe and νµ), and propagation in a vacuum, the mass eigenstates
can be written as:
|ν1⟩ = cos θ |νµ⟩ − sin θ |νe⟩ , (7.9)
and
|ν2⟩ = sin θ |νµ⟩+ cos θ |νe⟩ , (7.10)
where the choice of cosine and sine for the coefficients facilitates the normalization of the
quantum states, and θ plays the role of a mixing angle. The time evolution of these states
can be described using a plane wave solution (ℏ = c = 1):
|ν1(t)⟩ = e−iE1t |ν1(t = 0)⟩ , (7.11)
|ν2(t)⟩ = e−iE2t |ν2(t = 0)⟩ . (7.12)
Assuming that the initial state is an electron neutrino, that is |ν1(t = 0)⟩ = − sin θ |νe⟩ and
|ν2(t = 0)⟩ = cos θ |νe⟩, the time dependencies become:
|ν1(t)⟩ = − sin θe−iE1t |νe⟩ , (7.13)
|ν2(t)⟩ = cos θe−iE2t |νe⟩ . (7.14)
Using Equations 7.9, 7.10, 7.13 and 7.14, the time dependence for the muon neutrino state
is written as follows:
|νµ(t)⟩ = − sin θ cos θe−iE1t |νe⟩+ cos θ sin θe−iE2t |νe⟩ . (7.15)
The transition amplitude from electron to muon neutrino is given by:
Aµe = ⟨νe|νµ(t)⟩ = sin θ cos θ
(
−e−iE1t + e−iE2t
)
, (7.16)
and the transition probability is:
Pνe→νµ = |Aµe|2 = sin2 θ cos2 θ
(
2− ei(E2−E1)t − ei(E1−E2)t
)
=
[
sin(2θ) sin
(
(E2 − E1)t
2
)]2
1. (7.17)
1Identities used: cosx = − eix+e−ix
2 , sin2 θ cos2 θ = sin2(2θ)
4 and 1−cosx = 2 sin2 x
2 , where x = (E1−E2)t.
76CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
By taking the ultrarelativistic limit E ≈ p
(
1 + m2
2p2
)
, the approximation E1 − E2 ≈ ∆m2
2E
is
made, where ∆m2 = m2
2 −m2
1. Substituting in 7.17 and recovering the factors of c and ℏ,
the transition probability is written as follows:
Pνe→νµ =
[
sin(2θ) sin
(
∆m2c3
4ℏE
L
)]2
, (7.18)
where E is the neutrino energy, and L = ct is the distance referred to as the baseline. The
transition probability is maximized for Lmax = 2πℏE
∆m2c3
, and the distance at which the neutrino
oscillates back to its original flavor state, known as the oscillation length, is LO = 4πℏE
∆m2c3
.
Equation 7.18 reveals that for oscillations to occur, the masses m1 and m2 must be differ-
ent; and at most one of them can be 0, but not both. The phenomenon of neutrino oscillation
is unequivocal evidence that neutrinos have a mass, but only their squared difference can
be known by studying oscillations. Two different compatible orderings can be inferred for
the differences of the squared masses from oscillation data [138]: normal hierarchy (NH)
and inverted hierarchy (IH), visualized in Figure 7.2. In the NH, the masses follow the
ordering m1 < m2 << m3, while in the IH the ordering is reversed to m3 << m1 < m2.
The neutrino mass ordering remains an open question, and experiments such as the Jiang-
men Underground Neutrino Observatory (JUNO) [160] and the Deep Underground Neutrino
Experiment (DUNE) [161] are expected to provide new insights in the near future.
Figure 7.2: Possible hierarchies for the neutrino masses [162]. Note: ∆m2
atm is equivalent to
∆m2
32 and ∆m2
sol to ∆m2
21.
When generalizing to the three flavor and mass fields, the relationship between them is
described by the Pontecorvo–Maki –Nakagawa–Sakata (PMNS) matrix [163, 164]:
7.1. GENERAL ASPECTS ABOUT NEUTRINOS 77


νe
νµ
ντ

 =


c12c13 s12c13 s13e
−iδ
−s12c23 − c12s23s13e
iδ c12c23 − s12s23s13e
iδ s23c13
s12s23 − c12c23s13e
iδ −c12s23 − s12c23s13e
iδ c23c13




eiα1/2ν1
eiα2/2ν2
ν3

 , (7.19)
where cij is defined as cosθij and sij as sinθij [162]. In the PMNS matrix, there are three
mixing angles: θ12, θ13, and θ23, one Dirac phase δ, and, if there is a Majorana component
to the neutrino masses, two additional phases α1 and α2 [46]. These phases relate to a
currently open question about whether neutrinos are Dirac particles (with distinct neutrino
and antineutrino states) or Majorana particles (where neutrinos are their own antiparticles).
If neutrinos are Majorana in nature, this would lead to lepton number violating processes
such as neutrinoless double-beta decay (0νββ) [165], illustrated in Figure 7.3. As of the
writing of this work, neutrinoless double-beta decay has not been detected. Among the
experiments searching for neutrinoless double-beta decay are: Large Enriched Germanium
Experiment for Neutrinoless ββ Decay (LEGEND) [166], The Kamioka Liquid-scintillator
Anti-Neutrino Detector (KamLAND-Zen) [167], Sudbury Neutrino Observatory + (SNO+)
[168], Cryogenic Underground Observatory for Rare Events (CUORE) [169], Enriched Xenon
Observatory (EXO) [170] and Germanium Detector Array (GERDA) [171].
Figure 7.3: Left: Feynman diagram for double beta decay with two electron antineutrinos
produced (2νββ), the lepton number is conserved. Right: Feynman diagram for neutrinoless
double beta decay (0νββ). Two neutrons decay into protons and electrons, without neutrinos
in the final state. This process violates the conservation of lepton number, and would require
neutrinos to be their own antiparticle, referred to as Majorana particles.
The origin of neutrino masses is not explained within the SM, meaning that extensions
are required to account for this property. One prominent extension is the seesaw mechanism
[46], which introduces heavy, sterile neutrinos with right chirality that possibly only interact
via the gravitational force. These right-handed neutrinos couple to the left-handed neutrinos
via Yukawa interactions, leading to a mass matrix that, upon diagonalization, results in one
very light mass eigenstate (corresponding to the observed light neutrino) and one very heavy
78CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
mass eigenstate (the sterile neutrino). This mechanism naturally explains why neutrino
masses are much smaller than those of other fermions and also introduces sterile neutrinos
as a viable DM candidate (see Section 3.3).
7.2 Coherent Elastic Neutrino-Nucleus Scattering
The coherent elastic neutrino-nucleus scattering (CEνNS) is a neutral current interaction
of the form:
ν + A → ν + A, (7.20)
that is mediated by a Z0 boson (see Figure 7.4). It was first proposed in 1974 by D. Freedman
[172], and was first measured in 2017 by the COHERENT collaboration [173].
Figure 7.4: Feynman diagram for CEνNS. The coherent elastic scattering interaction between
a neutrino (ν) and an atomic nucleus A is mediated by a Z0 boson.
The property of coherence in CEνNS refers to the fact that the nucleus interacts as a
whole rather than as individual nucleons [174]. This occurs when the wavelength λ of the
momentum transferred during the scattering is comparable to, or larger than, the nuclear
radius R: λ ≳ R, which translates to a condition on q, the transferred momentum: q ≲ 1
R
.
As a result, all nucleons contribute constructively to the scattering process, leading to an
enhanced cross-section compared to other neutrino processes (see Figure 7.5).
The SM cross section for CEνNS is given by [175]:
dσ
dT SM
≈ G2
F
2π
MNQ
2
w
(
2− MNT
E2
)
2, (7.21)
where MN is the nuclear mass, GF the Fermi constant, E the incident neutrino energy, and
T is the recoil energy. The weak charge is:
Qw = ZgVp FZ(q
2) +NgVn FN(q
2), (7.22)
2Equation 7.21 is an approximation obtained by taking the limit T << E in the cross section given by
[176]: dσ
dT SM
=
G2
F
2π MNQ2
w
(
2− 2T
E
+
(
T
E
)2 − MNT
E2
)
.
7.3. CEνNS MEASUREMENT BY THE CONUS+ EXPERIMENT 79
Figure 7.5: Left: representation of CEνNS and subsequent detection mechanisms. Right:
comparison of the total cross-section of CEνNS and other neutrino couplings: neutrino-
electron scattering, charged-current interaction (CC), inverse beta decay (IBD) and neutrino-
induced neutron (NIN) [173].
with Z and N representing the numbers of protons and neutrons respectively, FZ and FN are
the proton and neutron form factors as function of the transferred momentum q =
√
2mT ,
where m is the nuclear mass, and
gVp =
1
2
− 2 sin2 θW , and gVn = −1/2, (7.23)
are the proton and neutron couplings respectively; where θW is the weak mixing angle, also
known as the Weinberg angle.
CEνNS measurements can be used to probe into the weak mixing angle, the magnetic
moment of the neutrino µν , and parameters of non-standard interactions (NSI) in extensions
of the SM, as will be seen in Section 7.4. Figure 7.6 illustrates potential CEνNS measurement
outcomes for different values of NSI parameters and µν .
7.3 CEνNS Measurement by the CONUS+
Experiment
7.3.1 Description of the CONUS+ Detector
The CONUS+ experiment aims at the detection of CEνNS between electron antineutrinos
and germanium nuclei in high-purity germanium (HPGe) crystals [179]. It is located in a
nuclear power plant in Leibstadt, Switzerland; the HPGe crystals are placed at a distance
of 20.7 m from the 3.6 GW reactor core (see Figure 7.7). The reactor building provides an
average of 7.4 meter water equivalent (m.w.e.) overburden.
The production of electron antineutrinos at a nuclear reactor occurs through chains of β
decays of the form n → p + e− + ν̄e, originating from the fission of 235U (see Figure 7.8),
238U, 239Pu and 241Pu. Nuclear reactors offer considerable advantages as a neutrino source
for experiments like CONUS+ compared to other sources [180]:
80CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
• The flux is considerably higher than that attainable at an accelerator.
• The cost is significantly lower than operating an accelerator, as commercial reactors
are already in operation for energy production.
• The flux consists exclusively of electron antineutrinos, which considerably facilitates
the determination of the flux uncertainty.
• Reactors can be temporarily shut down, providing a valuable opportunity to study
experimental backgrounds.
CONUS+ reuses the four HPGe diodes from the CONUS experiment [181], which were
refurbished and optimized for achieving a minimum ionization energy threshold of 160 eVee
(see Figure 7.9). When energy is deposited in a Ge nucleus by a neutrino in a CEνNS
interaction, the nucleus recoils and moves through the crystal lattice, losing energy primarily
through ionization and heat production, also known as quenching effects. The ionization
events generate electron-hole pairs, which drift in opposite directions under the influence of
an electric field applied across the diode, producing a measurable electrical signal [182]. The
fraction of the nuclear recoil energy (T ) that generates ionization after taking into account
the quenching effects, known as the ionization energy (K), is modeled by:
K =
kg(ϵ)
1 + kg(ϵ)
· T, (7.24)
where ϵ = 11.5Z−7/3T and g(ϵ) = 3ϵ0.15 + 0.7ϵ0.6 + ϵ, with Z = 32 for Germanium, and
k = 0.162± 0.004 is determined by experimental measurements [183]. The remaining recoil
energy dissipates as heat and is therefore not detected.
Figure 7.6: Left: nuclear recoil event rate of CEνNS in a germanium target for the SM (solid
black), and different values of µν normalized by the Bohr magneton µB: blue, green and red
for µν
µB
= 2.2× 10−12, 2.9× 10−11 and 3.0× 10−10, respectively. The dashed line represents a
typical background level [177]. Right: a deficit of CEνNS events with respect to the SM is
shown in pink, according to the shown non-standard interaction parameters [178].
7.3. CEνNS MEASUREMENT BY THE CONUS+ EXPERIMENT 81
Figure 7.7: Setup of the CONUS+ experiment inside the reactor building at the Leibstadt
nuclear power plant [179].
Figure 7.8: Production of electron antineutrinos trough chains of β decays from the fission
of 235U in nuclear reactors. In average, 6 ν̄e are produced per fission in a nuclear reactor.
The letter ν in this Figure represents ν̄e [180].
As can be seen in Equations 7.22 and 7.23, the CEνNS cross section scales as N2, where
N is the number of neutrons in the nucleus. This makes large nuclei attractive targets
for these experiments; however, the uncertainty in quenching parameters tends to increase
with heavier nuclei. As a result, the medium-sized Germanium nucleus serves as a suitable
82CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
balance, providing a detectable CEνNS signal while maintaining manageable uncertainties
in quenching factors [184].
The main background sources for this experiment include neutrons and electromagnetic
cascades originating from cosmic muons, as well as γ-rays produced in the decay of neutron-
capture-induced isotopes. To mitigate these background sources, an extensive characteriza-
tion campaign was conducted, incorporating Monte Carlo simulations and in situ measure-
ments during both reactor on and off periods. The background characterization efforts at the
CONUS+ experimental location included a detailed study of neutron fluence using Bonner
Sphere spectrometry, γ-ray spectroscopy with HPGe detectors, and muon flux measurements
with liquid scintillators [185]. These efforts led to the development of a background model
that enables the detection of CEνNS at sub-keV energy thresholds.
Figure 7.9: The four HPGe diodes used in the CONUS+ experiment, their height and
diameter is 62 mm [179, 182].
7.3.2 Results of the CEνNS Measurement by CONUS+
The CONUS+ collaboration reported the first evidence of CEνNS from reactor antineu-
trinos measuring 395 ± 106 events, with a statistical significance of 3.7σ [181]. This result
is consistent with the predicted number of 347 ± 59 events from calculations, as shown in
Figure 7.10.
The data was gathered between November 2023 and July 2024, including reactor on and
off periods. This resulted in a combined exposure for the reactor on period of 327 kg·days,
which was obtained using 3 out of the 4 HPGe detectors (Conus-4 was not included in the
analysis due to significant instabilities in the event rate). The flux was determined to be
7.3. CEνNS MEASUREMENT BY THE CONUS+ EXPERIMENT 83
Figure 7.10: The top image shows the predicted CEνNS signal as a black line with the
uncertainty in blue, the black squares are the data points after background subtraction,
and the red dotted lines indicate the energy threshold of each of the detectors used. The
bottom left figure shows the agreement between data and background model for an extended
ionization energy range. In the bottom right is a histogram of the data points with a gaussian
fit in red [181].
1.5× 1013 ν̄es
−1cm−2. The respective energy threshold, mass, livetime, and the detected and
predicted signals for each of the detectors are shown in Table 7.1.
An ionization energy window of 160 - 800 eVee was defined as the energy region of interest.
In this region, a good agreement between the background model and data was achieved. This
model includes contributions from cosmogenic neutrons and muons, as well as subdominant
inputs from radiogenic activity from isotopes present in the detector materials. The back-
ground model was validated using data from the reactor off period; which, together with
a rigorous characterization of the detectors’ trigger efficiency (see Figure 7.11), enabled a
satisfactory extraction of the neutrino signal using a PLR method.
84CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
Detector Energy Threshold (keVee) Mass (kg) Livetime (d)
Conus-2 180 0.95 ± 0.01 117
Conus-3 160 0.94 ± 0.01 110
Conus-5 170 0.94 ± 0.01 119
Total - 2.83 ± 0.02 -
Table 7.1: Data for the detectors used in the CONUS+ CEνNS measurement [181]. The
trigger efficiency for each detector is shown in Fig 7.11.
7.4 Study of Scenarios in the SM and Beyond
The CEνNS results published by CONUS+ [181] provide a framework for studying pa-
rameters of the SM and its extensions. In this work, a χ2 optimization approach is employed
to evaluate and constrain the weak mixing angle θW , the neutrino magnetic moment µν , and
the non-standard interaction (NSI) parameters ϵuVee and ϵdVee .
The χ2 function employed is defined as:
χ2 =
(
Nmeas − (1 + α)Npred(X)
σstat
)2
+
(
α
σα
)2
, (7.25)
where Nmeas is the number of events measured by CONUS+, and the statistical uncertainty
is given by σstat =
√
Nmeas. Npred(X) is the number of events calculated in this study, being
evaluated as a function of the parameter X (the weak mixing angle, the neutrino magnetic
moment, or the NSI parameters), which is to be fitted in the optimization. Lastly, α is
a nuisance parameter over which the χ2 function is marginalized. The uncertainty in α
accounts for the dominant sources of systematic uncertainties reported by CONUS+:
• Energy threshold: 14.1%,
• Quenching parameter: 7.3%,
• Reactor neutrino flux: 4.6%,
• CEνNS cross section: 3.2%,
• Active germanium mass: 1.1%,
• Trigger efficiency: 0.7%,
• Likelihood fit, fit method, background model, and non-linearity: 21.8%.
Consequently, the uncertainty in the nuisance parameter α is:
σα =
√
0.1412 + 0.0732 + 0.0462 + 0.0322 + 0.0112 + 0.0072 + 0.2182 = 0.276. (7.26)
In the following sections, the details and results of this study, which has been published
in the journal Physical Review D [186], will be presented.
7.4. STUDY OF SCENARIOS IN THE SM AND BEYOND 85
7.4.1 Calculation of the Number of events
The predicted number of events, Npred, was calculated using the following equation:
Npred = tNt
∫ Tmax
Tmin
ϵ(T )dT
∫ Emax
Emin(T )
dσ
dT
(T,E)Φ(E)dE, (7.27)
where:
• E is the energy of the incident neutrino,
• T is the recoil energy of the nucleus 3,
• t is the data taking livetime,
• Nt is the target number given by Nt = mtNA
A
; where mt is the target mass, NA is
Avogadro’s number and A is the target mass number,
• ϵ(T ) is the detector efficiency as a function of the recoil energy,
•
dσ(T,E)
dT
is the differential CEνNS cross section as specified in Equation 7.21, and
• Φ(E) is the incident neutrino flux. The Huber-Mueller spectrum for reactor antineu-
trinos [187, 188] was used in this study.
The limit of integration Emin(T ) =
T+
√
T (T+2m)
2
is the minimum neutrino energy required
to produce a recoil energy T , where m is the mass of the recoiling nucleus. Emax is the
maximum energy with which neutrinos are produced at the source. Tmin is the energy
threshold, a property specific for each detector, and Tmax is the upper limit for the energy
region of interest. The steps taken to determine the predicted number of events for this
study are described in this section.
To properly account for the differences in energy threshold, mass, livetime, and efficiency,
Equation 7.27 was applied separately to each HPGe diode. The efficiencies as a function of
ionization energy used for each one are shown in Figure 7.11; and the masses, livetimes, and
energy thresholds are presented in Table 7.1. Additionally, the calculations for each detector
included iterations over all five germanium isotopes (with mass numbers 70, 72, 73, 74, and
76), to obtain results with a better accuracy. The relative abundances used are presented in
Table 7.2.
The number of neutrons in each isotope has an effect on the target number, the recoil
energy, and the cross section trough the form factor and the weak charge. The Helm form
factor was used for this work [191], it is given by:
F (q2) =
3j1(qR0)
qR0
e
−(qs)2
2 , (7.28)
3For simplicity, Equation 7.27 is shown solely in terms of the nuclear recoil energy T . However, as
mentioned in Section 7.3.1, only a fraction of T is detected, the ionization energy K; the remainder dissipates
as heat. The efficiency and the integral with respect to T are actually applied with respect to K. The
relationship between T and K is given by Equation 7.24.
86CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
Figure 7.11: The trigger efficiency of each diode, as a function of ionization energy [179].
The Conus-4 diode was not included in the analysis due to an unstable event rate [189].
The efficiencies were interpolated as 0 for values less than the minimum ionization energy
shown in the image, this has no effect in the calculation of the number of events due to the
minimum energy shown being lower than the energy thresholds of the detectors.
Germanium Isotope (A) Relative Abundance (%)
70 20.57
72 27.45
73 7.75
74 36.50
75 7.73
Table 7.2: Natural abundances of the germanium isotopes, used in the calculation of the
target number for each isotope in each detector [190].
7.4. STUDY OF SCENARIOS IN THE SM AND BEYOND 87
where j1 is the first order Bessel spherical function, s = 0.9 fm is the surface thickness
parameter, and R0 =
√
c2 + 7π2
3
a2 − 5s2 is the effective radius of the nucleus, with c =
1.23A1/3 − 0.60 fm and a = 0.52 fm [192]. The dependence of A in the parameter c causes
significant differences for distinct isotopes. The form factors as a function of T for each
germanium isotope are shown in Appendix B, Figure B.1.
The total cross section further illustrates the difference caused by the isotopes. It is related
to the differential cross section shown in Equation 7.21 by:
σ(E) =
∫ Tmax
0
dσ
dT
(E, T )dT, (7.29)
where Tmax = 2E2
2E+m
. The total cross sections for all germanium isotopes in the neutrino
energy range of 0-10 MeV are shown in Figure 7.12. An increase in the cross section with a
higher neutron count is observed, as expected according to the discussion in Section 7.3.1.
Figure 7.12: Total CEνNS cross sections for all germanium isotopes, calculated for the
neutrino energy range of 0-10 MeV, the typical energy range for reactor neutrinos [181].
The differential event rate is the last step prior to obtaining the number of events. It is
88CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
defined as:
dN
dT
(T ) = tNt
∫ Emax
Emin(T )
dσ
dT
(T,E)Φ(E)dE, (7.30)
and is interpreted as the number of events in each ionization energy bin. As shown in
Equation 7.30, the target number and livetime play a significant role in the differential event
rate. The differential event rates for each isotope, adding together the contributions of all
three diodes, are shown in Figure 7.13. The contributions for each individual detector can
be seen in Appendix B, Figure B.2.
Figure 7.13: Event rates for each germanium isotope as a function of ionization energy. The
event rates and the number of events shown are the total contributions of all detectors:
CONUS-2, 3, and 5.
The number of events is calculated as the integral of the event rate with respect to the
ionization energy ϵ(K), applying Equation 7.24 to account for quenching effects, and the
efficiencies shown in Figure 7.11. This was calculated for each individual detector, taking
into account the different energy thresholds, and the upper limit for the energy region of
interest of 800 eVee, as discussed in Section 7.3.1. Lastly, the individual contributions for
each detector were added to obtain the overall result. The number of events calculated for
for Conus-2, 3, and 5 was 84, 135, and 111, respectively; bringing the total number to 330
7.4. STUDY OF SCENARIOS IN THE SM AND BEYOND 89
Detector Events Calculated Signal Detected Signal Predicted
in This Work by CONUS+ by CONUS+
Conus-2 84 69 ± 47 96 ± 16
Conus-3 135 186 ± 66 135 ± 23
Conus-5 111 117 ± 75 116 ± 20
Total 330 395 ± 106 347 ± 59
Table 7.3: Events calculated for each detector and the total number of events. Consistent
with the number of events calculated and measured by CONUS+ [181].
events (see Table 7.3). These results are consistent with both the measurements and the
calculations done by the CONUS+ collaboration.
7.4.2 Weak Mixing Angle
The weak mixing angle (θW ) is a parameter in the SM, proposed in the electroweak theory
[193–195]. It receives the name of mixing angle due to its role in the relation between the
photon (Aµ) and Z0 boson (Zµ) with the third component of the weak isospin triplet (W 3
µ)
and the weak hypercharge boson (Bµ) [46]:
Aµ = sin θWW 3
µ + cos θWBµ,
Zµ = cos θWW 3
µ − sin θWBµ. (7.31)
It also relates the masses of the W± and Z0 bosons through MW = MZ cos θW ; and the weak
isospin SU(2)L and hypercharge U(1)Y couplings, g and g′ respectively, via:
sin2 θW =
g′2
g2 + g′2
. (7.32)
The weak mixing angle is not constant but varies as a function of the transferred momentum
q, and determining its value for a given energy scale is an important precision test of the SM
[196].
CEνNS allows to probe this parameter at low energies, at which the form factor is close
to unity. As discussed in Section 7.2, the weak mixing angle is present in the CEνNS cross
section via the term gVp = 1
2
− 2 sin2 θW , in the weak charge. This characteristic of the
CEνNS cross section was employed to find a best fit value of the weak mixing angle using
the CONUS+ results.
The fitting process was done using the χ2 function defined in Equation 7.25, with X =
sin2(θW ) as the parameter to be fitted, calculating the predicted number of events, as de-
scribed in the Section 7.4.1, for each iteration. The minimization was performed using imi-
nuit, a Python implementation of the Minuit2 C++ library [197]. The procedure consisted
in minimizing the χ2 function for sin2(θW ) values in the [0, 1] interval, varying the nuisance
parameter α in the interval [−1, 1]. A minimization convergence was successfully achieved
for the best fit value sin2 θW = 0.268± 0.047, where the uncertainty interval corresponds to
1σ.
90CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
This result is shown in Figure 7.14, as a function of the energy scale. Additional results
from a variety of processes and experiments are included for comparison:
• Atomic parity violation (APV) [138, 198],
• elastic electron-proton scattering (Qweak) [199],
• Møller scattering (SLAC E158) [200],
• electron-deuteron deep inelastic scattering (eDIS) [201],
• neutrino-electron scattering (XENONnT) [202],
• CEνNS from spallation neutron source (COHERENT CsI & LAr) [203],
• and CEνNS from solar neutrinos (PANDAX-4T & XENONnT) [204].
The CONUS+ results for sin2 θW are consistent with all the other experiments considered
within the 1σ uncertainty interval. The results from experiments using electrons (APV,
Qweak and eDIS) have a significantly lower uncertainty than the experiments using neutri-
nos (CONUS+, XENONnT, PandaX-4T and COHERENT). This work imposed the first
CEνNS-derived limit on the weak mixing angle for reactor electron antineutrinos, from a
measurement with a significance greater than 3σ.
7.4.3 Magnetic Moment of the Neutrino
The magnetic moment is the most well studied of the electromagnetic properties of the
neutrino [205–217]. In the SM, neutrinos are considered as massless; however, as discussed
in Section 7.1, neutrinos must be massive in order to explain flavor oscillation. In extensions
of the SM that account for neutrino masses, these acquire a magnetic moment as well.
As an example, in a minimal extension of the SM that considers right handed neutrinos,
a diagonal magnetic moment for the Dirac neutrino arises as a product of loop corrections
involving W bosons and charged leptons. The magnetic moment produced by this model
has the characteristic of being proportional to the neutrino mass in the diagonal elements of
the neutrino mass eigenstates [218, 219]:
µD
ν,ii =
3eGFmν,i
8π2
√
2
≈ 3.2× 10−19
(mν,i
1eV
)
µB, (7.33)
where µD
ν,ii denotes the diagonal magnetic moment of the Dirac neutrino, mν,i represents
the mass of the ith neutrino mass eigenstate, and µB is the Bohr magneton. For Majorana
neutrinos, only non diagonal magnetic moments will be non-zero (µM
ν,ij ̸= 0 for i ̸= j).
The magnetic moment of the neutrino can be probed using CEνNS measurements trough
its cross section contribution, given by [203]:
dσ
dT µν
=
πα2
EMZ
2µ2
ν
m2
e
(
1
T
− 1
E
+
T
4E
)
F 2(q2), (7.34)
7.4. STUDY OF SCENARIOS IN THE SM AND BEYOND 91
10 5 10 4 10 3 10 2 10 1 100 101
[GeV]
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
sin
2
W
APV Qweak
SLAC E158
eDIS
CO
NU
S+
XE
NO
Nn
T 
e-
re
co
il
Pa
nd
aX
-4
T 
8 B
XE
NO
Nn
T 
8 B
CO
HE
RE
NT
(th
is 
wo
rk
)
Figure 7.14: Weak mixing angle as a function of the energy scale µ, in the modified minimal
subtraction renormalization scheme (MS). The fit achieved in this work for the CONUS+
data is shown in red [186]. The SM prediction is shown in black. Other results are also
presented for comparison [138, 198–204].
92CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
where µν is the neutrino magnetic moment normalized by the Bohr magneton, and αEM is
the fine structure constant. The total CEνNS cross section including the magnetic moment
contribution is:
dσ
dT
=
dσ
dT SM
+
dσ
dT µν
(7.35)
with dσ
dT SM
, the SM cross section, given by Equation 7.21. In this analysis, and in all
instances in which the mixing angle was not the parameter to be optimized, the value used
was sin2 θW = 0.2386 [220, 221].
A similar approach to the one outlined in Section 7.4.2 was used to impose an upper limit
on the neutrino magnetic moment. χ2 optimization was used, with the cross section from
Equation 7.35 implemented in Equation 7.27 for the calculation of the number of events,
and µν as the parameter to be minimized using iminuit. The main difference was that rather
than pursuing an absolute minimum, a χ2 profile was produced, in order to impose an upper
limit. In this procedure, the χ2 function (equation 7.25) returns a value by optimizing the
parameter α for µν values in the interval [0, 4.0×109] and subtracting the minimum for each
iteration; the χ2 values are subsequently plotted as a function of µν (see Figure 7.15). This
allowed to impose a 90% CL. upper limit of µν ≤ 5.6× 10−10µB.
Figure 7.15: Neutrino Magnetic moment χ2 profile for CONUS+, the dashed line marks the
90% CL. upper limit, at µν ≤ 5.6× 10−10µB.
The limit to the neutrino magnetic moment imposed in this analysis is shown in Figure
7.16. Also shown in the same Figure are results from direct DM detection experiments using
elastic neutrino-electron scattering [222], and CEνNS limits from 8B solar neutrinos [223];
7.4. STUDY OF SCENARIOS IN THE SM AND BEYOND 93
and from a combined CsI and LAr detection using a spallation neutron source by the CO-
HERENT collaboration [203]. Additional results from experiments using HPGe detectors
with a reactor as a neutrino source by TEXONO [224] and GEMMA [225] are also shown,
including a previous limit imposed by the CONUS experiment at the Brokdorf site [226].
This is a more stringent limit due to a larger energy window and a longer exposure than
that of the data used in this analysis. A limit for accelerator neutrinos by the Liquid Scin-
tillator Neutrino Detector (LSND) collaboration is also included [227]. Other experiments
included that imposed limits with data from solar neutrinos are: SuperKamiokande [228],
and Borexino [229].
The result for the neutrino magnetic moment achieved in this analysis is more stringent
than those obtained by COHERENT and the CEνNS direct DM detection experiments, and
is also competitive when compared to the accelerator neutrino results by LSND. TEXONO,
GEMMA and CONUS produced more stringent limits with reactor antineutrinos. The most
stringent limits are imposed by the direct DM detectors using electron-neutrino scattering.
94CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
 e eff  
Neutrino flavor
10 12
10 11
10 10
10 9
10 8
Ne
ut
rin
o 
m
ag
ne
tic
 m
om
en
t 
 [
B
]
CONUS+
(this work)
TEXONO
CONUS
GEMMA
COHERENT
LSND
DM (8B)
DM (e recoil)
KAMLAND
BOREXINO
Figure 7.16: 90% CL. upper limit for the neutrino magnetic moment normalized by the Bohr
magneton, for the CONUS+ results [186]. Also shown in the same Figure are: direct DM
detection experiments using elastic neutrino-electron scattering (e-recoil) [222] and CEνNS
limits from 8B solar neutrinos [223], COHERENT [203], TEXONO [224], GEMMA [225],
CONUS [226], LSND [227], KamLAND [228], and Borexino [229].
7.4. STUDY OF SCENARIOS IN THE SM AND BEYOND 95
7.4.4 Non-Standard Interactions
Within the SM, neutrinos participate in weak interactions and undergo flavor oscillations
due to their small but nonzero mass. Various Beyond Standard Model (BSM) frameworks
propose additional Non-Standard neutrino Interactions (NSI), which can modify neutrino
propagation and interactions with matter. NSI typically arise from SM extensions that
introduce new mediators, such as additional U(1) gauge symmetries with a Z ′ gauge boson
[175, 230–234]. As a result, NSI provide a promising window for probing new physics.
The effective neutral current NSI Lagrangian for neutrinos in matter (considering only
vector interactions), takes the form [235, 236]:
LNSI = −2
√
2GF ϵ
fV
ℓℓ′
(
ν̄αγ
ρPLνβ
)(
f̄γρf
)
, (7.36)
where:
• GF is the Fermi constant,
• ϵfVℓℓ′ is the parameter describing the strength of the NSI,
• f denotes a first generation SM fermion (e, u, d),
• and the indices ℓ and ℓ′ represent the neutrino flavors (e, µ, τ).
The SM CEνNS weak charge, Equation 7.22, is generalized to include NSI in the following
way (assuming that flavor changing parameters are negligible, i.e ϵfVℓℓ′ ≈ 0 for ℓ ̸= ℓ′ [232,
237, 238]):
QNSI
w,ℓ = Z
(
gVp + 2ϵuVℓℓ + ϵdVℓℓ
)
FZ(q
2) +N
(
gVn + ϵuVℓℓ + 2ϵdVℓℓ
)
FN(q
2). (7.37)
Notice the dependence of ℓ in the NSI weak charge, indicating that the weak charge—and
consequently, the differential cross section are now flavor-dependent:
dσ
dT ℓ
=
G2
F
2π
MN(Q
NSI
w,ℓ )2
(
2− MNT
E2
)
. (7.38)
The number of predicted events for each neutrino flavor can be calculated with a slightly
modified version of Equation 7.27:
Npred,ℓ = tNt
∫ Tmax
Tmin
ϵ(T )dT
∫ Emax
Emin(T )
dσ
dT ℓ
(T,E)Φℓ(E)dE, (7.39)
where the flavor dependence is made explicit in the cross section and the flux. Following
this reasoning, the total number of events is the sum over the distinct flavors:
Npred =
∑
ℓ
Npred,ℓ. (7.40)
As discussed in Section 7.3, the antineutrino flux produced at a nuclear fission reactor
consists entirely of electron antineutrinos. This simplifies the analysis of NSI parameters for
96CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
CONUS+ data, as all CEνNS events originate from a single neutrino flavor, eliminating the
need for flavor-dependent calculations, i.e. QNSI
w,ℓ = QNSI
w,e and Npred = Npred,e.
The NSI parameters in the CONUS+ results were analyzed using a χ2 optimization ap-
proach, similar to the procedures employed for the weak mixing angle and the neutrino
magnetic moment. However, significant differences were introduced to reduce computational
time, requiring specific simplifications. The χ2 function was evaluated over a 400×400 grid
of ϵuVℓℓ and ϵdVℓℓ values, spanning the interval [−1, 1]. To expedite the process, the nuissance
parameter α was analitically minimized. This was achieved by taking the derivative of the
χ2 function, equating to 0 and solving for α̂, the minimum value of α, as follows:
dχ2
dα
=
1
σstat
(
2αN2
pred + 2N2
pred − 2NpredNmeas
)
+
2α
σ2
α
= 0,
α̂ = σ2
α
[
NpredNmeas −N2
pred
N2
predσ
2
α + σ2
stat
]
4. (7.41)
To further optimize the analysis, Npred was obtained using a scaling method based on the
previously obtained SM event count. This approach exploits the fact that the Helm form
factor (equation 7.28) takes the same form for the proton and neutron terms; as a result the
weak charge squared term of the cross section can be written as follows:
(
QNSI
w,ℓ
)2
=
[
Z
(
gVp + 2ϵuVℓℓ + ϵdVℓℓ
)
+N
(
gVn + ϵuVℓℓ + 2ϵdVℓℓ
)]2
F (q2)2.
Consequently, the weak charge term can be factored out of the integral in Equation 7.39,
allowing for the scaling to be implemented:
Npred,ℓ = (QNSI
w,ℓ )2tNt
∫ Tmax
Tmin
ϵ(T )dT
∫ Emax
Emin(T )
G2
F
2π
MN × 1×
(
2− MNT
E2
)
Φℓ(E)dE,
= (QNSI
w,ℓ )2tNt
∫ Tmax
Tmin
ϵ(T )dT
∫ Emax
Emin(T )
G2
F
2π
MN × Q2
w
Q2
w
×
(
2− MNT
E2
)
Φℓ(E)dE,
=
(QNSI
w,ℓ )2
Q2
w
tNt
∫ Tmax
Tmin
ϵ(T )dT
∫ Emax
Emin(T )
G2
F
2π
MN ×Q2
w ×
(
2− MNT
E2
)
Φℓ(E)dE,
Npred,ℓ =
(QNSI
w,ℓ )2
Q2
w
Npred,ℓ(SM); (7.42)
Npred,e =
(
QNSI
w,e
)2
1959.3
330. (7.43)
In the last step, the SM number of events was substituted (Npred(SM) = 330, as shown in
Table 7.3); as well as the SM weak charge for the HPGe detectors (Q2
w = 1959.3). This
approach led to the following flavor-dependent expression for the χ2 function:
4The second derivative confirms that α̂ corresponds to a minimum: d2χ2
dα2 = 2
[
N2
pred
σ2
stat
+ 1
σ2
α
]
> 0.
7.4. STUDY OF SCENARIOS IN THE SM AND BEYOND 97
χ2
NSI,ℓ =
(
Nmeas,ℓ − (1 + α̂)Npred,l(X)
σstat
)2
+
(
α̂
σα
)2
. (7.44)
This method eliminates the need to recalculate the convolution in Equation 7.39 at ev-
ery iteration by replacing it with the calculation of the weak charge, which is significantly
less computationally demanding. Moreover, this procedure does not introduce any loss of
generality in the analysis.
Additionally, to further minimize computing time, a parallel computation approach was
implemented using the Python library multiprocessing [239]. This strategy allowed simulta-
neous evaluations of different sets of parameter values, significantly improving efficiency in
the use of computation resources.
A 95% CL. limit contour was imposed in the ϵuVee − ϵdVee plane (see Figure 7.17). The
results indicate that, along the allowed combinations of parameter values, the ϵuVee = ϵdVee = 0
point—which corresponds to the scenario in which the measurements are consistent with
exclusively SM contributions, is within the contour. Furthermore, the limits imposed in
this analysis are consistent with those from a similar study with data by the COHERENT
experiment [238], which used CsI, LAr and HPGe detectors.
The analysis presented here, which evaluates the weak mixing angle, the magnetic moment
of the neutrino, and the NSI parameters for the CONUS+ results, was published in the
journal Physical Review D [186], achieving to be the first analysis of the CONUS+ data to
appear in a peer-reviewed publication.
98CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
CO
N
U
S+
(this
w
ork)
CO
H
EREN
T
(CsI+
LAr+
G
e)
-1.00 
-0.75 -1.00 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 
-0.75 
-0.50 
-0.25 
0.00 
0.25 
0.50 
0.75 
1.00 
dV
eeε
u
V
e
e
ε
Figure 7.17: 95% CL. limits for the NSI parameters ϵdVee and ϵuVee [186], compared with limits
imposed with COHERENT measurements [238].
7.5. NEUTRINO PRODUCTION IN CORE-COLLAPSE SUPERNOVAE 99
7.5 Neutrino Production in Core-Collapse Supernovae
An additional case of interest for the study of neutrinos are those produced at a Supernova
(SN). As a complement to the reactor antineutrinos analysis, in the following sections a
study using simulations of SN neutrinos is presented, as well as the signals in the noble
liquid detectors DEAP-3600 and LUX-ZEPLIN. This study aims to serve as the initial steps
on evaluating the weak mixing angle, neutrino magnetic moment, and NSI parameters, for
a signal of SN neutrinos.
A Core-collapse SN, also known as a Type II SN, occurs at the end of a massive star’s
life cycle. At this stage, the star’s core can no longer sustain nuclear fusion reactions to
counteract gravitational forces, due to the accumulation of iron; this leads to a rapid collapse
of the stellar core. This event occurs when the mass of the progenitor star is approximately
between 8 and 30 M⊙ [240]. Core-collapse supernovae (SNe) are among the most energetic
events in the universe, releasing approximately 1053 erg (1046 J) of energy, with 99% of this
energy emitted as ∼ 1058 neutrinos of all flavors, with average energies ranging from 10 to
20 MeV [241, 242].
The core-collapse process of a SN can be summarized in five main stages, during which
various neutrino production mechanisms occur (see Figure 7.18).
1. In the last stages of its life cycle, a massive star develops an onion-like layered structure
with heavier elements like oxygen, silicon, and iron, concentrated towards the core.
2. As nuclear fusion becomes unsustainable due to the accumulation of iron, the in-
ward gravitational pressure overcomes the outward thermal pressure. The iron-rich
core, a “white dwarf”, remains stable due to electron degeneracy pressure until the
Chandrasekhar limit is reached (∼1.4-1.5 M⊙) [243, 244]. At this critical point, the
degeneracy pressure is overcome, triggering electron capture processes that produce
electron neutrinos. Simultaneously, the photo-disintegration of iron nuclei within the
core further reduces pressure support, rendering the core gravitationally unstable and
leading to collapse. During this phase, electron captures continue, generating a signifi-
cant flux of electron neutrinos. This process is known as neutronization, during which
the lepton number in the core decreases, resulting in a neutron-rich environment.
3. As the core reaches nuclear densities, it undergoes a sudden rebound, launching a shock
wave. This event, known as the core bounce, produces a burst of electron neutrinos.
This is the first observable neutrino signal from the SN.
4. After the prompt electron neutrino burst is emitted, the outward moving shock wave
is stalled due to the infalling material from the outer layers, in whats known as the
accretion phase. This results in an increase of the core’s temperature, which is now
effectively a proto-neutron star. The core’s temperature rises significantly, leading to
the production of both electron neutrinos and electron antineutrinos through charged-
current interactions: e− + p → n + νe and e+ + n → p + ν̄e. Additionally, muon
and tau neutrinos, and their antineutrinos, are also produced trough neutral current
processes such as: electron-positron annihilation e− + e+ → ν + ν̄, nucleon–nucleon
bremsstrahlung N + N → N + N + ν + ν̄, and plasmon decay γ∗ → ν + ν̄, where N
100CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
represents a proton or a neutron, and ν and ν̄ denote neutrinos and antineutrinos of all
flavors. This phase lasts until the stalled shock wave emitted in the bounce is revived
by neutrino heating, leading to the explosion of the SN.
5. The final stage of the SN is the cooling phase, during which neutrino emission continues,
via direct Urca processes [245, 246] ((A,Z − 1) → (A,Z) + e− + νe and (A,Z) + e− →
(A,Z − 1) + ν̄e), as well as trough the continuation of the neutral current processes
from the previous phase. During this phase, the proto-neutron star gradually cools
down, stabilizing as a cold (T ∼1 MeV) neutron star.
The flavor oscillations of neutrinos are modified in a SN due to their interactions with elec-
trons. As neutrinos travel through regions with varying electron densities, this phenomenon,
known as the Mikheyev–Smirnov–Wolfenstein (MSW) effect [248, 249], plays a significant
role in the flavor composition of the neutrino flux. This phenomenon arises because electron
neutrinos experience coherent forward scattering via charged-current weak interactions with
electrons in matter, effectively modifying their propagation characteristics. Such interactions
can lead to resonant flavor conversion that occur when the effective mass difference between
neutrino flavors, modified by their interactions with electrons in matter, matches the local
electron density. At this resonance point, the probability of a neutrino changing from one
flavor to another is significantly enhanced, leading to substantial alterations in the flavor
composition of the neutrino flux as it propagates outward from the supernova core.
The flavor conversions favored by the MSW effect in SNe depend on the neutrino mass
ordering hierarchy [250]. In the NH, the resonance conditions favor the conversion of electron
neutrinos to other flavors; conversely, in the IH, electron antineutrinos are more likely to
undergo resonant conversion (see Figure 7.19). Although the MSW effect alters the flavor
composition of the neutrino flux, it does not change the total number of neutrinos.
The galactic average rate for core-collapse SNe in the Milky Way is approximately 1.63
events per century; which is equivalent to a time between SNe of ∼61 years [252]. However,
this rate is not uniform throughout the galaxy. A more localized study estimates a SN rate
of 5-6 times the galactic average, at a distance of 600 pc from the Sun [253]. This elevated
rate in the solar neighborhood is attributed to a higher density of massive stars in nearby
star-forming regions, which are progenitors of core-collapse SNe.
The most recent record of a core-collapse SN in the vicinity of the Milky Way is SN1987A,
which occurred at approximately 51 kpc from the Sun, in the Large Magellanic Cloud [254].
It was discovered on February 23, 1987, and was visible to the naked eye. Recent observations
with the James Webb Space Telescope have provided compelling evidence for the existence
of a neutron star within the remnants of SN1987A [255].
Notably, several neutrino observatories made detections two to three hours before the
visible light from SN1987A reached Earth:
• Kamiokande II detected 12 neutrinos [256].
• Irvine-Michigan-Brookhaven (IBM) detected 8 neutrinos [257].
• Baksan Underground Scintillation Telescope detected 5 neutrinos [258].
7.5. NEUTRINO PRODUCTION IN CORE-COLLAPSE SUPERNOVAE 101
Figure 7.18: Stages of a Core-collapse SN [242, 247]. A late-stage massive star with onion-like
structure of heavy elements concentrated towards the core (top left). Nuclear fusion becomes
unsustainable due to the accumulation of iron; the gravitational pressure is balanced by the
electron degeneracy pressure of the “white dwarf” until in reaches the Chandrasekhar mass
limit (∼1.4-1.5 M⊙) [243, 244]. The degeneracy pressure is overcome, and neutrinos are
emitted trough electron capture, triggering neutronization. Photo-disintegration of the iron
nuclei further enables the core collapse (bottom left). As the iron core reaches nuclear
densities, it rebounds, launching a burst of νe (bottom right). In the accretion phase, the
SN shock wave is stalled due to the infall of material (top right). Core temperature rises,
leading to the production of νe and ν̄e in e− and e+ captures. Neutrinos of all flavors (ν)
are also produced in neutral current processes such as: pair annihilation, nucleon–nucleon
bremsstrahlung and plasmon decay. The shock wave is revived by neutrino heating, and
the SN explosion is launched. Lastly, the cooling phase (center), during which neutrino
emission of all flavors continues via direct Urca processes [245, 246], and the continuation of
the neutral current processes from the previous phase. The remnant of the SN is a neutron
star.
102CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
Figure 7.19: Simulated SN neutrino fluences (denoted as λ in this Figure) as a function of
the neutrino energy E. The Figure compares different cases of the adiabatic MSW effect
[251]: (a) MSW effect not considered (νx refers to the sum of νµ, ντ and the respective
antineutrinos), (b) MSW effect considered assuming the NH neutrino mass ordering, and (c)
MSW effect considered assuming the IH neutrino mass ordering.
7.6. CEνNS SIMULATIONS FOR DEAP-3600 AND LUX-ZEPLINWITH ESTRELLANUEVA103
These detections provided observational support for theoretical supernova models, confirming
that approximately 99% of the collapse energy is emitted as neutrinos of all flavors [259].
Additionally, the observations coincided with predictions estimating the emission of around
1058 neutrinos, each with average energies in the range of a few tens of MeV [260].
Having established the importance of neutrino astronomy and the effectiveness of reactor
neutrino CEνNS experiments in probing new physics, this study serves as an initial effort
in constraining the weak mixing angle, the neutrino magnetic moment, and non-standard
neutrino interaction (NSI) parameters using simulated SN neutrinos. The following sections
outline a methodology and show potential implications for future research involving SN
neutrinos, with CEνNS as the detection channel.
7.6 CEνNS Simulations for DEAP-3600 and LUX-ZEPLIN
with EstrellaNueva
The simulations for this analysis were done using EstrellaNueva [251], an open-source
software designed to study the interactions of neutrinos emitted by SNe 5. It provides a
computational framework to calculate the cross sections, fluences and the expected inter-
action rates of SN neutrinos in various detector materials, incorporating multiple detection
channels, including CEνNS, and allowing for custom target compositions.
EstrellaNueva implements the analytical SM CEνNS cross section (equation 7.21), and
various nuclear form factors, including Helm (equation 7.28). The adiabatic MSW effect can
be incorporated into the simulations in either mass ordering hierarchy; both of which are
considered in the relevant analysis in this work. Additionally, EstrellaNueva allows users to
set SN distances from Earth, and choose from various progenitor star models. These features
make it a valuable tool for studying SN neutrinos in detectors, like DM experiments, which
are particularly sensitive to CEνNS interactions.
Following the approach taken in [262], three SN distances were selected to represent dif-
ferent astrophysical scenarios: regions close to the Sun, a medium-range galactic distance,
and areas near the edge of the Milky Way disk. These distances, as measured from Earth,
were chosen as follows:
• 0.196 kpc (640 ly): the approximate distance to Betelgeuse, a red supergiant with a
mass of ∼15 M⊙ [263].
• 10.0 kpc (32600 ly): roughly equivalent to the distance to the center of the Milky Way.
• 20.0 kpc (65200 ly): a distance approaching the opposite outer limits of the galactic
stellar disk.
Additionally, the chosen SN model uses the equation of state for hot dense matter proposed
by Latimer and Swesty [264], with a nuclear incompressibility of 220 MeV (LS220-s15.0
EoS). Developed by the Core-Collapse Modeling Group at the Max Planck Institute for As-
trophysics, this model was implemented in EstrellaNueva [251, 265]. It assumes a progenitor
star of 15 M⊙, coinciding with the approximate mass of Betelgeuse.
5EstrellaNueva Version 1.1 was used for this work [261].
104CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
The targets chosen for this study were two noble liquid DM detectors: DEAP-3600 (see
Section 4.1), and LUX-ZEPLIN (LZ), the largest detector currently in operation [266].
LZ is a scintillation detector, consisting of a liquid xenon (LXe) time projection chamber
(TPC) with an active mass of 7 tonne (see Figure 7.20). It makes use of the LXe scintillation
properties that enable pulse shape discrimination, allowing for the distinction between nu-
clear and electron recoils. LZ is located underground at the Sanford Underground Research
Facility, at Lead, South Dakota, shielded by an overburden of 4300 m water-equivalent [63].
It started taking data on December, 2021; and currently holds the record for the most strin-
gent limit on spin-independent WIMP-nucleon cross section, at 2.1×1048cm2 at the 90% CL.
for a WIMP mass of 36 GeV/c2 [71] (shown in Figure 3.5).
Figure 7.20: Diagram of the LZ detector structure [63]. 1) The LXe TPC, monitored by 2
arrays of PMTs. 2) Double-walled vacuum insulated titanium cryostat, surrounded by an
outer detector consisting of an organic liquid scintillator loaded with gadolinium (GdLS). 3)
Array of 8” PMTs monitoring the GdLS. 4) Water shield. 5) High voltage connection for
the cathode. 6) Conduit for neutron calibration sources.
The procedure for calculating the number of events in this analysis closely resembles the
one outlined for the CONUS+ detector in Section 7.4.1; however, there is a significant
difference related to the fluxes. In the CONUS+ analysis, the assumption was made that
the neutrino flux remained approximately constant during reactor on periods, this allowed
for the flux and the livetime to be treated as independent. In the case of a neutrino burst in
a SN, this assumption no longer holds, as the neutrino flux varies heavily during the different
stages of the SN (see Figure 7.21). For this reason, instead of using the flux and the livetime
separately to calculate the number of events, as in Equation 7.27, the fluence (φD(t, E)) was
used, which relates to the flux as follows6:
6In the case of a time independent flux and a constant distance to the source, this reduces to ϕ(t, E) =
∫ t2
t1
Φ(E)dt = ∆tΦ(E), recovering Equation 7.27.
7.6. CEνNS SIMULATIONS FOR DEAP-3600 AND LUX-ZEPLINWITH ESTRELLANUEVA105
φD(t, E) =
∫ t2
t1
ΦD(t, E)dt (7.45)
where t1 and t2 denote the starting and ending times of the SN neutrino detection, and the
dependence on the SN distance has been made explicit in the subindex D.
Figure 7.21: Simulation of the fluxes of distinct neutrino species during a SN, as a function
of time measured after the bounce [267]. The neutrino denoted as νµ represents the sum of
all the remaining neutrino species (νµ, ν̄µ, ντ and ν̄τ )
After this adjustment, the equation for the number of events is:
Npred,D = Nt
∫ Tmax
Tmin
ϵ(T )dT
∫ Emax
Emin(T )
dσ
dT
(T,E)φD(t, E)dE, (7.46)
where the livetime is implicit in the fluence. This equation is used to calculate the number
of events for each detector, at a distance D = (0.196, 10.0, 20.0) kpc.
The CEνNS cross section is given by Equation 7.21, the total cross sections (equation
7.29) for the Xe isotopes and 40Ar are shown in Figure 7.22. The form factors as a function
of the recoil energy for Xe and Ar are shown in Appendix B, Figure B.3. The other elements
needed for calculating the number of events are: the number of targets, efficiency functions,
fluences, energy thresholds, and the energy resolution functions. The number of targets was
determined using the total active noble liquid masses for each detector, 3.3 and 7 tonne, for
DEAP and LZ, respectively. In the case of DEAP, the LAr composition was assumed to be
100% 40Ar, while for the LXe in LZ, the natural relative abundances of the Xe isotopes were
used, as shown in Table 7.4.
106CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
Figure 7.22: Total CEνNS cross sections for all Xe isotopes and 40Ar.
Xenon Isotope (A) Relative Abundance (%)
124 0.095
126 0.089
128 1.910
129 26.401
130 4.071
131 21.232
132 26.909
134 10.436
136 8.857
Table 7.4: Natural abundances of the xenon isotopes, used in the calculation of the target
number for each isotope in LZ [268].
7.6. CEνNS SIMULATIONS FOR DEAP-3600 AND LUX-ZEPLINWITH ESTRELLANUEVA107
The recoil energy detector efficiencies used were the trigger efficiencies for each detector (see
Figure 7.24), assuming that no further cuts would be needed for the detectors in the case of
a highly time-localized and signal-dominant event such as a SN neutrino burst. The fluences
were obtained from the EstrellaNueva simulations (see Figure 7.23), which cover a range of
incident neutrino energies up to 100 MeV. The energy threshold for LZ was found to be 1
keV [269], while a threshold of 52 keV was used for DEAP-3600 [80]. Lastly, the energy
resolution functions model the fraction of the nuclear recoil energy that is collected by the
PMTs, analogous to the quenching function in Section 7.4.1. For both detectors, the energy
resolution was modeled as a gaussian function, with a standard deviation that varies as a
function of the recoil energy. The standard deviation for DEAP is [81]:
σDEAP (T ) =
√
1.4× 10−3T + 4.0× 10−7T (7.47)
where T denotes the recoil energy function. The energy resolution implemented for LZ
was a combination of a linear segment, and a fit of the general form σLZ = A√
T
, where the
constant A was determined by the resolution values specified in [270]. The resulting function
is represented as follows:
σLZ(T ) =



4.7×10−6
√
T
for T ≤ 3.5 keV,
3.0× 10−2T for T > 3.5 keV.
(7.48)
A gaussian sampling was applied to the event rates with the resolution functions as the
standard deviation for each detector, resulting in the event rates shown in Figure 7.25. The
total number of events at a given distance was obtained using Equation 7.46, and adding the
contributions for all isotopes in each noble liquid target material. The results are presented
in Table 7.5.
A steep decline in the number of events as a function of distance is observed, corresponding
to an inverse square law in the neutrino fluence emitted by the SNe. LZ is able to detect a
significant signal across the entire galactic disk, at all distances probed; while DEAP-3600 is
only able to gather a number of events greater than 1 at 0.196 kpc. This can be attributed
mainly to the CEνNS cross section for 40Ar being approximately one order of magnitude
lower compared to the same cross section for the Xe isotopes, as shown in Figure 7.22. The
significantly higher target mass of LZ, nearly double that of DEAP-3600, is also a significant
factor. In the following section these results are used to show potential implications for the
weak mixing angle, the neutrino magnetic moment and the NSI parameters.
Detector Distance [kpc]
0.196 10.0 20.0
LZ 104809 40 10
DEAP 468 <1 <1
Table 7.5: Simulated SN neutrino CEνNS at different distances for LZ and DEAP-3600
detectors.
108CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
Figure 7.23: Fluences simulated with EstrellaNueva. Top: flavor composition of the fluences
at 0.196 kpc, accounting for the MSW effect assuming the NH ordering. Bottom: total
fluences for each distance considered.
6 
5 
.......... 4 
N 
I 
E 
u 
r-i 
I 3 
> 
Q) 
::E 
S-2 
1 
o 
1e13 
(\ 
I 
\ 
\ , 
\ 
A \ 
~ '- ~ 
I " 
t 
" ~s 
1'---
o 20 40 
E [MeV] 
~---" ............. ,/ ' :-- " 
60 
1 1 
SN Distance = 0.196 kpc t-
-- Ve 
-- Vil 
-- VT 
--- Ve 
--- Vil 
--- vT 
-- Total 
80 100 
.L .1 
Total Fluences at 
SN Distances [kpc] 
t-
-
, 
1- - 1 ' ... ".-------+------------+------------1 : "" 
0.196 
10 
20 J , " , , , " , 
" " ", 
1011, - -+----------r----------r-------- ~~ --------_r--------~--- 1 
""'" N 
" : ... " 
:' /'-'-'-. ...... ~, 
:'/' ....... , ". "" 
: . ' '''-. __ ----=....0.-:-+-__________ +--________ --+-_____ '-0,.------__ +--_1 
:/ ' ..... " .... ,~ 
1 ", 
I 
E 
u 
r-i 
I 109 
> 
Q) 
::E 
". 
; '. ", ' .. 
"" 
S-
107 
". ", ..... . 
I 
·'·,·1········ .. 
"" ..... . 
105, - -+ ----------+-----------r----------r----------r---- ·, ~ -- ~ --- 1 I ". I '. 
O 20 40 60 80 100 
E [MeV] 
7.7. SN NEUTRINO PARAMETER ANALYSIS: SM AND BEYOND 109
Figure 7.24: Detection efficiencies for DEAP-3600 (left) [81] and LZ (right) [270]. For both
detectors, the trigger efficiency curves were used (the light blue curve labeled “high upper
bound” for DEAP-3600, and the blue “Trigger” curve for LZ).
7.7 SN Neutrino Parameter Analysis: SM and Beyond
This section presents a proposed methodology for utilizing the previously discussed results
to derive implications for the weak mixing angle, the neutrino magnetic moment, and the
NSI parameters. To this end, the approach described in Sections 7.4.2, 7.4.3 and 7.4.4 was
adapted, with modifications that account for the physical differences between reactor and
SNe neutrinos, and the simulated nature of the data. This analysis represents an early effort
in using DM detectors and SN neutrinos to investigate scenarios in the Standard Model and
beyond, laying the ground work for future studies.
Equation 7.25 was implemented for a χ2 optimization approach, under the assumption that
for a highly time-localized SN neutrino burst, the background contribution can be neglected.
This approach requires predicted and measured numbers of events, the predicted events
are the results presented in Table 7.5. To emulate the role of measurements, a 1σ interval
is constructed for each predicted result, by assuming a Poisson statistical distribution to
calculate upper and lower bounds, as follows:
N+ = Npred +
√
Npred,
N− = Npred −
√
Npred. (7.49)
The upper and lower bounds for Nmeas, denoted as N+ and N− respectively, are presented
in Table 7.6.
Under these circumstances, the χ2 function for a given distance and detector takes the
following form:
χ2
b =
(
Nmeas,b − (1 + α)Npred(X)
σstat,b
)2
+
(
α
σα
)2
, (7.50)
110CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
Figure 7.25: Event rates for CEνNS at various SN distances. DEAP-3600 and LZ at 0.196
kpc (top left and right respectively), and LZ at 10.0 kpc (bottom left) and 20.0 kpc (bottom
right). The event rates for DEAP at 10.0 and 20.0 kpc can be seen in Appendix B, Figure
B.4.
7.7. SN NEUTRINO PARAMETER ANALYSIS: SM AND BEYOND 111
Detector Distance [kpc]
0.196 10.0 20.0
Npred N+ N− Npred N+ N− Npred N+ N−
LZ 104809 105133 104485 40 46 34 10 13 7
DEAP 468 490 446 <1 <1 <1 <1 <1 <1
Table 7.6: Predicted and measured events with 1σ intervals for SN neutrino CEνNS at
different distances for LZ and DEAP-3600 detectors.
where the subindex b represents an upper or lower bound, thus Nmeas,b = (N+, N−) and
σstat,b = (
√
N+,
√
N−). This approach resulted in sets of 2 minima for the optimized physical
parameters, one for each of the bounds. These minima were combined, or a conservative
value was taken, depending on the specific circumstances and practicality associated with
each parameter.
The nuisance parameters in this analysis are conservative values that account for the main
astrophysical uncertainty sources, and detector efficiencies:
• Distance to SN: 25% [271],
• Helm form factor: 5% [272],
• Neutrino flux for all 6 species: 10% [273],
• DEAP-3600 efficiency: 10% [81], and LZ efficiency: 15% [270].
The uncertainty in the nuisance parameter α for each detector is the following:
σα,DEAP =
√
0.252 + 0.052 + 0.102 + 0.102 = 0.29, (7.51)
σα,LZ =
√
0.252 + 0.052 + 0.102 + 0.152 = 0.31. (7.52)
σα,LZ is slightly higher due to LZ’s efficiency, and both have similar values to the uncertainty
used for the CONUS+ study, shown in Equation 7.26.
7.7.1 Results for the Weak Mixing Angle
Following the order in the CONUS+ analysis, the first parameter to be optimized was
the weak mixing angle (see Section 7.4.2). The χ2 function with upper and lower bounds
yielded two optimal values for sin2 θW . The values were subsequently combined under the
assumption of a squared distribution, constructing upper and lower limits by adding or
subtracting its uncertainty to the upper and lower optimal values, respectively. The midpoint
between these limits was then calculated, representing the central value of the combined 1σ
uncertainty interval. The findings are presented in Table 7.7. The values for sin2 θW,+ are
higher than those of sin2 θW,− for both detectors at 0.196 kpc and across all distances for
LZ; however, the uncertainty intervals make these results consistent with the SM prediction
of sin2 θW = 0.238 [220, 221]. As the distance increases, the central values deviate further,
increasing for sin2 θW,+ and decreasing for sin2 θW,−, this accounts for the significant increase
112CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
in the combined uncertainty interval. The uncertainties for sin2 θW,+ and sin2 θW,− increase
for more distant SNe, this is expected due to the statistical uncertainty becoming more
significant at greater distances.
Distance to Supernova [kpc]
Detector 0.196
sin2 θW,+ sin2 θW,− sin2 θW,c
DEAP 0.245± 0.044 0.232± 0.042 0.239± 0.050
0.239± 0.055 0.238± 0.055 0.238± 0.055
10.0
LZ 0.265± 0.064 0.210± 0.057 0.241± 0.088
20.0
0.289± 0.082 0.179± 0.070 0.240± 0.131
Table 7.7: Upper (sin2 θW,+), lower (sin
2 θW,−) and combined (sin2 θW,c) weak mixing angle
intervals for LZ and DEAP-3600.
The central values and combined uncertainty intervals are plotted as a function of the SN
distance in Figure 7.26. LZ is capable of setting limits for the weak mixing angle for SNe
occurring all across the galactic disk. At the shortest distance considered in this study, the
combined uncertainty of LZ is slightly larger than that of DEAP, due to a higher uncertainty
in the nuisance parameter, that can be traced back to a higher conservative estimate in the
efficiency for LZ. The combined uncertainty interval increases with distance, as discussed
previously. This can be interpreted as an interval in which the central value for a sin2 θW
measurement would be contained, if the difference between the predicted and measured
number of SN CEνNS is within 1σ.
Lastly, Figure 7.27 compares the sin2 θW results from this study with those from CONUS+
and other experiments. For SNe at distances comparable to Betelgeuse, both detectors
demonstrate the capability to constrain sin2 θW with a precision similar to that of CONUS+.
At greater distances within the Milky Way, LZ achieves precision comparable to experi-
ments utilizing solar neutrinos and neutrino-electron scattering, such as PANDAX-4T and
XENONnT. These findings support the feasibility of probing the weak mixing angle with
SN CEνNS measurements from DM detectors like LZ and DEAP-3600.
7.7.2 Findings for the Neutrino Magnetic Moment
The next parameter to be fitted was the magnetic moment of the neutrino. Similar
to the case of the weak mixing angle, two minima per detector were obtained for each
distance, accounting for the N+ and N− bounds. These findings are listed in the Table
7.8. LZ sets bounds for all distances evaluated, and as the distance increases the magnetic
moment limit for the upper bound (µν [µB]+) increases as well, while the lower bound value
(µν [µB]−) decreases. This inverse trend can be explained by referring back to the CEνNS
differential cross section with the µν contribution (equations 7.34 and 7.35). The magnetic
moment contribution is added to the SM cross section, this implies that a lower number of
events than predicted by the SM, as is the case for N−, would require a lower contribution
7.7. SN NEUTRINO PARAMETER ANALYSIS: SM AND BEYOND 113
Figure 7.26: Central values and combined uncertainty intervals for sin2 θW as a function of
SN distance.
114CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
Figure 7.27: Weak mixing angle results for SN simulations, compared to the CONUS+ work
described in Section 7.4.2, and other experiments [138, 198–204]. The SM prediction is
shown in black.
7.7. SN NEUTRINO PARAMETER ANALYSIS: SM AND BEYOND 115
from the magnetic term, thus resulting in a lower µν . The opposite is true for the case
of a measurement resulting in more events than the SM prediction, this implies a stronger
magnetic contribution and a larger µν . This relationship enables the magnetic moment
derived from the lower bound (µν [µB]−) to set more stringent limits.
Distance to Supernova [kpc]
Detector 0.196
µν [µB]+ µν [µB]−
DEAP 3.7× 10−9 3.4× 10−9
2.0× 10−9 2.0× 10−9
10.0
LZ 2.4× 10−9 1.9× 10−9
20.0
2.8× 10−9 1.9× 10−9
Table 7.8: LZ and DEAP-3600 90% CL. upper limits for the upper (µν [µB]+) and lower
(µν [µB]−) bounds of the neutrino magnetic moment.
The limits for µν as a function of the SN distance are shown in Figure 7.28. The upper
limits were not combined in this analysis. Although a variety of methods exist to achieve
this [274, 275], their implementation requires significant computational resources, which
were unavailable and beyond the primary scope of this study. Instead, the least stringent
limits were chosen as conservative estimates. At 0.196 kpc LZ is able to set a lower limit
than DEAP-3600, this is attributed to statistical effects due to LZ detecting more events
than DEAP-3600 by a factor of ∼220. The statistical uncertainty is also responsible for the
gradual increase in the limit set by LZ with increasing SN distance.
The limits set in this study for 0.196 kpc were compared to the results obtained for
CONUS+ in Section 7.4.3, and other experiments, this is shown in Figure 7.29. These re-
sults are less stringent than those set with the CONUS+ analysis, however, are comparable
to those by COHERENT [203] and limits from 8B solar neutrinos [223]. The results pre-
sented here indicate that limits imposed on the neutrino magnetic moment via SN neutrinos
measurements on DM detectors would be comparable and complementary to studies using
other detection mechanisms. The SN distance does not play a significant role in this re-
gard, since the difference in the limits is not significant at the scale shown in Figure 7.29.
The cross section difference between LXe and LAr, as well as the target mass difference
between LZ and DEAP-3600, account for an appreciable difference, however, it is negligible
when compared to the differences with limits set by other detection channels such as elastic
neutrino-electron recoil ([222] and [229]).
116CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
Figure 7.28: LZ and DEAP-3600 90% CL. upper limits for µν as a function of SN distance.
The limits shown are the most conservative limits imposed by each detector at a given
distance.
7.7. SN NEUTRINO PARAMETER ANALYSIS: SM AND BEYOND 117
Figure 7.29: Upper limits at the 90% CL. set for SN simulations. The limits shown here are
the results for the SN distance of 0.196 kpc, the variation in the limits due to the distances
studied in this work is not significant at this scale. The CONUS+ limit obtained in Section
7.4.3 is also shown. Other limits shown in the same Figure are: direct dark matter detection
experiments using elastic neutrino-electron scattering (e-recoil) [222] and CEνNS limits from
8B solar neutrinos [223], COHERENT [203], TEXONO [224], GEMMA [225], CONUS [226],
LSND [227], KamLAND [228], and Borexino [229].
118CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
7.7.3 Implications for Non-Standard Interactions
The NSI parameters were analyzed last in this study. As discussed in Section 7.4.4,
these parameters are flavor-dependent, requiring flavor-specific number of events for the χ2
optimization process. This poses a significant challenge when analyzing NSI parameters with
SN neutrinos, as the SN flux, unlike that of reactor neutrinos, is composed of multiple flavors.
Furthermore, CEνNS measurements do not allow for the differentiation between neutrino
flavors. As a consequence, the results obtained are sensitive to the hierarchy in the neutrino
mass ordering trough the influence of the MSW effect. Both hierarchies are considered in
this study.
One possible approach to estimating the flavor composition of a SN neutrino flux and
probing NSI parameters is to use SM predictions to determine the expected flavor ratios in
the event count. These ratios can then be applied to the measured event count to infer the
flavor composition. EstrellaNueva provides flavor-specific fluences, facilitating this method.
The flavor ratios are defined as follows:
rℓ =
Npred,ℓ
Npred
, (7.53)
where ℓ = (e, µ, τ) is the flavor index. Subsequently, the event count for each flavor is
determined as:
Nmeas,ℓ = rℓNmeas. (7.54)
This approach was used to determine the flavor-dependent upper and lower bounds:
N±,ℓ = rℓ
(
Npred ±
√
Npred
)
= Npred,ℓ ±
√
Npred,ℓ
Npred
Npred,ℓ.
7 (7.55)
The predicted event count, along with the flavor compositions provided by EstrellaNueva,
as well as the upper and lower bounds estimated using the described method, are presented
in Table 7.9. Significant differences in the flavor composition were observed for all neutrino
flavors; however, these differences were particularly pronounced when comparing e and µ
neutrinos at closer distances. This is a direct consequence of hierarhcy dependence in the
MSW effect.
The NSI contours were obtained by following the procedure detailed in Section 7.4.4,
utilizing a 400×400 grid for evaluating the ϵuVℓℓ and ϵdVℓℓ parameter pairs in the χ2 function
in Equation 7.44. The contours for the upper and lower bounds were combined by selecting
the points in the grid with the lower χ2 value from each bound. This resulted in 95%
CL. contours including all the points from both bounds that satisfy the threshold criterion,
therefore setting a conservative contour. Another significant difference compared to the
CONUS+ contour, is that in this analysis contours can be obtained for all neutrino flavors,
thanks to the composition of the SN fluences.
7The total upper and lower bounds are recovered from the flavor-dependent bounds as follows:
N± =
∑
ℓ
(
Npred,ℓ ±
√
Npred,ℓ
Npred
Npred,ℓ
)
=
∑
ℓ Npred,ℓ ± 1√
Npred
∑
ℓ
√
N2
pred,ℓ = Npred ±
√
Npred.
7.7. SN NEUTRINO PARAMETER ANALYSIS: SM AND BEYOND 119
Distance to Supernova [kpc]
Detector Event Count 0.196
e µ τ Total
Normal Hierarchy Mass Ordering
Npred,ℓ 171 145 152 468
DEAP N+,ℓ 179 152 159 490
N−,ℓ 163 138 145 446
Npred,ℓ 35880 34119 34810 104809
N+,ℓ 35991 34225 34917 105133
N−,ℓ 35769 34014 34702 104485
10.0
Npred,ℓ 14 13 13 40
LZ N+,ℓ 16 15 15 46
N−,ℓ 12 11 11 34
20.0
Npred,ℓ 4 3 3 10
N+,ℓ 5 4 4 13
N−,ℓ 3 2 2 7
0.196
Inverted Hierarchy Mass Ordering
Npred,ℓ 145 165 158 468
DEAP N+,ℓ 152 173 165 490
N−,ℓ 138 157 151 446
Npred,ℓ 31184 37042 36583 104809
N+,ℓ 31280 37156 36697 105133
N−,ℓ 31087 36927 36471 104485
10.0
Npred,ℓ 12 14 14 40
LZ N+,ℓ 14 16 16 46
N−,ℓ 10 12 12 34
20.0
Npred,ℓ 3 4 3 10
N+,ℓ 4 5 4 13
N−,ℓ 2 3 2 7
Table 7.9: Flavor compositions of event counts for DEAP-3600 and LZ, for both mass
ordering hierarchies. The predicted counts (Npred,ℓ) were calculated with Equation 7.46,
using the flavor-specific fluences provided by EstrellaNueva. The upper and lower bounds
(N+,ℓ and N−,ℓ) were estimated with the ratio-based method defined in Equation 7.55.
120CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
The combined contours for LZ and DEAP-3600 at 0.196 kpc are shown in Figures B.5 and
B.6, in Appendix B. Due to the small variation in the upper and lower bounds, attributable to
the low statistics, the analysis for LZ at 10.0 and 20.0 did not produce meaningful contours.
The contours set by DEAP-3600 are narrower than those set by LZ; however, both detectors
are capable of probing the NSI parameters for SNe at 0.196 kpc.
The electron NSI parameters were also compared with the CONUS+ contour obtained
in Section 7.4.4 of this work, this is presented in Figure 7.30. The DM detector contours
are more stringent than those set from the CONUS+ analysis. This is explained by the
larger relative difference between measured and predicted events for CONUS+, 395 and 330
respectively; while the upper and lower bounds for DEAP and LZ are closer to the predicted
values, as shown in Table 7.9. The mass hierarchies also produce a variation in the contours
when comparing the DM detectors, this is due to the statistical difference in the electron-
flavored fluxes in each mass ordering scenario. A comparison of NH vs IH contours for LZ
and DEAP is shown in Figure B.7, in Appendix B.
7.8 Conclusions from the Parameter Analysis with SN
Neutrinos
This study represents an initial step toward exploring potential implications for SM and
beyond parameters through the measurement of SN CEνNS in noble liquid DM detectors.
The results achieved support the feasibility of using SN neutrinos to probe the weak mixing
angle, the neutrino magnetic moment, and, with some limitations, the NSI parameters.
The weak mixing angle and the neutrino magnetic moment can be probed by a detector
such as LZ for SNe occurring all across the stellar disk of the Milky Way. A LAr detector, like
DEAP-3600, is capable of probing the same parameters at distances near the solar vicinity.
The potential values and upper limits obtained by these means are comparable to those set
by reactor, spallation neutron sources, and solar neutrino experiments.
The NSI analysis faces various limitations, the most significant ones encountered in this
study being: the inability of obtaining flavor-specific event counts via CEνNS, the depen-
dence on the assumed neutrino mass ordering hierarchy due to the influence of the MSW
effect, and the low statistics for SNe ocurring deeper in the galaxy. The approach taken here
to approximate the flavor composition of a SN neutrino burst allows for setting NSI contours
for all three flavors at closer distances. However, the two mass hierarchy cases remain indis-
tinguishable through methods incapable of measuring flavor-specific events, both should be
treated as separate scenarios since there are significant differences in the flavor composition
for neutrino bursts at short SN distances.
Future extensions of this study could incorporate different stellar masses and SN models.
The upper and lower bounds could be extended to 2 or 3σ, this would provide further insights
into the role of SN neutrinos in future research. The range of considered detectors could also
be broadened to include current DM experiments, such as PandaX-4T [66] and XENONnT
[276]. Additionally, potential implications could be explored for future multi-ton detectors,
such as DarkSide-20k [277], DARWIN/XLZD [278], and ARGO [279].
 
 
  1.00 
    
  
3600 (NH) -——— —3 
NH) | ( Ma LZ 
CONUS+ 
 
 
  
0.75 
  
1 o 
LA 
LA 
N 
o 
o 
-0.754 E DEAP- 
0.25 -
O (LAA 
-1.00 
-0.50 0.25 0.00 0.25 0.50 0.75 
¿dv 
== 
0.75 1.00 
 
 
  
In Lz 1H) ( 
    
0 
CONUS+ 
  
 
 
1.00 
0.7543 
0.50 7 
1 19) 
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0.00 e AAA EU OS 
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-0.50. 0.25 0.00 0.25 0.50 0.75 
¿dv 
ee 
0.75 -1.00 
NA”
7.8. CONCLUSIONS FROM THE PARAMETER ANALYSIS WITH SN NEUTRINOS121
Figure 7.30: 95% CL contours for NSI electron parameters from DEAP-3600 (green), LZ
(purple), and CONUS+ (red). The CONUS+ result was obtained in Section 7.4.4. The
DEAP-3600 and LZ contours correspond to a SN at a distance of 0.196 kpc. NH mass
ordering is shown at the top, IH mass ordering at the bottom image.
~QJ 
:JQJ 
Lo 
~QJ 
:JQJ 
Lo 
. 0 
.75 
0.50 
_____________________ 1- ________ _ 
, , 
---------------------¡---------------------¡---------, , 0.25 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ---------------------r--------------------r--------------------r------, , , 0.00 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , 
I I I I 
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I I I I _____________________ 1- ____________________ 1- ____________________ L ____________________ L ___ _ 
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-0.
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I I I I 
I I I I 
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I I I I 
I I I I 
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I I I I 
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I I I I I 
I I I I I ---------------------¡---------------------¡---------------------¡---------------------¡---------------------1"--
I I I I I -0.50 
I [[[[I] ~ Z ( ) : l I I 
-0.75 ' E3 ~~~~~~OO {NH),' ¡....,.. , 
-l. 0 +------+------+-------I---+-----+-----+--- ~ -----....; ""-'-'""=-===-q 
-l.00 -0.75 . 0 -0.25 . 0 . 5 0.50 
. 0 
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5  
0.25 
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---------------------1----------
, , 
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E
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ee 
I I I I 
I I I I 
I I I I _____________________ 1- ____________________ 1- ____________________ L ____________________ L ___ _ 
I I I I 
I I I I 
I I I I 
I I I I 
I I I I 
I I I I 
I I I I 
I I I I 
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I I I I 
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I I I I I 
I I I I I 
I I I I I , , , , , , 
I [[[[I] LZ (1 ) i i i 
. 5 1.00 
' E3 ~~~~~~OO (lH) ¡¡" 
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l 0 -0.75 .50 -0.25 . 0 . 5 0.50 
E
dV 
e 
. 5 1.00 
122CHAPTER 7. EXPLORATION OF NEUTRINOS IN THE STANDARDMODEL AND BEYOND
8 Conclusions
Radiogenic neutrons constitute a significant background source that requires dedicated
strategies to mitigate their impact on the detector’s sensitivity. Their characterization is
carried out within the Profile Likelihood Ratio (PLR) statistical framework. Numerous
probability density functions for the radiogenic neutron background in DEAP-3600 were
achieved, resulting in a methodical characterization of this background in the most relevant
variables for the WIMP search being currently undertaken by the DEAP collaboration. This
characterization supports ongoing efforts to implement the PLR method in the WIMP search.
A machine learning approach is used to explore an alternative method for the mitigation
of radiogenic neutrons. This method exploits the substantial difference in mean free paths
between WIMPs and neutrons in argon, leading to a much higher probability of multiple
scatters for neutrons than for WIMPs. Neutron simulations were conducted in which the
trajectory of the particle and its interactions provided information on the number of nuclear
recoils. It was found that approximately 80% of neutrons that scatter off an argon nucleus
undergo multiple scatterings.
Several binary classification algorithms were trained with the simulated data and evalu-
ated using metrics such as the confusion matrix and receiver operating characteristic (ROC)
curve. The best performing algorithm was a boosted decision tree (BDT), which has been
used previously by other particle physics experiments. The BDT was tested with two simu-
lated datasets, producing encouraging results with validation and testing accuracy scores of
77% and 72% respectively. Additional notable evaluations include precision scores of 78%
and 90%, and area under the curve (AUC) scores from the ROC curves of 0.85 and 0.80,
respectively for the validation and test datasets.
An additional test was conducted on physical data gathered by DEAP-3600 when a neutron
source was deployed. Using the ratio of multiple to single recoils found in a previous stage
of this investigation, an approximate total of 263 multiple recoils were expected for this
dataset, the BDT was able to classify 104+14
−12 of the events as multiple recoils. While lower
than the expected number of multiple recoils, the ability to filter a significant fraction of
events remains valuable for mitigating radiogenic neutrons as a background source.
Although the BDT did not reach the evaluation performance seen at production level in
other experiments, the results demonstrate a promising starting point for reliable multiple
nuclear recoil identification. The classification notably outperformed random guessing, and
tests in a realistic application scenario showed successful identification of a significant frac-
tion of expected multiple recoil events. Future improvements could come from integrating
algorithms that incorporate spatial information from the detector. This line of research
could benefit various WIMP search experiments that must address radiogenic neutrons as a
123
124 CHAPTER 8. CONCLUSIONS
substantial background source.
This work also presents a contribution in the background model for the search of solar
axions, also referred to as axion-like particles (ALPs) in DEAP-3600. The results achieved in
this work have significantly improved the background model, as evidenced by the change in
p-value from 0.5±0.3% to 25±1% after incorporating the Mo and Co isotopes. This p-value
indicates that, assuming the background-only hypothesis, there is a 25±1% probability of
obtaining results at least as extreme as those observed. The solar axion search is an ongoing
effort being undertaken by the DEAP collaboration.
The results of the CEνNS measurements reported by the CONUS+ experiment were
replicated using the defining parameters of CONUS+. This resulted in 330 events, which is
consistent with the observed data. This analysis was used to study SM and BSM parameters
using a χ2 optimization approach, where systematic uncertainties were incorporated as nui-
sance parameters. This study was published in the journal Physical Review D, achieving to
be the first analysis of the CONUS+ data to be accepted for publication in a peer-reviewed
journal.
The first parameter to be studied was the weak mixing angle (θW ). The best fit value
obtained from this analysis is sin2 θW = 0.268 ± 0.047, which is consistent with measure-
ments from other experiments within the 1σ interval. This analysis produced the first limits
on sin2 θW via the CEνNS process for reactor antineutrinos. The following parameter to
be probed was the magnetic moment of the neutrino (µν). This study produced a 90%
CL. upper limit of µν ≤ 5.6 × 10−10µB. This analysis sets a more stringent limit on µν
than COHERENT and CEνNS-based DM experiments, and is competitive with LSND re-
sults. However, more stringent constraints have been obtained by TEXONO, GEMMA,
and CONUS using reactor antineutrinos, with the strongest limits coming from direct DM
detectors via electron-neutrino scattering.
The last scenario to be investigated was the BSM framework of the Non-Standard Inter-
actions (NSI). In this investigation, a 95% CL. contour was achieved in the ϵuVee -ϵ
dV
ee plane,
which is comparable to that produced by the COHERENT experiment.
The results from the CONUS+ study demonstrate that CEνNS offers a valuable framework
for probing electroweak parameters such as θW and µν . It also provides meaningful insights
into BSM scenarios, including those involving NSIs. These results can be further improved
by reducing both statistical and systematic uncertainties in the measurements.
Additionally, a complementary study of CEνNS using simulated SNe neutrinos was con-
ducted. CEνNS signals from a 15 M⊙ core-collapse SN at various distances were simulated
using the EstrellaNueva software, targeting the noble liquid dark matter detectors DEAP-
3600 and LZ. The signal observed by each detector was calculated considering their energy
resolutions and efficiencies. LZ is capable of detecting CEνNS from simulated SNe occurring
across nearly the entire galactic disk, whereas DEAP-3600 is limited to nearby events at dis-
tances comparable to that of Betelgeuse. Differences in the CEνNS differential cross section
between LAr and LXe, along with the target mass, play a significant role in the capability
attainable comparing both detectors.
Upper and lower event bounds were established using a χ2 method inspired by the CONUS+
study to probe θW , µν , and NSI parameters, with astrophysical and detector systematic un-
certainties treated as nuisance parameters. The study of θW yielded results for all distances
considered with LZ, where uncertainties increased with distance; and for DEAP-3600 at the
125
closest distance. These results are comparable to those obtained in the CONUS+ study and
similar experiments. The exploration of µν produced conservative limits for both detectors
at 0.196 kpc, with the sensitivity decreasing for LZ at larger distances. The sensitivities
projected for θW , µν are comparable to those from reactor, spallation, and solar neutrino
experiments.
The NSI analysis faces additional limitations due to the inability to resolve flavor-specific
events, the dependence on the assumed mass hierarchy, and reduced statistics for distant
SNe. However, a methodology was proposed to study the NSI parameters for all neutrino
flavors under both mass orderings by approximating the flavor composition of the SN burst
using simulation-based flavor ratios. As a result, exclusion contours similar to those of
CONUS+ were obtained at the closest distance evaluated.
126 CHAPTER 8. CONCLUSIONS
A Acronyms and Abbreviations Used
List of the acronyms and abbreviations most commonly used in this work.
ALP: axion-like particle.
AmBe: Americium-Beryllium, neutron source.
AUC: area under the curve, classification metric.
AV: acrylic vessel.
BDT: boosted decision tree, classification algorithm.
BRR: background rejection rate, classification metric.
BSM: beyond Standard Model.
CEνNS: coherent elastic neutrino-nucleus scattering.
CL: confidence level.
CMB: cosmic microwave background.
CsI: cesium iodide.
DM: dark matter.
ER: electron recoil scattering interaction.
FN: false negative, evaluation metric.
FP: false positive, evaluation metric.
FPR: false positive rate, evaluation metric.
F1: F1 score, evaluation metric.
127
128 APPENDIX A. ACRONYMS AND ABBREVIATIONS USED
GAr: gaseous argon.
HPGe: high purity germanium, material used in the crystals of the CONUS+ experiment.
IH: inverted hierarchy neutrino mass ordering.
LAr: liquid argon.
LXe: liquid xenon.
LZ: LUX-ZEPLIN, a liquid xenon dark matter detector.
MBR: mblikelihoodR, variable for analysis in DEAP-3600, represents the reconstructed ra-
dial position of events.
MC: Monte Carlo, statistical analysis methods based on simulations.
MR: multiple nuclear recoil.
NH: normal hierarchy neutrino mass ordering.
NR: nuclear recoil scattering interaction.
NSC: nSCBayes, a variable that measures of the energy captured from the interactions
in DEAP-3600.
NSI: non-standard interactions.
PDF: probability density function.
PE: number of registered photoelectrons.
PIFGAR: Pulse Index First Gaseous Argon: a variable of analysis in DEAP-3600 that quan-
tifies how many PMTs captured a signal in the liquid argon before any PMTs gathered
scintillation light in the gaseous argon region.
PLR: profile likelihood ratio.
PMT: photo-multiplier tubes.
PSD: pulse shape discrimination.
qPE: quenched photo-electrons (pulse charge divided by the average single photo-electron
charge for each PMT).
129
RAT: Reactor Analysis Tool, simulation and analysis software.
ROC: receiver operating characteristic, a graph used as a classification metric.
ROI: region of interest.
RPR: Fprompt (Rprompt in newer analysis). Variable used for pulse shape discrimination in
the DEAP collaboration.
SM: Standard Model of particle physics.
SN, SNe: supernova, supernovae.
SR: single nuclear recoil.
TN: true negative, evaluation metric.
TP: true positive, evaluation metric.
TPB: tetraphenyl-butadiene, wavelength shifter.
TPR: true positive rate, evaluation metric
WIMP: weakly interacting massive particle.
130 APPENDIX A. ACRONYMS AND ABBREVIATIONS USED
B Supplementary Plots for the CEνNS
Studies
Compendium of relevant plots for the CEνNS analyzes in Chapter 7.
Figure B.1: Squared Helm form factors for germanium, as a function of the recoil energy T .
131
132 APPENDIX B. SUPPLEMENTARY PLOTS FOR THE CEνNS STUDIES
Figure B.2: Event rates for each individual detector in CONUS+. Conus-2 and 3 are in
the top left and right, and Conus-5 and the total event rate in the bottom left and right
respectively.
133
Figure B.3: Helm form factors for Xe and Ar, used in the calculation of the number of events
for LZ and DEAP-3600.
Figure B.4: DEAP-3600 event rates at 10 and 20 kpc.
134 APPENDIX B. SUPPLEMENTARY PLOTS FOR THE CEνNS STUDIES
Figure B.5: NSI parameter 95% CL. contours for DEAP-3600 (green) and LZ (purple)
at 0.196 kpc. The parameter flavors are identified with distinctive patterns as follows:
horizontal lines for e, diagonal lines for µ, and dotted for τ . The NH in the neutrino mass
ordering is assumed.
L OO LOO 
0.75 0.75 
0.50 0.50 
0.25 0.25 
:::'ClJ 
::JClJ 0.00 
:::'ClJ 
::JClJ 0 .00 
LV LV 
-0.25 -0.25 
-0.50 -0.50 
- 0.75 - 0.75 
95% Cl. DEAP-3600 0.196 kpc (N H) - 95% e l. l Z 0.196 kpc (NH) 
- LOO - LOO 
-LOO -0.75 -0 .50 -0.25 0.00 0 .25 0.50 0 .75 LOO -LOO -0.75 -0.50 -0.25 0 .00 0.25 0.50 0.75 LOO 
EdV 
ee EdV 
ee 
LOO LOO 
0.75 0.75 
0.50 0.50 
0.25 0.25 
:::'::t :::'::t 
::J::t 0.00 ::J::t 0 .00 
LV LV 
-0.25 -0.25 
- 0 .50 - 0.50 
- 0 .75 - 0 .75 
95% el. DEAP-3600 0 .196 kpc (NH) -95% el. l Z 0.196 kpc (NH) 
-LOO - 1.00 
- LOO - 0 .75 - 0 .50 - 0 .25 0.00 0.25 0.50 0 .75 LOO - LOO - 0 .75 - 0.50 - 0.25 0.00 0 .25 0.50 0.75 LOO 
EdV 
J1I-l 
EdV 
J.1J.1 
LOO LOO 
0.75 0.75 
0.50 0.50 
0.25 0.25 
:::. .... :::. .... 
::J .... 0 .00 ::J .... 0.00 
LV LV 
-0.25 -0.25 
-0.50 -0.50 
-0 .75 -0.75 
95% Cl. DEAP-3600 0.196 kpc (NH) -95% el. LZ 0.196 kpc (NH) 
- LOO - LOO 
- l.00 - 0.75 - 0.50 - 0.25 0.00 0.25 0.50 0.75 LOO - l.00 - 0 .75 - 0.50 - 0.25 0.00 0.25 0.50 0.75 l.00 
EdV 
TT EdV 
TT 
135
Figure B.6: NSI parameter 95% CL. contours for DEAP-3600 (green) and LZ (purple)
at 0.196 kpc. The parameter flavors are identified with distinctive patterns as follows:
horizontal lines for e, diagonal lines for µ, and dotted for τ . The IH in the neutrino mass
ordering is assumed.
L OO LOO 
0.75 0.75 
0.50 0.50 
0.25 0.25 
:::'ClJ 
::JClJ 0.00 
:::'ClJ 
::JClJ 0 .00 
LV LV 
-0.25 -0.25 
-0.50 -0.50 
- 0.75 - 0.75 
95% Cl. DEAP-3600 0.196 kpc (lH) - 95% e l. l Z 0.196 kpc (IH) 
- LOO - LOO 
-LOO -0.75 -0 .50 -0.25 0.00 0 .25 0.50 0 .75 LOO -LOO -0.75 -0.50 -0.25 0 .00 0.25 0.50 0.75 LOO 
EdV 
ee EdV 
ee 
LOO LOO 
0.75 0.75 
0.50 0.50 
0.25 0.25 
:::'::t :::'::t 
::J::t 0.00 ::J::t 0 .00 
LV LV 
-0.25 -0.25 
- 0 .50 - 0.50 
- 0 .75 - 0 .75 
95% el. DEAP-3600 0 .196 kpc (lH) -95% el. l Z 0.196 kpc (lH) 
-LOO - 1.00 
- LOO - 0 .75 - 0 .50 - 0 .25 0.00 0.25 0.50 0 .75 LOO - LOO - 0 .75 - 0.50 - 0.25 0.00 0 .25 0.50 0.75 LOO 
EdV 
J1I-l 
EdV 
J.1J.1 
LOO LOO 
0.75 0.75 
0.50 0.50 
0.25 0.25 
:::. .... :::. .... 
::J .... 0 .00 ::J .... 0.00 
LV LV 
-0.25 -0.25 
-0.50 -0.50 
-0 .75 -0.75 
95% Cl. DEAP-3600 0.196 kpc (lH) -95% el. LZ 0.196 kpc (IH) 
- LOO - LOO 
- l.00 - 0.75 - 0.50 - 0.25 0.00 0.25 0.50 0.75 LOO - l.00 - 0 .75 - 0.50 - 0.25 0.00 0.25 0.50 0.75 l.00 
EdV 
TT EdV 
TT 
  
  0.75 
  0.50 
0.25 
    
   
           
—0.25 
0.50 
    
       
0.75 
     -1.00 
1) DEAP-3600 NH 
1 DEAP-3600 IH           
  
-1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 
dv 
Ese 
  0.75 
  0.50 
0.25 
   
      
           
—0.25 
 
0.50 
    
 
0.75 y                
-1.00 0.75 0.50 
NT 
0.25 0.00 0.25 0.50 0.75 1.00 
dv 
Ese
136 APPENDIX B. SUPPLEMENTARY PLOTS FOR THE CEνNS STUDIES
Figure B.7: 95% CL NSI parameter contours, NH (blue) vs IH (red), for DEAP-3600 (top)
and LZ (bottom) at 0.196 kpc.
~<l.J 
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