UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO
PROGRAMA DE POSGRADO EN CIENCIAS FÍSICAS
INSTITUTO DE FÍSICA
FÍSICA DE ALTAS ENERGÍAS, FÍSICA NUCLEAR, GRAVITACIÓN Y FÍSICA
MATEMÁTICA
Scintillating Bubble Chamber with Argon for Measurement of Coherent Elastic
Neutrino-Nucleus Scattering and Dark Matter Search
TESIS
QUE PARA OPTAR POR EL GRADO DE:
DOCTOR EN CIENCIAS (FÍSICA)
PRESENTA:
ERNESTO ALFONSO PITA
TUTOR: Dr. Eric Vázquez Jáuregui
Instituto de Física - UNAM
Ciudad Universitaria, CD. MX, Mayo 2024
©Ernesto Alfonso Pita 2024
 
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ii
Scintillating Bubble Chamber with Argon for Measurement of
Coherent Elastic Neutrino-Nucleus Scattering and Dark Matter
Search
by
Ernesto Alfonso Pita
a dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy (Ph.D.)
at
National Autonomous University of Mexico (UNAM)
Graduate Program
Physical Sciences
Supervisor: Prof. Dr. Eric Vázquez Jáuregui
Institute of Physics - UNAM
CDMX, Mexico
May 2024
©Ernesto Alfonso Pita 2024
Contact details: Ernesto Alfonso Pita
Instituto de Física (IFUNAM)
Universidad Nacional Autónoma de México
Circuito de la Investigación Cientíőca, Ciudad Universitaria
CDMX, México CP 04510
ernestoalfonso92@gmail.com
Prof. Dr. Eric Vázquez Jáuregui
Instituto de Física (IFUNAM)
Universidad Nacional Autónoma de México
Circuito de la Investigación Cientíőca, Ciudad Universitaria
CDMX, México CP 04510
ericvj@ősica.unam.mx
iii
iv
PROTESTA UNIVERSITARIA DE INTEGRIDAD Y 
HONESTIDAD ACADÉMICA Y PROFESIONAL 
(Graduación con trabajo escrito) 
De conformidad con lo dispuesto en los artículos 87, fracción V, del Estatuto General, 68, primer 
párrafo, del Reglamento General de Estudios Universitarios y 26, fracción 1, y 35 del Reglamento 
General de Exámenes, me comprometo en todo tiempo a honrar a la Institución y a 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 t itulado: 
Scintillating Bubble Chamber with Argon for Measurement of Coherent Elastic Neutrino-Nucleus 
Scattering and Dark Matter Search 
que presenté para obtener el grado de ----Doctorado--- es original, de mi autoría y lo realicé con 
el rigor metodológico exigido por mi programa de posgrado, citando las fuentes de 
ideas, textos, imágenes, gráficos u otro tipo de obras empleadas para su desarrollo. 
En consecuencia, acepto que la falta de cumplimiento 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 
Ernesto Alfonso Pita 
518493198 
(Nombre, firma y Número de cuenta de la persona alumna) 
Contents
1 Abstract 1
2 Acknowledgements 2
3 Introduction 3
3.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 Scintillating Bubble Chamber Detector Overview 5
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.2 The SBC Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.3 Detector Design and Functionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5 Sources of neutrons 10
5.1 (α, n) Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5.2 Sources-4C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5.3 Neutrons from spontaneous őssion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5.4 (γ, n) Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.5 Muon-induced neutrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.5.1 SNOLAB underground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6 Monte-Carlo (MC) simulations 14
6.1 Introduction to GEANT4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.1.1 The Physics Behind GEANT4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.1.2 GEANT4’s Flexibility and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.1.3 The Role of GEANT4 in MC Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 15
6.2 GEANT4 implementation of the detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7 Neutron backgrounds in LAr SBC 17
7.1 Acoustic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.2 Optical system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.3 Inner assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
7.4 Radon exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
7.5 Radon diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
7.6 Radon daughter deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
v
7.7 Radon emanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
7.8 Dust deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.9 (γ, n) reactions at SNOLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
8 Physics reach of a low threshold scintillating argon bubble chamber in coherent elastic
neutrino-nucleus scattering reactor experiments 35
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
8.2 Experimental Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
8.2.1 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
8.2.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.3 Physics Reach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
8.3.1 Standard Model Cross-Section for CEνNS . . . . . . . . . . . . . . . . . . . . . . . . . . 41
8.3.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
8.3.3 The Weak Mixing Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
8.3.4 Investigating a Light Gauge Boson Mediator . . . . . . . . . . . . . . . . . . . . . . . . 41
8.3.5 Assessing the Neutrino Magnetic Moment . . . . . . . . . . . . . . . . . . . . . . . . . . 42
8.3.6 Light Scalar Mediator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
8.3.7 Sterile Neutrino Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
8.3.8 Unitarity Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
8.3.9 Non-standard Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
9 Conclusions 55
9.1 Background Suppression and Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
9.2 Detector Reőnement and Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
9.3 Exploration of New Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
9.4 Operational Versatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
9.5 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Bibliography 63
vi
1. Abstract
The Scintillating Bubble Chamber (SBC) represents a pivotal innovation in the őeld of particle physics, offering
a unique approach to detect elusive neutrinos and dark matter. With a keen focus on reducing background
radiation to a minimum, the SBC operates in an environment that curtails undesirable interactions, facilitating
the distinct detection of these mysterious constituents of the universe. This dissertation details the design,
operation, and scientiőc reach of the SBC, providing insight into its ability to discern Weakly Interacting
Massive Particles (WIMPs) and observe Coherent Elastic Neutrino-Nucleus Scattering (CEνNS).
Chapters detail the sophisticated technology behind the SBC, its neutron sources and backgrounds, the role
of Monte-Carlo simulations in preempting real-world challenges, and the deployment of GEANT4 software for
accurate modeling. The thesis culminates in a discussion of the detector’s sensitivity to new physics scenarios
and its future prospects, underpinned by a meticulous approach to background suppression, detector reőnement,
and calibration.
As a key outcome, this research underlines the SBC’s potential to transcend conventional detection methods,
enhancing our grasp of fundamental particles and contributing to the broader spectrum of high-energy physics.
1
2. Acknowledgements
The author wish to acknowledge the support from CONAHCyT´s postgraduate scholarship, as well as the fund-
ing from the UNAM-PAPIIT Programs IN108020 and IN105923. Additionally, the project received őnancial
support from the CONAHCyT project CB-2017-2018/A1-S-8960.
2
3. Introduction
Dark matter and neutrinos are two of the most enigmatic constituents of our universe, driving contemporary
physics research toward new frontiers. While dark matter remains undetected, its gravitational effects suggest
a profound impact on the cosmos. Neutrinos, elusive yet ubiquitous, offer a window into processes that govern
stellar and galactic evolution. The study of Coherent Elastic Neutrino-Nucleus Scattering (CEνNS) provides
a unique opportunity to investigate these fundamental particles, offering insights into their interactions and
properties.
Detecting neutrinos and dark matter by the Scintillating Bubble Chamber (SBC) collaboration necessitates
an operation with minimal background radiation. Undesirable interactions within the detector result from
radioactive processes in its components, materials that constitute the site of the detector, and cosmic radia-
tion. The main problem caused by background radiation is that distinguishing them is not always feasible.
Consequently, many such events are indistinguishable from the events of interest. The particles that generate
undesired interactions in the detector include alpha (α), beta (β), gamma (γ), and neutrons. Fortunately,
bubble chambers have exceptional gamma-ray discrimination, as the likelihood that such particles cause nucle-
ations is typically around 10−10 [1]. Similarly, beta particles with extensive mean-free paths fail to deposit the
required energy within the critical radius to form a bubble, with over 98% of these particles passing through
the detector without causing nucleations [1]. Discrimination through the acoustic signal generated by alpha
particles is constructive for identifying this background. However, neutrons represent a signiőcant source of
background, as they can develop simple or multiple interactions, with simple interactions being nearly indistin-
guishable from the signal generated by a Weakly Interacting Massive Particle (WIMP) or a neutrino (CEνNS).
Therefore, reducing neutron sources to a maximum is the primary challenge in this type of detector.
The Scintillating Bubble Chamber detector, with its reőned detection techniques and background suppression
strategies, is poised to make signiőcant strides in studying CEνNS. Its capabilities extend beyond merely
detecting these elusive particles; it provides a platform to probe new physics scenarios, shedding light on the
mysteries surrounding dark matter and neutrino properties. The physics reach of the SBC detector in the
realm of CEνNS is vast, encompassing the detection of low-energy neutrinos from reactors and natural sources,
testing beyond the Standard Model neutrino interactions, and exploring potential deviations from the Standard
Model. The detector’s sensitivity to CEνNS events and its ability to discriminate against background positions
it as a crucial tool in advancing our understanding of fundamental physics and the universe.
3.1 Chapter Overview
• Chapter 4 sets the stage, offering a comprehensive overview of the Scintillating Bubble Chamber Detector.
It introduces the motivation for employing such sophisticated detection technology and explains the
collaborative journey leading to its conception and operational readiness.
• Chapter 5 delves into the heart of neutron sources, a pivotal factor in our quest. It details the origins and
contributions of neutrons from various reactions and processes, establishing the necessity of mitigating
these background signals to discern the subtle whispers of new physics phenomena.
3
• Chapter 6 transitions to the intricacies of Monte-Carlo simulations, where the virtual realm allows us to
preempt the challenges of the real. The chapter pays homage to the GEANT4 software, an indispensable
ally in modeling and predicting the interactions within the detector.
• Chapter 7 navigates through the complexities of neutron backgrounds in the Liquid Argon Scintillating
Bubble Chamber (LAr SBC) context. It meticulously evaluates the intricate systems and materials
that make up the SBC, scrutinizing their contribution to background levels and examining strategies to
enhance signal clarity.
• Chapter 8 is dedicated to unraveling the physics potential of the low-threshold LAr SBC in CEνNS and
dark matter detection. The chapter discusses experimental design, calibration procedures, sensitivity
analyses, and the ramiőcations for standard model and beyond standard model physics.
• Chapter 9 concludes with synthesizing the research őndings, discussing the implications for background
suppression, detector reőnement, and new physics exploration. It reŕects on the operational versatility
of the SBC and envisions the future trajectory of neutrino physics research and dark matter detection.
4
4. Scintillating Bubble Chamber Detector Overview
4.1 Introduction
The Scintillating Bubble Chamber detector is a cutting-edge instrument at the forefront of particle physics
research [2, 3], particularly in the study of coherent elastic neutrino-nucleus scattering. This innovative detector
combines the principles of a traditional bubble chamber with the modern technology of liquid scintillation,
offering unique capabilities in neutrino detection and exploring new physics. The concept of the SBC detector
originates from the need to probe interactions at low energy thresholds, which are crucial for detecting and
analyzing neutrino events with unprecedented precision [4].
CEνNS, a process predicted by the Standard Model of particle physics, was observed only recently due to the
challenges in detecting low-energy recoils [5, 6]. Observing CEνNS opens up new avenues in understanding
neutrino properties, including their interactions with nuclei, offering potential insights into dark matter and
other beyond-the-Standard-Model phenomena. The SBC detector, with its innovative design, is poised to play
a pivotal role in these investigations.
At the core of the SBC detector is a liquid argon target, chosen for its favorable properties in neutrino detection.
The scintillating component of the detector enhances its sensitivity, allowing for the detection of low-energy
nuclear recoils, which are indicative of neutrino interactions. This sensitivity is complemented by the chamber’s
ability to suppress background, a crucial feature for high-precision experiments.
The SBC Collaboration, comprising a diverse group of researchers and institutions, has been instrumental in
developing and reőning this technology. Through collaborative efforts, the SBC detector has evolved into a
sophisticated instrument capable of probing the frontiers of particle physics. The ongoing development and
operation of the SBC detector not only demonstrate the feasibility of this technology in neutrino research but
also pave the way for future discoveries in the őeld.
This section introduces the SBC detector’s background, its operational principles, and its signiőcance in the
őeld of neutrino physics. It sets the stage for a detailed exploration of the detector’s capabilities, design
features, and the potential impact of its research in advancing our understanding of the universe.
4.2 The SBC Collaboration
The Scintillating Bubble Chamber Collaboration is a multinational and multi-institutional effort ( Fig. 4.1),
combining expertise from various universities in the United States, Mexico, and Canada. This collaboration
plays a pivotal role in advancing the őeld of particle physics through the development and utilization of
innovative bubble chamber technology.
The universities that form the backbone of this collaboration include the University of Alberta, the University
of Chicago, Fermilab, Northwestern University, the University of Texas at Arlington, and the National Au-
tonomous University of Mexico, among others. Each institution brings unique skills and resources to the table,
contributing to the collaboration’s diverse and rich research environment.
5
This collaborative endeavor is focused on harnessing the scintillating bubble chamber technology’s capabilities
for detecting and analyzing rare events, particularly in the context of dark matter searches and CEνNS ex-
periments. The cutting-edge technology developed by the SBC collaboration is characterized by its ability to
maintain target ŕuid in a superheated state. It enables high efficiency in detecting low-energy nuclear recoils
and offers excellent discrimination against electromagnetic backgrounds.
The SBC Collaboration’s efforts are distributed across various facilities, including the SBC-LAr10 at Fermilab
for engineering and calibration purposes and the SBC-SNOLAB at SNOLAB for low background dark matter
searches. These facilities are equipped with state-of-the-art detectors, each comprising 10 kg of liquid argon
and xenon as a wavelength shifter, aiming to achieve a 100 eV nuclear recoil threshold. The innovative design
of these detectors, integrating components like SiPM panels, fused silica vessels, piezoelectric transducers, and
multiple camera systems, plays a crucial role in enhancing measurement detection capabilities and accuracy.
Overall, the SBC Collaboration, with its diverse expertise and advanced technological approach, is at the fore-
front of exploring new frontiers in particle physics, particularly in understanding dark matter and neutrino
properties. The collaboration’s plans include underground operation at Fermilab, with ongoing construction
and component procurement for SNOLAB, highlighting its ongoing commitment to advancing scientiőc knowl-
edge in this domain.
Figure 4.1: The SBC collaboration holds meetings every six months to exchange the current state of research
with a hybrid schema. The images in this őgure correspond to two of these meetings in 2022 in Queens, Canada
(left) and in 2023 in Fermilab, USA (right).
4.3 Detector Design and Functionality
SBC is a groundbreaking detector for sensitively detecting rare particle interactions, such as CEνNS. The core
design principle of the SBC combines the traditional bubble chamber technology with innovative scintillating
features, resulting in a highly efficient and versatile detection system.
The detector’s structure comprises several key components that will be described from the exterior to the
interior and are visualized in Fig. 4.2. The outermost layer consists of a stainless steel vacuum jacket weighing
approximately 120 kg, isolating the detector from external environmental inŕuences. Within this structure is a
pressure vessel weighing approximately 80 kg, equipped with three optical ports on its top, featuring sapphire
windows for internal imaging. An optical system comprising a set of cameras and lenses captures images
following interactions within the detector.
6
Figure 4.2: Schematic illustration of the Scintillating Bubble Chamber. The main components include a
stainless steel vacuum jacket that isolates the detector from the external environment, a pressure vessel with
sapphire optical ports for image capture, and a hydraulic cylinder for liquid argon compression and expansion.
The vessel houses two transparent fused silica jars (outer and inner jars) that contain the LAr. The Outer
Jar is encased in an HDPE castle with embedded copper panels, holding the SiPM array for photon detection.
The lower section includes piezoelectric sensors that detect bubble formation acoustics, and the entire assembly
operates within a controlled temperature range to ensure stable detection conditions.
Two transparent quartz containers, the outer and inner Jars, are inside the pressure vessel (Fig. 4.3). These
jars conőne the LAr and are designed for independent movement, facilitating the compression and expansion
of the LAr. The Outer Jar is encased in a high-density polyethylene (HDPE) castle, which acts as a thermal
insulator and supports a copper panel structure. This structure houses 40 Silicon Photomultipliers (SiPMs,
for SNOLAB chamber FBK with 25-30 % QE and Hamamatsu with 20-25 % QE for Fermilab chamber) that
detect photons emitted from the LAr scintillation (Fig. 4.4).
Beneath the Outer Jar is an array of eight piezoelectric sensors (customs PZT piezo transducers) that form
the detector’s acoustic system. These sensors capture vibrations generated by bubble formation in the LAr,
which propagate through the outer jar’s walls to the piezoelectrics. The detector’s hydraulic system, located
beneath the Inner Jar, controls the LAr’s compression and expansion during different operational phases.
The working principle of the SBC is based on the phase transition of the superheated liquid in the LAr. When
a particle interacts with the liquid, it deposits energy, forming a bubble if the deposited energy exceeds a
certain threshold. This threshold is adjustable by controlling the temperature and pressure conditions within
the chamber, making the SBC versatile for different types of particle detections.
Simultaneously with bubble formation, the LAr scintillating emits light due to the particle interaction. This
scintillation light is detected by an array of SiPMs arranged around the outer chamber. The combination of
bubble formation and scintillation provides a unique signature for particle interactions, enhancing the detector’s
ability to distinguish between different types of particles and reject backgrounds.
The Scintillating Bubble Chamber utilizes a carefully controlled pressure cycle to detect particle interactions
within its liquid argon target volume. The chamber operates by ŕuctuating between a highly pressurized state
7
stabilizing the LAr and a lower pressure superheated state, which renders the LAr sensitive to interactions that
can induce bubble formation. The transition from a stable to a superheated state is managed via a hydraulic
system that responds to pressure readings, maintaining the pressure within an acceptable margin of the desired
threshold.
Once in the superheated state, the chamber is primed to detect particle interactions. A potential interaction
can be identiőed by bubble formation within the LAr. This event triggers a rapid recompression, reverting the
chamber to its initial high-pressure state, which stops further bubble development and prepares the detector
for the next cycle. This stable state has a resting period to ensure conditions are optimal before the cycle
recommences.
This pressure cycling is critical to the chamber’s function, allowing for distinct periods of detection and reset.
The speciőc parameters of pressure levels, temperature, and cycling duration may vary according to the par-
ticular design and operational requirements of the SBC. Still, the underlying process remains consistent across
different bubble chamber detectors. This method ensures sensitive detection while providing clear data capture
and analysis intervals.
Figure 4.3: Images of the components located inside the pressure vessel. The two quartz jars placed over the
hydraulic system’s bellows are on the left. On the right, a section of the HDPE castle is shown; within it, the
copper structure with the SiPMs supports.
Calibration of the SBC chamber is critical for its accurate operation. This is achieved using controlled radi-
ation sources to produce known interactions within the chamber. The calibration process helps őne-tune the
detector’s sensitivity and threshold for bubble formation, ensuring precise measurement of particle interactions.
The primary application of the SBC is in particle physics, particularly for the study of CEνNS and the search
for dark matter. Its high sensitivity and low background make it an ideal detector for observing rare particle
interactions crucial for understanding fundamental physics and the universe.
The detector leverages the unique properties of the superheated liquid, where neutrino interactions lead to the
formation of microscopic bubbles. These bubbles are then magniőed and analyzed to extract valuable physics
8
Figure 4.4: Images of the bubble chamber currently under construction showcase the various components of
the detector in progressive stages. From left to right, the components are (a) the pressure vessel, (b) the inner
assembly accompanied by partial insulation and copper structures, (c) the copper support with an array of
Silicon Photomultipliers (SiPMs), and (d) the outer and inner jars [3].
data. The SBC Detector stands out for its low-energy threshold and high sensitivity to neutrino interactions.
These attributes are crucial for probing new physics phenomena and enhancing our understanding of neutrino
properties.
9
5. Sources of neutrons
5.1 (α, n) Reactions
The production of neutrons via α-induced reactions can be a source of background radiation for experiments
that require low levels of neutron background, such as searches for dark matter or neutrinos via Coherent
Elastic Neutrino-Nucleus Scattering. Therefore, it is essential for experimental collaborations to consider the
sources of background radiation in their detectors carefully and to take measures to reduce or eliminate them.
This can include selecting materials with low levels of α-induced neutron production or shielding the detector
from sources of background radiation.
Internal backgrounds arise due to the radioactive decay generated in the materials from which the detector is
built. Traces of the principal radioactive chains are present in all components of the detector (238U , 232Th y
40K), which are part of all the materials that are found in nature; therefore, the detector components must be
chosen with high levels of radio-purity.
238U has a half-life of t1/2 = 4.47 · 109 years. This isotope is found in small concentrations (ppm or ppb) in
the materials in which the detector is constructed. The amount present during the detector simulations must
be estimated due to the events caused by its disintegration. The 238U chain has nine radio-isotopes with a
half-life greater than one day, several nuclei with a very short lifetime, and a stable isotope at the end of the
chain, 206Pb. The 238U decays to 226 Ra, with an average lifetime of 1600 years, through four intermediate
isotopes, secular balance in the chain is broken at 226Ra because this element is an alkali metal while all its
precursors are actinides. Because these two groups have different chemical properties, some chemical processes
may affect them differently. Also, since the 226Ra has a very long half-life, the secular equilibrium will remain
broken if the 226Ra is removed from equilibrium with its predecessors.
The 232Th has a half-life of t1/2 = 1.4× 1010 years and is also present in the different parts of the detector. In
nature, this element is part of all types of materials and is estimated to be present in soils in a concentration
of 6 parts per million (ppm). Around 99% of Thorium exists in nature and is composed of 232Th. The most
critical isotopes, concerning background noise that originate from the decay of 232Th are 212Bi and 208T l; these
decay chains emit rays α, β, and γ.
The third radioactive family is 40K; this isotope is also naturally present in the detector components, with its
half-life being t1/2 = 1.24× 109 years. The primary mode of disintegration of the 40K is via β in the 89.5% of
the cases, producing a stable isotope of 40Ca. In the remaining cases, it is disintegrated by electronic capture,
generating an isotope of 40Ar and a γ particle of 1.46 MeV.
In the case of neutrons, their interactions are very similar to those expected by WIMP. They are also elec-
trically neutral and interact elastically with atomic nuclei, representing the most complicated background to
characterize and identify. Neutrons originate primarily from the decay of radioactive families in őssion (238U)
and from reactions (α, n) caused by α particles, from decays of the families of 238U , 235U and 232Th, in the
different components of the detector. Cosmic rays also cause neutrons. The (α, n) reactions occur mainly with
the 13C and 18O isotopes; however, to obtain the probability of a neutron emission by (α, n) it is necessary
to consider several factors such as the distribution of energy levels of the target nucleus, parity, spin, and the
states accessible to the residual nucleus. To obtain the production of neutrons by the reaction (α, n), in the
10
different components of the detector, the code Sources-4C [7] was used, which performs one of the complete
descriptions of the (α, n) reactions currently.
Generally, the energy of the muons at sea level is in the order of the GeV; for this reason, they interact with
matter mainly by ionization. The electrons generated in this process have initial energies on the MeV scale,
but after being dispersed and producing electronic cascades, they reach tens of eV. Due to this mechanism of
interaction of the muons coming from cosmic rays, they do not represent an important source of background
in the bubble chamber due to their high levels of discrimination for processes that generate ionization and
radiation that produce electronic recoils.
5.2 Sources-4C
Sources-4C [7] is a computer code used to calculate neutron production from various sources, including alpha
particles, cosmic rays, and spontaneous őssion. It is designed to model the transport of neutrons, gamma rays,
and charged particles through materials and to calculate the resulting neutron production rates.
The code is based on Monte Carlo methods, which use random sampling to simulate the behavior of particles
as they interact with matter. Sources-4C uses Monte Carlo simulations to track the production and transport
of neutrons, gamma rays, and charged particles and their interactions with materials and other particles. The
code includes a variety of models for nuclear reactions, energy deposition, and particle transport, allowing it
to simulate a wide range of neutron production scenarios.
Sources-4C is used in various applications, including radiation shielding design, nuclear waste management, and
radiation protection. In experiments requiring low levels of neutron background, such as dark matter searches
and neutrino detectors, the code can be used to model the neutron production rates from various sources and
optimize the design of the detector and shielding materials.
The code Sources-4C determines neutron production rates and energy spectra from (α, n) reactions, sponta-
neous őssion, and delayed neutron emission due to the decay of radioactive nuclei. The code allows calculating
(α, n) source rates and spectra in four types of problems: homogeneous media, two-region interface problems,
three-region interface problems, and (α, n) reactions induced by a mono-energetic beam of α particles incident
on a layer of the target material.
Overall, Sources-4C is a powerful tool for the calculation of neutron production rates and the design and
optimization of radiation shielding systems in a variety of applications.
5.3 Neutrons from spontaneous fission
Spontaneous őssion (SF) is a nuclear decay mode in which the nucleus of a heavy radionuclide splits into
two őssion fragments and emits more than one neutron on average, without any external inŕuence. This
phenomenon occurs with radionuclides of high mass number, typically A≥230. SF is an essential process in
nuclear physics and has several applications, including producing neutron sources for scientiőc and industrial
purposes.
Around 100 radionuclides are known to undergo SF, which is considered an alternative to other decay modes,
such as alpha decay. The SF process releases a considerable amount of energy in the form of the kinetic energy
of the őssion fragments and the emitted neutrons. The average number of neutrons emitted per SF event varies
with the radionuclide, ranging from one to more than őve.
The radionuclide 252Cf is a well-known and commercially available SF neutron source widely used in various
applications such as neutron radiography, neutron activation analysis, and nuclear reactor control. The neutrons
emitted from 252Cf have a broad energy spectrum, ranging from thermal to fast neutrons, making it an ideal
source for various experiments and applications.
11
SF is a quantum mechanical process due to the barrier tunneling effect, where the heavy nucleus tunnels through
the potential barrier that opposes the separation of the two fragments. The probability of SF strongly depends
on the atomic number of the heavy element and increases rapidly with the atomic number. For instance, 230Th,
which has an atomic number Z = 90, has a half-life for SF of approximately 1.5 · 1017 years, whereas for 254Cf,
which has Z = 98, the half-life is about 60 days for this mode of decay. Thus, SF plays a crucial role in the
decay of heavy radionuclides and contributes signiőcantly to understanding nuclear physics.
5.4 (γ, n) Reactions
Photoneutron reactions (γ, n) occur when a gamma ray interacts with the nucleus of an atom, producing a
neutron and leaving the atom in an excited state. These reactions signiőcantly impact nuclear physics, as
they can be used for nuclear structure studies, element identiőcation, and isotope production. Additionally,
photoneutron reactions play a signiőcant role in astrophysics by contributing to the production of heavy
elements in stars. This occurs when emitted neutrons are captured by other atomic nuclei, forming heavier
isotopes through neutron capture reactions.
In the context of cosmic rays, photoneutron reactions are of particular interest. Cosmic rays are high-energy
particles originating outside the solar system and interacting with the Earth’s atmosphere. These cosmic rays
include gamma rays, which can initiate photoneutron reactions in the atmosphere, producing neutrons. These
neutrons can then interact with matter on the Earth’s surface, contributing to the neutron background.
The neutron background is essential for experiments that detect neutrons, such as scintillating bubble chambers.
In these experiments, neutrons can be generated by various sources, including cosmic rays and radioactive decay
processes. The background neutrons can mask the detection of signals from interesting events, leading to a
reduction in the experiment’s sensitivity.
Therefore, understanding the contribution of photoneutron reactions to the neutron background is crucial
for designing and operating scintillating bubble chambers. Characterizing the neutron background allows for
optimizing the detector’s performance and improving its sensitivity to signals from interesting events, such as
those produced by dark matter or neutrinos.
5.5 Muon-induced neutrons
Muons are subatomic particles similar to electrons but with a much greater mass. They are often produced in
cosmic ray showers when high-energy cosmic rays interact with the Earth’s atmosphere. Muons can interact
with atomic nuclei, inducing various physical reactions, including producing neutrons.
The most common reaction involving muons and neutrons is the muon-induced spallation reaction, where a
muon collides with a nucleus, causing it to break up into smaller fragments, including neutrons. Muon-induced
spallation reactions can occur in various materials, including metals, minerals, and gases.
Muon-induced neutron production has been identiőed as a signiőcant background source in many underground
physics experiments due to the high ŕux of atmospheric muons. For example, neutron production from muon
interactions can mimic or obscure the desired signal in experiments searching for dark matter, neutrino os-
cillations, or proton decay. Therefore, accurate characterization and modeling of muon-induced neutrons are
crucial for the success of these experiments. To mitigate this background, shielding, and veto systems reduce
neutrons reaching the detector. Additionally, sophisticated simulation tools have been developed to accurately
predict the neutron ŕux and energy spectrum, which can be used to optimize the experimental design and data
analysis.
Another critical application of muon-induced neutron production is studying nuclear reactors. In a nuclear
reactor, neutrons initiate and sustain the őssion process. By using muon-induced neutrons, researchers can
12
gain insights into the behavior of neutrons in a nuclear reactor, which can help improve reactor safety and
efficiency.
In the context of scintillating bubble chambers, muon-induced neutrons can be a signiőcant source of back-
ground. These neutrons can interact with the detector materials, producing signals that can be mistaken for
signals from WIMPs or neutrinos. As a result, researchers must carefully study and control the effects of
muon-induced neutrons in scintillating bubble chambers to ensure accurate and reliable results.
5.5.1 SNOLAB underground
SNOLAB is an underground laboratory in Sudbury, Canada, designed to host a wide range of particle astro-
physics and nuclear physics experiments [8]. The laboratory is situated 2 km underground in the Vale Creighton
Mine and is shielded from cosmic rays by a layer of rock. SNOLAB has been home to several signiőcant ex-
periments, including the Sudbury Neutrino Observatory (SNO) [9, 10], the DEAP-3600 dark matter detector
[11, 12], and the HALO experiment [13].
SNO was a groundbreaking experiment that observed solar neutrinos and conőrmed the solar neutrino problem.
SNO measured three neutrino ŕuxes, including electron neutrinos, muon and tau neutrinos, and electron-
ŕavored neutrinos produced in the sun’s core. The experiment’s results demonstrated that the deőcit in the
solar neutrino ŕux was due to neutrino oscillation, which occurs when neutrinos change ŕavor as they travel.
The DEAP-3600 dark matter detector is another experiment housed at SNOLAB. This experiment uses liquid
argon as a target material and aims to detect WIMPs, which are hypothesized to be a component of dark
matter. The detector is shielded from background radiation and employs several layers of shielding to further
reduce the background signal.
HALO is a low-background germanium detector experiment designed to search for neutrinoless double-beta
decay of 76Ge. This rare process, if observed, would indicate that neutrinos are their antiparticles, which would
have signiőcant implications for particle physics and cosmology.
Currently, the Scintillating Bubble Chamber collaboration plans to install a bubble chamber at SNOLAB. The
SBC is a detector technology that uses superheated liquids, such as LAr or CF3I, to detect dark matter and
other rare particle interactions. Its sensitivity to low-energy nuclear recoils makes it a promising technology
for detecting light WIMPs. By installing a bubble chamber at SNOLAB, the SBC collaboration aims to use
the low-background environment to study rare particle interactions, including dark matter.
SNOLAB is a unique facility that enables cutting-edge research in particle astrophysics and nuclear physics.
The experiments hosted at the laboratory, such as SNO, DEAP-3600, and HALO, have contributed signiőcantly
to our understanding of the universe. The future installation of the Scintillating Bubble Chamber at SNOLAB
offers an exciting prospect for advancing our understanding of dark matter and other rare particle interactions.
13
6. Monte-Carlo (MC) simulations
6.1 Introduction to GEANT4
GEANT4 is a software toolkit [14, 15, 16] for the simulation of the passage of particles through matter. Its
application areas include high energy, nuclear, and accelerator physics, as well as medical and space science
studies. The toolkit is developed by a collaboration of physicists from around the world and is used by a vast
community to simulate complex experimental setups in various research domains.
The core advantage of GEANT4 lies in its ability to model interactions of particles with materials across a wide
range of energies, accounting for the various physical processes that can occur. These include electromagnetic
interactions, hadronic processes, and optical photons, all the way to handling complex geometries and materials.
6.1.1 The Physics Behind GEANT4
GEANT4 provides a comprehensive set of physics models that describe the interactions of particles with matter
based on theoretical predictions and experimental data. The physics processes cover a broad range of domains,
from standard model particle physics to specialized models for low-energy phenomena and radioactive decay.
The modular structure of the toolkit allows for the customization of physics lists according to the speciőc needs
of the simulation project at hand. For this work, all the simulations were built on top of the GEANT4 example
named "Underground Physics" to use the same physics lists, which had been tested previously with excellent
results for PICO simulations.
6.1.2 GEANT4’s Flexibility and Applications
One of GEANT4’s key features is its ŕexibility. It allows users to deőne their experimental setup’s geometry,
select the materials involved, specify the primary particles of interest, and choose among various physics
processes. This adaptability makes GEANT4 suitable for simulating experiments in particle detectors, space
missions’ instrumentation, radiation therapy, imaging techniques, and more.
A GEANT4 simulation typically consists of the following components:
• Geometry and Materials: Users deőne the spatial layout of the experimental setup, including the
size, shape, and positioning of various components, along with the materials they are made of.
• Primary Generator: This involves specifying the primary particles to be simulated, including their
type, energy, direction, and point of origin.
• Physics List: A selection of physics models that will govern the interactions of particles within the
deőned materials.
• Event and Track Management: GEANT4 handles each simulated interaction as an event, where the
trajectories of particles (tracks) are computed step by step.
14
• Visualization and Output: The toolkit provides options for visualizing the simulation geometry and
particle tracks and recording the simulation results for further analysis.
6.1.3 The Role of GEANT4 in MC Simulations
In Monte Carlo simulations, GEANT4 is pivotal in accurately depicting particle interactions. Employing
stochastic methods allows researchers to predict the behavior and response of a physical system under random
processes, which is essential for designing experiments and interpreting data.
In the following sections, we will delve into the speciőcs of how GEANT4 is utilized within our research
framework to conduct Monte Carlo simulations for the Scintillating Bubble Chamber (SBC) detector, analyze
neutron backgrounds, and assess the detector’s sensitivity to rare event searches such as those for WIMPs.
6.2 GEANT4 implementation of the detector
The development of the GEANT4 model has been a cornerstone throughout the entire process of the detector’s
design and development. In the initial design stages of this new bubble chamber, there was already a general
concept of how it was intended to be designed, mainly derived from the learnings and proof of principles
provided by the őrst scintillating xenon-based bubble chamber.
There were many questions about the levels of backgrounds that would be present in the detector, especially
those arising from (α, n) reactions, which stemmed from the detector’s dimensions and the large number of
components for which radiopurity measurements were not available at the outset of the model construction.
The approach taken in constructing the GEANT4 code was to begin with the simulation of the heaviest
components (vacuum jacket and pressure vessel), using the radiopurity measurement values obtained by the
PICO collaboration at SNOLAB (stainless steel in the case of PV and VJ) as a őrst approximation. Another
important criterion when choosing the order of priority in the development of the model was the proximity of
the components to the detector’s sensitive material (LAr), which is why the quartz jars were also among the
őrst components to be simulated.
The third criterion of priority in deőning the path of the simulations was the neutron yield for (α, n) reactions
of the materials involved in the design, as materials like aluminum present very high values (two orders of
magnitude greater than others like steel or plastic).
In this manner, the model in GEANT4 was constructed, building the detector mainly from the LAr outward,
őrst with the more signiőcant components, until őnally, after four years of reőning the model and adapting and
modifying components (a general view of the model is presented on Fig. 6.1), a level of detail was reached where
practically all relevant components (many with masses on the order of grams) of the detector were simulated,
and many of them on several occasions, testing different geometries and materials to őnd the optimal balance
between costs, real possibilities of constructing the components, and background levels.
The development of the model and simulations were fundamental in constructing the detector. Leading the
way in the choice of materials and arrangement of the components, always with the ultimate goal of ensuring
that the contribution of backgrounds derived from (α, n) reactions remained in the order of 0.1 events/year for
simple interactions, considering a detector threshold of 100 eV.
15
(a) (b) (c)
Figure 6.1: (a) Detailed GEANT4 simulation of the SBC’s inner assembly highlighting the HDPE Castle and
Camera Ports. (b) Overview of the SBC’s GEANT4 model displaying the comprehensive detector structure,
including the vacuum jacket (VJ). (c) GEANT4 representation of the SBC’s pressure vessel (PV), showcasing
the placement of cameras and bellows. These images collectively provide a multi-faceted visualization of the
SBC detector as modeled in GEANT4, emphasizing the critical components and their spatial arrangements.
16
7. Neutron backgrounds in LAr SBC
The sensitivity of the scintillating bubble chamber using liquid argon will be achieved by minimizing back-
grounds in the energy region of interest. To search for Weakly Interacting Massive Particles, a background
level of less than one event per year is required for each potential source, including β, γ events, and neutrons,
while accounting for electromagnetic and alpha backgrounds. A maximum of 0.1 neutron background events per
year is allowed in the LAr volume, considering various sources that could contribute to the overall background
and meet the total budget requirement. Monte Carlo simulations are utilized to determine the probability of
neutron leakage Pleak for each neutron source, and these results are summarized in Table 7.1.
We can now set the upper limits for radio purities inside various detector components using the following
equation:
R =
N
Yppm · t ·m · Pleak
(7.1)
where N ≤ 0.1 neutron leakage in t = 1 years of data taking. m is mass from each detector component, and
Yppm is neutron yield from each material used in simulations (Table 7.11).
7.1 Acoustic System
One of the ways to record particle interactions in the SBC is by measuring the acoustic signal they generate.
When a WIMP and neutrino interacts with an argon nucleus, it is expected to create nuclear recoil, causing
one or more bubbles in the detector. The process of growth of the bubbles generates an acoustic signal that
propagates through the LAr until it reaches the walls of the Outer Jar, from where it spreads throughout the
quartz in the container. To ensure the highest efficiency in the collection of the acoustic signal, an arrangement
of 8 piezoelectrics is placed in the lower part of the Outer Jar, surrounding it (Figure. 7.1).
The piezo should be placed as far as possible from the LAr to reduce their contribution to the background
that their components generate. Each piezo is structured as follows: On the outside, it is made up of a copper
container placed next to the quartz of the outer jar. Inside the copper container, the piezoelectric material
is placed, which is adhered to the copper employing silver epoxy; the remaining space inside the container is
őlled with MAS Epoxy; and, outside the container, on the opposite side to the quartz, a PCB is placed.
In Table. 7.2 the background contributions of each component of the piezoelectrics and the masses considered
in each case are represented. In the case of piezoelectric material, due to having lead in its composition, in
addition to 238U and 232Th, the (α, n) reactions caused by 210Pb were also considered.
7.2 Optical system
In the process of the WIMPs and neutrinos interacting with the argon nuclei and creating bubbles, photons
are also emitted due to the scintillation of the LAr. This process contributes to a better characterization of
17
Table 7.1: Probability of a neutron mimicking a WIMP event inside the liquid argon volume. Only statistical
uncertainties are included in this Table.
Component Probability ×10−3
238U low 238U up 232Th
Outer Jar 152± 1.07 156± 1.10 148± 1.5
Inner Jar 152± 1.07 153± 1.08 154± 1.09
Pressure vessel 50.1± 0.35 45.8± 0.32 50.9± 0.36
Vacuum vessel 3.89± 0.012 4.31± 0.014 3.75± 0.012
SiPM Window 1 154± 0.98 162± 0.13 156± 0.99
SiPM Window 2 165± 1.4 168± 1.6 167± 1.6
SiPM Window 3 165± 1.4 168± 1.6 166± 1.5
SiPM Window 4 152± 0.96 155± 0.98 153± 0.97
SiPM Silicon 1 143± 0.91 144± 0.91 145± 0.92
SiPM Silicon 2 151± 0.95 152± 0.96 152± 0.96
SiPM Silicon 3 145± 0.92 139± 0.88 147± 0.93
SiPM Silicon 4 118± 0.74 121± 0.76 122± 0.77
SiPM Ceramic 1 137± 0.86 134± 0.85 138± 0.87
SiPM Ceramic 2 143± 0.93 148± 0.93 147± 0.93
SiPM Ceramic 3 141± 0.89 141± 0.89 138± 0.88
SiPM Ceramic 4 119± 0.75 119± 0.76 121± 0.76
Nanoguide 0.74± 0.031 7.24± 0.032 8.66± 0.039
Camera 2.1± 0.009 1.7± 0.008 0.24± 0.009
Lens 2.08± 0.009 2.36± 0.016 2.0± 0.008
Piezo 79.6± 0.53 79.0± 0.49 84.8± 0.54
Piezo PCB 62.7± 0.39 57.5± 0.36 59.2± 0.38
Piezo Cu encapsulation 53.0± 0.34 76.2± 0.48 68.3± 0.43
Piezo MAS Epoxy 39.1± 0.25 36.3± 0.23 36.4± 0.23
Piezo Silver Epoxy 108.0± 0.68 111.0± 0.70 110.0± 0.69
Table 7.2: Background events caused in the SBC due to neutrons coming from the different components of
the piezoelectric. The concentration of the components was measured at SNOLAB low background counting
facility [17].
Component m (g) Concentration 238U , 232Th and 210Pb Events/year (Events/year)x8
Copper container 32.7 PICO 77 <2.03 · 10−2 <1.63 · 10−1
MAS epoxy 5 PICO 47 <4.85 · 10−2 <3.88 · 10−1
PCB 1.3 COUPP 9 <1.33 · 10−3 <1.07 · 10−2
Silver epoxy 0.2 PICO 28 <5.42 · 10−3 <4.34 · 10−2
Piezo material 0.6 PICO CW26 <9.77 · 10−5 <7.81 · 10−4
Piezo material 0.2 PICO CW27 <7.45 · 10−5 <5.96 · 10−4
Piezo material 1.3 PICO CW35 <1.08 · 10−4 <8.68 · 10−4
Piezo material 1.4 PICO CW38 <1.22 · 10−4 <9.80 · 10−4
Total 42.7 <7.31 · 10−2 <5.84 · 10−1
18
Figure 7.1: Detailed views of the Scintillating Bubble Chamber’s acoustic system. The left image showcases
the GEANT4 model displaying the SiPMs and RTDs embedded within the chamber structure. The Piezos
arrangement is visualized on the right, highlighting their placement relative to the chamber. Insets provide
a focused look at the CAD model detailing the copper encapsulation, silver epoxy, and the piezo component,
along with a schematic of the vacuum space and PCB layout.
19
Figure 7.2: Visualization of the SiPM array within the Scintillating Bubble Chamber detector. (Left) 3D
representation of the detector highlighting the SiPMs and RTDs within the Cu Reŕector Structure. (Right)
Physical assembly of the SiPM array, showcasing the intricate layout and mounting of the SiPMs on the copper
structure. The inset provides a detailed view of the SiPMs holder and the Cirlex PCB, illustrating the precision
engineering required for the detector’s operation.
the interactions that occur in the detector, and for this, it is necessary to measure the emitted photons. For
the measurement of this emitted light by argon, an array of eight columns, each containing őve SiPMs, Fig.
7.2, have been installed around the detector to achieve a good collection of light with a total of 40 SiPMs.
A reŕector has been placed around the Outer Jar and up to its upper part to ensure that the light emitted
in the scintillation does not escape from the LAr without being registered by the SiPMs. This reŕector has a
layered structure that is ordered as follows, starting with the one closest to the Outer Jar: őrst a 0.5 mm thick
PTFE layer; then another aluminum layer of the same thickness; and, őnally, a sheet of 3.2 mm thick copper
that supports the reŕector.
SiPMs are encapsulated in aluminum oxide (alumina) ceramic. Inside, they have an arrangement of four silicon
pixels covered by a quartz window that allows the arrival of photons to the Si. The SiPMs are placed inside
holders made of plastic, which keeps them őxed in the reŕector structure.
The position and size of the bubbles are parameters that are recorded in the SBC through pictures. Each event
that causes a bubble activates a system of three cameras and lenses placed in the detector’s vacuum jacket;
the images are captured through the ports placed in the pressure vessel, which have quartz windows. After
passing through the ports, the light reaches the cameras through the nanoguides (Fig. 7.3).
In the case of the camera system, an alternative conőguration called the relay lens system is available, which
differs from the previous one mainly because it does not use the nanoguides and places the cameras closer to
the ports of the pressure vessel using an array of three lenses. The relay lens system currently provides sharper
images, so it will ultimately be used for both detectors (Fig. 7.4).
The results of the simulations for the optical system are summarized in the following Table. 7.3; in each case,
the goal is that each component contributes a maximum of 0.1 events/year. In these results, it is evident that
the SiPM’s ceramics (Hamamatsu in this case, which will be used for the Fermilab detector) contribute ∼ 50
20
Figure 7.3: Comparison between the CAD model of the three cameras array (top left), the GEANT4 simulation
model (bottom left), and a combined CAD and GEANT4 model of a single camera (right) comprising the optical
system of the Scintillating Bubble Chamber with the nanoguide setup. Key components, including the sensor
cover, camera, peak rods, nanoguide, springs, alignment ring, and camera lens holder, are labeled for reference.
The sapphire viewport allows for visual access, while the intricate nanoguide structure is critical for the precise
guidance of photons to the SiPM sensors. The physical assembly illustrates the integration of these components
into the detector system.
21
Figure 7.4: Comparison between the CAD model and GEANT4 simulation model of the SBC’s optical system
showcasing the relay lens system. The diagram identiőes the sensor cover, camera, copper rods, aspheric lenses,
stainless steel (SS) rods, lens holders, iris holders, camera lens holders, and sapphire viewports. This alternative
conőguration to the nanoguide system places cameras closer to the pressure vessel ports for enhanced image
clarity.
22
events/year; in this instance, it does not pose a problem as this detector will be primarily used for calibration
purposes.
Table 7.3: Background events caused in the SBC due to neutrons coming from the different components of
the optical system. The masses in the table are for a single component, and the events/year are for the total
number of components: for SiPM, it is x8, and for nanoguides, cameras, and lenses, x3. The concentration of
the components was measured at SNOLAB low background counting facility [17].
Component m (g) Concentration 238U , 232Th and 210Pb Events/year
SiPM quartz 1 0.30 SBC P02 (2.37± 0.25) · 10−1
SiPM quartz 2 0.30 SBC P02 (2.50± 0.27) · 10−1
SiPM quartz 3 0.30 SBC P02 (2.50± 0.27) · 10−1
SiPM quartz 4 0.30 SBC P02 (2.30± 0.25) · 10−1
SiPM silicon 1 0.05 SBC P02 (8.27± 0.93) · 10−3
SiPM silicon 2 0.05 SBC P02 (8.69± 0.98) · 10−3
SiPM silicon 3 0.05 SBC P02 (8.78± 0.99) · 10−3
SiPM silicon 4 0.05 SBC P02 (7.99± 0.90) · 10−3
SiPM ceramic 1 0.96 SBC P02 13.80± 2.08
SiPM ceramic 2 0.96 SBC P02 14.40± 2.16
SiPM ceramic 3 0.96 SBC P02 14.40± 2.17
SiPM ceramic 4 0.96 SBC P02 13.20± 1.99
SiPM holder 1 22.68 SBC P01 <1.02 · 10−2
SiPM holder 2 22.68 SBC P01 <1.09 · 10−2
SiPM holder 3 22.68 SBC P01 <1.07 · 10−2
SiPM holder 4 22.68 SBC P01 <9.67 · 10−3
Nanoguide 415.80 SBC P06 <3.27 · 10−2
Cameras 1.05 SBC P03 <1.53 · 10−2
Lenses 10.60 SBC P04 <1.96 · 10−1
Reŕector PTFE 43.54 PICO 70 <1.32 · 101
Reŕector Cu 1.19 · 103 PICO 87 <5.85 · 10−1
Total 1590 <57.88
For the SNOLAB detector, due to the signiőcant background levels produced by Hamamatsu SiPMs, a mea-
surement campaign of different SiPM options was required. The SiPMs from FBK proved to be the purest,
as indicated by measurement results SBC L04 and P01, which can be accessed [17]. Subsequent simulations
demonstrated that the contribution to the background from all components of the FBK SiPMs (Quartz win-
dow, ceramic package, silicon and holder) turned out to be less than 0.06 events/year. Therefore, the total
contributions of the optical system for the SNOLAB chamber can be reviewed in Table 7.4.
23
Table 7.4: Background events caused in the SBC due to neutrons coming from the different components of
the optical system for the SNOLAB chamber. The masses in the table are for a single component, and the
events/year are for the total number of components: for SiPM, it is x8, and for nanoguides, cameras, and
lenses, x3. The concentration of the components was measured at SNOLAB low background counting facility
[17].
Component m (g) Concentration 238U , 232Th and 210Pb Events/year
SiPMs 24 SBC P01 and SBC L04 <6.00 · 10−2
Nanoguide 415.80 SBC P06 <3.27 · 10−2
Cameras 1.05 SBC P03 <1.53 · 10−2
Lenses 10.60 SBC P04 <1.96 · 10−1
Reŕector PTFE 43.54 PICO 70 <1.32 · 101
Reŕector Cu 1.19 · 103 PICO 87 <5.85 · 10−1
Total 1466 <13.25
7.3 Inner assembly
This section will group the results of the simulations of all the components located inside the vacuum vessel
that have not been taken into account in the previous sections. Several factors are taken into account to decide
which components of the SBC should be simulated, the most important of which is the distance at which the
LAr component is, its mass, and the material from which it is made.
The components that will be taken into account in this section are: HDPE cast, this shield is a block in the
form of a cylindrical ring that surrounds the outer jar to shield the LAr from neutrons; the outer and inner jars
are the quartz containers that conőne the LAr and have relative movement between them to vary the pressure
of the liquid; pressure vessel, inside is contained the CF4 that constitutes the hydraulic ŕuid of the detector
(Table 7.5).
Approximately seventy-őve resistance temperature detectors (RTDs) are distributed within the pressure vessel,
which was also simulated due to their proximity to the LAr. However, their contribution to the backgrounds
is not signiőcant. Their geometry and distribution in the simulations are represented in Fig. 7.5.
Table 7.5: Background events caused in the SBC due to neutrons coming from the different components of
the inner assembly. The concentration of the components was measured at SNOLAB low background counting
facility [17].
Component m (kg) Concentration 238U , 232Th and 210Pb Events/year
Inner jar 4.00 PICO 46 <3.53
Outer jar 5.02 PICO 46 <4.43
HDPE castle 5.00 PICO 34 <3.34 · 10−1
PV 80 SBC CW04 <1.09
VJ 120 SBC CW04 <3.30
Inner Bellows 2 SBC V01 <1.20 · 10−2
Outer Bellows 4 SBC V01 <3.70 · 10−2
RTDs 0.1 SBC CW05 and SBC CW06 (5.50± 1.08) · 10−1
24
Figure 7.5: A visual representation of the SBC detector’s internal assembly showcasing the SiPMs and RTDs
integrated within the copper reŕector structure. The CAD model offers a detailed perspective of the arrange-
ment, complemented by the GEANT4 model simulation that highlights the strategic placement of components
to optimize detection efficiency. The inset provides a close-up view of the RTD unit, detailing the connectivity
and thermal management components critical to the detector’s functionality.
25
7.4 Radon exposure
Radon exposure generates surface contamination in the SBC from radon diffusion and radon daughter depo-
sition lead to α-decaying 210Po. These alphas interact with detector material and produce (α, n) neutrons.
To have N ≤ 0.1 neutron leakage in the LAr in one year of data taking, the maximum alpha rate from 210Po,
RPo, is shown in Table. 7.6 , calculated from the following:
RPo =
N
t · Yα · Pleak
(7.2)
Table 7.6: Maximum activity allowed due to 210Po to ensure that each component contributes no more than
0.1 events per year.
Component Yα (neutronss·Bq ) RPo (Bq)
Outer Jar 8.95 · 10−08 3.37± 0.51 · 10−03
Inner Jar 8.95 · 10−08 2.90± 0.44 · 10−03
Pressure vessel 1.53 · 10−08 1.49± 0.22 · 10−01
where neutron yield Yα = 8.95 · 10−08 per 210Po decay in quartz and Pleak = 1.55 · 10−01 is the probability of
a 210Po (α, n) neutrons in the Outer Jar producing a background event. The maximum alpha rate from 210Po
tolerable in the Outer Jar is 3.37± 0.51 · 10−03 Bq.
7.5 Radon diffusion
Radon can diffuse into materials, and the long-lived 210Pb can build up in the surface layer and then feed the
210Po, which undergoes α-decay. We can assume that every 222Rn decay populates the same surface layer
region with one 210Pb atom. There will be a lag between the 210Pb deposition and the α-decay of the 210Po,
where the latter catches up over time and eventually reaches equilibrium. We will assume equilibrium here,
leading to more conservative radon exposure tolerance calculations.
The parameters of interest for radon diffusion into quartz are the diffusion length de = 1 mm and the solubility
S = 10. Rate of 210Po decay is then:
RPo = de · S ·Rn · T ·A · 1
τ
(7.3)
T =
RPo · τ
de · S ·Rn ·A (7.4)
Where Rn is the radon concentration, T is the maximum exposure time, A is the surface area, and τ = 32.2
years is the lifetime of 210Pb. Radon concentration underground at SNOLAB is Rn ≈ 100Bq/m3; Table 7.7
lists the areas and maximum exposure time for the pressure vessel, outer and inner jar.
7.6 Radon daughter deposition
The 210Po deposition rate on surfaces from exposure to radon in the air depends on many factors, including
aerosol concentration in the room environment, relative humidity, and air velocity. We use an average deposition
26
Table 7.7: Maximum exposure time (T) allowed due to 210Po to ensure that each component contributes no
more than 0.1 events per year.
Component A (m2) T (month)
Outer Jar 3.70 · 10−01 3.03± 0.46
Inner Jar 3.07 · 10−01 4.24± 0.64
Pressure vessel 1.35 42.58± 6.41
rate D = 10−3Bq/m2 210Po per Bq/m3 of 222Rn per year of exposure [18]. The maximum exposure time T in
the air to limit the amount of 210Po introduced from 222Rn daughter implantation is then:
T ≤ RPo
D ·Rn ·A (7.5)
The application of equation 7.5 to the components with the largest surface area yields the maximum allowed
exposure time, as shown in Table 7.8.
Table 7.8: Maximum exposure time (T) in the air allowed to limit the amount of 210Po introduced from 222Rn
daughter implantation to guarantee no more than 0.1 events per year.
Component A (m2) T (month)
Outer Jar 3.70 · 10−01 0.94± 0.14
Inner Jar 3.07 · 10−01 1.32± 0.20
Pressure vessel 1.35 13.22± 1.99
7.7 Radon emanation
The alpha backgrounds constrain radon emanation limit for detector materials inside the pressure vessel we
can tolerate. Radon atoms emanating from the detector materials outside of the Pressure Vessel and inside the
CF4 shell are likely trapped on the outer surface of the Outer Vessel. They interact with stainless steel and
quartz to produce (α, n) neutrons. The maximum radon emanation rate from Outer Jar, RRn < 2.74 · 10−4Bq
can be calculated from Equation 7.2, with neutron yield on CF4 Yα = 6.95 · 10−5 including all four alphas in
the 222Rn decay chain. This case where all the 222Rn is being assumed to be emanating from the outer jar is
the worst-case scenario, and we will consider it an extreme case.
The radon emanation limit we can tolerate, R, can be calculated by
R = RRn/A
∗ (7.6)
Where A∗ is the surface or length for different detector components; Table. 7.9 summarizes our radon emanation
limits for different detector components.
A more realistic case is to assume that 222Rn emanation takes place in the hydraulic ŕuid; in this situation,
the maximum radon emanation rate from CF4, RRn < 1.02 · 10−3Bq can also be calculated from Equation 7.2,
using a neutron yield on CF4 Yα = 6.95 · 10−5. The results of this simulation are listed in the Table. 7.10.
27
Table 7.9: Maximum allowed activity (R) to limit the amount of 222Rn emanation to guarantee no more than
0.1 events per year, an extreme case where 222Rn is assumed to emanate from the outer jar.
Component A(m2)[A∗(m)] R(mBq/m2)[R∗(µBq/m)]
Outer Jar 0.37 0.74± 0.11
Inner Jar 0.31 0.89± 0.13
Pressure vessel 1.35 0.20± 0.03
HDPE Shielding 0.72 0.38± 0.06
Reŕector 0.56 0.49± 0.07
SiPM Cable 15∗ 18.20± 2.81∗
Table 7.10: Maximum allowed activity (R) to limit the amount of 222Rn emanation to guarantee no more than
0.1 events per year, where 222Rn is assumed to emanate from the hydraulic ŕuid.
Component A(m2)[A∗(m)] R(mBq/m2)[R∗(µBq/m)]
Outer Jar 0.37 2.76± 0.42
Inner Jar 0.31 3.33± 0.50
Pressure vessel 1.33 .76± 0.11
HDPE Shielding 0.72 1.41± 0.21
Reŕector 0.56 1.81± 0.27
SiPM Cable 15∗ 68.10± 10.22∗
Table 7.11: Neutron yield for the material used in the SBC. Neutron production is calculated from SOURCES-
4C, and its uncertainty is 15%.
Material 238U low (n/s/g/ppb) 238U up (n/s/g/ppb) 232Th (n/s/g/ppb)
Acrylic 8.50 · 10−12 1.50 · 10−11 3.98 · 10−12
Alumina 1.04 · 10−10 2.24 · 10−11 5.48 · 10−11
Aluminum 1.47 · 10−10 1.80 · 10−11 8.20 · 10−11
Beryllium 6.53 · 10−9 1.49 · 10−9 2.93 · 10−9
CF4 9.04 · 10−10 1.18 · 10−10 4.41 · 10−10
Copper 5.22 · 10−13 1.36 · 10−11 7.34 · 10−13
Epoxy 5.26 · 10−10 1.19 · 10−10 2.40 · 10−10
Fluorine 1.07 · 10−9 1.37 · 10−10 5.23 · 10−10
PCB 9.31 · 10−12 1.50 · 10−11 4.42 · 10−12
Photopolymer 6.88 · 10−12 1.49 · 10−11 3.13 · 10−12
Piezo 5.79 · 10−12 1.49 · 10−11 3.62 · 10−12
Polyethylene 8.63 · 10−12 1.49 · 10−11 4.10 · 10−12
Quartz 1.24 · 10−11 1.47 · 10−11 6.31 · 10−12
Silicon 2.02 · 10−11 1.44 · 10−11 1.08 · 10−11
Stainless steel 8.68 · 10−13 1.36 · 10−11 6.23 · 10−12
Titanium 3.47 · 10−11 1.96 · 10−11 2.60 · 10−11
PTFE 9.60 · 10−10 1.24 · 10−10 4.68 · 10−10
Norite 3.95 · 10−11 1.60 · 10−11 2.10 · 10−11
28
7.8 Dust deposition
In SNOLAB, we can safely assume a dust deposition rate of < 0.01 g/m2/year (after cleaning the surface of
interest). With an exposure time of 1 year, the amount of dust is 0.0412 g on the Vacuum Vessel (4.12 m2 of
the surface) outer surface and 0.0133 g on the Pressure Vessel (1.33 m2 of the surface). Since the dust is from
the mine, it is expected that the uranium and thorium contents are the same as the rock, i.e., S = 1.11 ppm
for 238U and 5.56 ppm for 232Th. The background event rate can be calculated by:
N = S · Yppm · t ·m · Pleak (7.7)
With Yppm from Table 7.11 for norite in Vacuum and Pressure vessel, Table. 7.1 for Pleak, this contributes a
total of N < 9.16 · 10−3 for Pressure vessel and N < 8.89 · 10−4 for Vacuum vessel background events per year.
The same calculations can be performed for the inner and outer jars; these results are in Table 7.12.
Table 7.12: Rate of events in the LAr caused neutrons from the dust deposition in different detector components.
Component A(m2) Events/year
Vacuum vessel 4.12 <8.89 · 10−4
Inner Jar 0.31 <2.64 · 10−3
Outer Jar 0.37 <3.12 · 10−3
Pressure vessel 1.33 <9.16 · 10−3
7.9 (γ, n) reactions at SNOLAB
In the speciőc context of the Scintillating Bubble Chamber planned for deployment at SNOLAB, photoneutron
(γ, n) reactions are paramount in shaping the overall background landscape. The necessity for effective shielding
to attenuate external background signals to acceptable thresholds implies the presence of substantial shielding
materials ś typically in the range of several tons. These materials are potential sites for photonuclear reactions,
leading to the production of neutrons. These neutrons, in turn, represent a signiőcant source of background
events for the detector. Thus, a meticulous analysis of the materials and their spatial arrangement is crucial.
The strategic positioning of shielding against external radiation must be carefully planned to avoid inadvertently
introducing new background sources.
At SNOLAB, the proposed shielding design, primarily aimed at curtailing backgrounds induced by cosmic
muons, involves a rectangular enclosure with a half-inch thick high-density polyethylene (HDPE) structure.
This enclosure is intended to house a water-based shielding system, enveloping the detector with a 50 cm
thickness on all sides except the bottom. Supporting the detector is an HDPE platform, also 50 cm thick and
square-shaped with each side measuring 2 meters. This speciőc shielding and support structure conőguration,
designed to optimize the balance between effective radiation attenuation and minimal introduction of new
background sources, is illustrated in Fig. 7.6.
To conduct the simulations of backgrounds generated by photonuclear reactions, a piecemeal approach was
employed; in essence, the most straightforward path would have been to simulate the gamma-ray ŕux over the
detector and subsequently tally the number of argon nuclei scattered within due to elastic neutron scattering.
However, multiple simulations were undertaken to validate the (γ, n) reactions in GEANT4, and the őndings
indicated that the code version in use (10.03.p03) did not simulate this process correctly. For this reason, the
decision was made to simulate each component of the process separately.
29
Figure 7.6: Visual representation of the shielding and photonuclear reaction simulation for the Scintillating
Bubble Chamber at SNOLAB. The left image displays the chamber encased by a 50 cm water shield housed
within a half-inch thick polypropylene box designed to attenuate muon-induced background radiation. On
the right, two scenarios of gamma-ray distributions used in (γ, n) reaction simulations are exhibited: The top
right image demonstrates gamma rays in the 10 to 100 MeV range, which are generated above the detector
to simulate cosmic-ray-induced cascades. The bottom right image showcases the 2 to 10 MeV gamma rays
originating from an encompassing sphere, simulating radiation from radioactive isotopes in the surrounding
rock of SNOLAB. This spherical distribution reŕects the isotropic nature of gamma radiation emanating from
the decay of environmental isotopes, further illustrating the intricate levels of realism incorporated into the
simulation to ensure comprehensive background analysis.
30
Table 7.13: Flux of gamma rays per energy range and their respective sources used on SNOLAB´s (γ, n)
simulations.
Energy (MeV) Flux (γ/cm²/year) Data source
2-3 (7.96± 0.80)× 105 SNO Gamma-Rays Measurements Report [19]
3-4 (2.1± 0.2)× 104 Alan Robinson´s PhD Dissertation [18]
4-5 195.0± 31
5-6 46± 17
6-7 34± 13
7-8 52± 10
8-9 31.79± 0.7 Calculations by UNAM´s group (Internal comunication)
9-10 1.50± 0.04
10-11 (1.71± 0.4)× 10−1
11-13 (4.38± 0.2)× 10−2
13-15 (1.70± 0.5)× 10−3
15-20 (2.46± 0.6)× 10−3
20-30 (1.35± 0.5)× 10−3
30-60 (1.87± 0.6)× 10−3
60-100 (9.74± 3)× 10−4
The initial step involved acquiring the gamma ŕux present in the SNOLAB cavern, gleaned from various sources
and corroborated by multiple results, accessible in Table 7.13. The gamma-ray ŕux can primarily be bifurcated
into two sources: the őrst for gammas with energies ranging from 2 to 10 MeV that originate from the decay
of radioactive elements within the cavern’s rock. These particles were generated from a sphere encircling the
detector for simulation purposes, with gammas emitted inward from its surface. For gammas with energies
between 10 and 100 MeV, their origin is principally linked to cascades generated by cosmic rays; hence their
trajectory is predominantly from top to bottom. They were generated on a square surface above the detector,
pointing downwards; the described geometries are depicted in Fig. 7.6. Once the simulations were performed,
the gamma ŕuxes were recorded in the detector’s heaviest components and the water shield for subsequent
propagation (Fig. 7.7).
Upon capturing the gamma particle ŕuxes within each of the signiőcant mass components of the detec-
torÐnamely the Water Shield, Pressure Vessel (PV), Liquid Argon (LAr), High-Density Polyethylene (HDPE),
and Carbon Tetraŕuoride (CF4)Ðnormalized histograms for each constituent were constructed. Thereafter,
leveraging the known cross-sections of (γ, n) reactions [20] in tandem with the natural abundance of each iso-
tope present within the materials, the neutron rate for each component was ascertained. The culmination of
this process involved multiplying the neutron rates derived from (γ, n) reactions by the probability of these
neutrons triggering bubble formation in the LAr. This probability, denoted as Pleak, is determined by simu-
lating neutrons isotropically in each material with energies ranging from 0.1 to 1 MeV, thus yielding the őnal
rate of LAr bubble-inducing events produced by these neutrons.
A more reőned data processing approach was necessary for the water shield due to the extensive amount of
shielding, which resulted in a substantial contribution to background events, exceeding a hundred background
events per year. In this instance, the neutrons generated in the water were not simulated using a homogeneous
energy spectrumÐa method corresponding to a preliminary approximation. Instead, equation 7.8 was employed
to more precisely determine the emission energy of the neutrons, yielding the spectrum displayed in Fig. 7.8.
The following equation is essential in determining the kinetic energy, Epn, of a neutron after a photonuclear
interaction, where a gamma-ray photon impacts a nucleus, causing the ejection of the neutron:
31
Figure 7.7: Gamma ŕux spectra measured for various components of the detector, arranged from top-left to
bottom-right: Water Shield, Pressure Vessel (PV), Liquid Argon (LAr), High-Density Polyethylene (HDPE),
and Carbon Tetraŕuoride (CF4). An order of 108 gamma particles was simulated for each component to assess
their ŕux distribution. These spectra provide critical insights into the photonic background, inŕuencing the
design and material choices for the detector’s construction to minimize backgrounds.
Figure 7.8: (Left) Schematic representation of the inelastic photonuclear interaction where a photon impacts a
target nucleus, resulting in the emission of a neutron. (Right) The energy spectrum of neutrons generated in
water through photonuclear reactions involving 2D, 16O, 17O, and 18O nuclei, calculated using equation 7.8.
32
Epn ≈ A− 1
A
(
Eγ −Q−
E2
γ
2mnc2(A− 1)
)
+
Eγ
A
√
2(A− 1)
mnc2A
(Eγ −Q) cos θ, (7.8)
where:
• Epn is the kinetic energy of the neutron post-reaction.
• A denotes the mass number of the target nucleus, indicating the sum of protons and neutrons.
• Eγ represents the energy of the inciting gamma-ray photon.
• Q is the reaction’s Q-value, indicating the energy released or absorbed during the reaction.
• mn is the rest mass of the neutron.
• c stands for the speed of light in a vacuum.
• θ is the angle at which the neutron is emitted concerning the direction of the incident photon, which
affects the kinetic energy distribution of the ejected neutrons and was assumed with an average value of
60◦ [21].
Using the previously described methods, the contributions from the detector’s most massive components to
the background events were determined arising from γ, n reactions. For each material, isotopes that could
potentially yield neutrons, corresponding to the energy spectrum of gamma rays, were considered. The results
are displayed in Table 7.14, and as evidenced, neutrons produced in water constitute the most signiőcant
contribution to the background events.
Table 7.14: Contributions of detector components to single bubble events in LAr due to photonuclear reactions.
Component Area (cm2) Pleak Used Isotopes Flux (γ/cm2/year) Event/year
Water Shield 30.4× 104 5.83× 10−6 2H,16 O,17 O,18 O (1.71± 0.17)× 106 0.59± 0.06
PV 9.76× 103 8.77× 10−3 12C,13 C,53 Cr,54 Cr,57 Fe (1.24± 0.12)× 106 0.26± 0.03
61Ni,62 Ni,64 Ni,33 S,34 S,36 S,29 Si,30 Si
LAr 2.79× 103 0.24 38Ar,40 Ar (3.83± 0.39)× 105 0.001± 0.0001
HDPE 4.27× 103 3.59× 10−2 2H,12 C,13 C (4.06± 0.41)× 105 0.013± 0.0014
CF4 9.76× 103 4.82× 10−2 12C,13 C,19 F (9.41± 0.95)× 105 0.007± 0.0007
Total 0.895± 0.0671
7.10 Conclusions
The meticulous examination of neutron backgrounds in the Scintillating Bubble Chamber with Liquid Argon
underscores the paramount signiőcance of background suppression for directly detecting Weakly Interacting
Massive Particles. By imposing stringent upper limits on radio purities within detector components and
leveraging comprehensive Monte Carlo simulations, we have identiőed a path toward achieving the desired
background level of less than one event per year for neutron backgrounds. This rigorous approach, encapsulated
by Equation 7.1, is pivotal for distinguishing potential WIMP signals from the underlying background.
Our analyses, Table 7.15, revealed that reŕector systems represent the most signiőcant contributor to the overall
background (∼ 50%); the rest of the components contribute minimally to backgrounds thanks to the strategic
placement of piezoelectrics and the utilization of a sophisticated SiPM array. Adopting the relay lens system
33
promises enhanced image clarity, optimizing the detector’s performance. Equally crucial is the management of
radon exposure, which has been meticulously controlled to prevent signiőcant contributions to the background.
In summary, the SBC LAr’s design and operational strategies, including radon emanation mitigation and dust
deposition management, are poised to fulőll the background event criteria essential for the elusive WIMP
search. We are conődent that the collective measures described herein will fortify the SBC-LAr’s capability to
detect WIMPs, bringing us closer to unraveling the mysteries of dark matter.
Table 7.15: Summary of the bulk simulation results showing the contribution of background events generated
by (α,n) reactions on the detector components. The contributions are listed in descending order, with the
reŕector system identiőed as the primary source of neutron backgrounds.
Component Events/year with Th = 100 ev
Full Reŕector System <13.78
Outer Jar <4.43
Inner Jar <3.53
Vacuum jacket (VJ) <3.30
Pressure vessel (PV) <1.09
PV Cables <0.63
RTDs <0.56
HDPE Castle <0.34
SiPMs system <0.06
Bellows outer <0.037
Bellows inner <0.012
Cameras relay lens system 1.03± 0.15
Piezos system 0.61± 0.15
Total <27.25
34
8. Physics reach of a low threshold scintillating argon bub-
ble chamber in coherent elastic neutrino-nucleus scat-
tering reactor experiments
8.1 Introduction
Investigating neutrino properties and interactions remains one of the most intriguing areas in modern particle
physics. Despite their elusive nature, neutrinos provide a window into physics beyond the Standard Model
and are crucial to understanding fundamental aspects of the universe. The discovery of neutrino oscillations,
which implies that neutrinos have mass, has been a breakthrough in the őeld [22, 23, 24]. This phenomenon
is not accounted for in the Standard Model and points towards new physics, such as non-standard neutrino
interactions (NSI) or additional neutrino states like sterile neutrinos [25, 26, 27].
Coherent elastic neutrino-nucleus scattering has recently emerged as a powerful tool for probing neutrino
properties and interactions [28, 29]. The CEνNS process, in which a neutrino scatters off an entire nucleus
coherently, was őrst observed by the COHERENT collaboration using cesium iodide and liquid argon detectors
[30]. This discovery opens new avenues for investigating NSI [31, 32] and measuring the weak mixing angle at
low momentum transfer [33].
The challenge lies in designing a detector sensitive enough to detect the low-energy nuclear recoils characteristic
of CEνNS while also capable of operating at sub-keV thresholds over extended durations to reduce background.
Currently, various detectors are either operational or under construction to meet these criteria [34, 35, 36, 37,
38, 39, 40, 41, 42]. A notable development in this context is the SBC collaboration’s efforts to create a low-
threshold argon scintillating bubble chamber, aiming for a threshold as low as 100 eV. This innovative device
demonstrates a remarkable insensitivity to electromagnetic interactions, signiőcantly reducing the majority of
background interferences [43, 44].
The neutrino sector’s landscape is further enriched by the possibility of CP violation and the existence of light
sterile neutrinos [45, 46]. The possibility of light sterile neutrinos can be explored in reactor-based experiments
like CONUS [35], which are sensitive to the electron anti-neutrino ŕux from nuclear reactors. Such experiments
can signiőcantly improve our understanding of neutrino properties, including their mass ordering [47].
The potential of the Scintillating Bubble Chamber in probing various aspects of new physics is substantial.
This work has highlighted its sensitivity to key parameters such as the weak mixing angle, neutrino magnetic
moment, and the pursuit of a light Z′ gauge boson mediator [44]. Additionally, exploring the detector’s
capability in investigating other new physics scenarios, such as light scalar mediators, sterile neutrinos, unitarity
violation, and non-standard interactions, would be beneőcial. The comprehensive analyses presented here
are also relevant to other techniques capable of achieving 100-eV nuclear recoil thresholds while eliminating
electron-recoil backgrounds and scaling effectively to 10ś100-kg target masses.
This chapter focuses on the development and physics reach of a novel detector technology: a low threshold
scintillating argon bubble chamber [48]. This technology combines the advantages of a bubble chamber’s
background rejection capabilities with the energy resolution of a scintillator. It has the potential to measure
35
CEνNS with unprecedented precision and explore new physics scenarios, such as NSI and sterile neutrinos, in
the neutrino sector [39, 49, 50].
Furthermore, the unique properties of argon as a target material offer sensitivity to low-energy neutrino interac-
tions, which are crucial for understanding the neutrino-nucleus interaction cross-sections at low recoil energies
[51, 52]. This approach provides a new method to probe the Standard Model and opens up possibilities for
direct detection of dark matter particles [53, 54].
8.2 Experimental Description
Superheated liquids have been a cornerstone in the quest for dark matter, particularly in the search for Weakly
Interacting Massive Particles. This approach has been notably utilized in the PICO Collaboration’s ŕuorocar-
bon bubble chambers [1, 55, 56, 57]. In these devices, nuclear recoils in the superheated targets generate single
bubbles, which grow to a macroscopic size if the nuclear recoil energy surpasses a threshold determined by the
temperature and pressure of the target ŕuid [58].
These bubble chambers are notably insensitive to electron recoils when operated with nuclear recoil thresholds
above a few keV, as nucleation efficiency falls below 10−10 [59]. This insensitivity is due to the nucleation
process depending on the energy deposited and the stopping power of the incoming particle.
Recent advancements by the SBC Collaboration have highlighted the enhanced performance of liquid-noble
bubble chambers over ŕuorocarbon-based detectors. These chambers can operate at signiőcantly higher degrees
of superheat, allowing for lower thresholds [4]. A xenon bubble chamber recently demonstrated operation at
thresholds as low as 500 eV while remaining insensitive to electron recoil backgrounds [51]. This achievement
proves the feasibility of lowering thresholds using noble liquids and demonstrates the simultaneous occurrence
of bubble nucleation and scintillation by nuclear recoils.
Building on these developments, the SBC Collaboration is designing a 10-kg liquid argon bubble chamber
with an energy threshold target of 100 eV. This innovative detector will incorporate Silicon Photomultipliers
(SiPMs) to collect scintillation light, aiding in the vetoing of high-energy events around or above 5-keV nuclear
recoil equivalent [60]. Such experimental techniques and developments pave the way for new opportunities
to study CEνNS in nuclear reactors, employing noble liquids at very low thresholds devoid of electron recoil
backgrounds.
This work considers two primary detector conőgurations (Table 8.1). The őrst, setup A, involves a 10-kg LAr
chamber with a 100-eV energy threshold, positioned 3 meters from a 1-MWth reactor (Fig. 8.1). In this setup,
approximately eight neutrino events per day above the threshold are anticipated [48]. The second, setup B,
entails a 100-kg LAr chamber with the same energy threshold but located 30 meters from a 2000-MWth power
reactor. This conőguration is expected to detect around 1570 neutrino events per day above the threshold [48].
Both setups account for a 2.4% uncertainty in the anti-neutrino ŕux and a 5% systematic uncertainty in the
energy threshold. Additionally, a variant of setup B, referred to as setup B(1.5), assumes a 1.5% uncertainty
in the anti-neutrino ŕux and a 2% systematic uncertainty in the energy threshold [48].
Through these innovative conőgurations and the deployment of low-threshold noble liquid technologies, the SBC
Collaboration aims to signiőcantly advance the őeld of neutrino physics and our understanding of CEνNS.
8.2.1 Backgrounds
To estimate the primary background contributions, mainly from cosmic ray-induced neutrons and the reactor
itself, a GEANT4 Monte Carlo simulation was developed [14, 15, 16]. While cosmic ray backgrounds can be
statistically subtracted using a reactor-off dataset, reactor-induced backgrounds require in-situ measurements
and simulations for accurate estimation.
36
Figure 8.1: Schematic representation of the CEνNS experimental setup at ININ, showcasing the liquid argon
bubble chamber and its multi-layered shielding system, including borated concrete, water, polyethylene, and
lead walls, all meticulously arranged to optimize neutrino detection while minimizing backgrounds [44].
37
Table 8.1: Reactor and cosmogenic backgrounds for the conőgurations A, B, and B(1.5). In the case of the
(γ,n) reactions, the isotopes 2H, 207Pb y 208Pb where considered in water and lead, respectively. The muon-
induced neutrons were calculated, assuming the interactions occur in the shielding of water and concrete. For
conőgurations B and B (1.5), the backgrounds generated by the reactor are not included because the detector
is at a sufficient distance (30 m) to be considered negligible.
Setup LAr Power Distance CEνNS Anti-ν ŕux Threshold Backgrounds (events/day)
mass events per uncertainty uncertainty Reactor Cosmogenic Total
(kg) (MWth) (m) day (%) (%)
Neutrons (γ,n) Thomson Neutrons (µ,n)
A 10 1 3 8.1 2.4 5 0.003 0.22 0.0002 0.38 0.47 1.07
B 100 2000 30 1565.2 2.4 5 0 0 0 125 55 180
B(1.5) 100 2000 30 1565.2 1.5 2 0 0 0 125 55 180
Background studies were conducted at the National Institute for Nuclear Research (ININ) near Mexico City for
the 1 MWth reactor conőguration and at Laguna Verde on the east coast of Mexico for a 2000 MWth reactor
(cosmic rays only, not reactor). For setup A, the simulation includes the ININ experimental hall, surrounded
by approximately 3 meters of high-density borated concrete, which shields cosmogenic neutrons. Additional
shielding consists of 25 cm of water, 5 cm of polyethylene, a 30 cm thick lead wall, and another 20 cm thick
lead wall adjacent to the bubble chamber. The bubble chamber is positioned 3 meters from the reactor core
center, including 1.6 meters of water shielding provided by the reactor pool.
Neutron production by the reactor core was estimated using measurements at ININ [61, 62]. Nuclear recoils due
to (γ, n) reactions and Thomson (γ-nucleus elastic) scattering from reactor-produced γ-rays were estimated
using a gamma ŕux simulation for a TRIGA Mark III reactor, modeled in MCNP [37].
Cosmogenic neutrons were simulated using the CRY code [63] (Fig. 8.2), and neutrons induced by muons
interacting with materials at the deployment site were estimated using a parametrization from [64]. The
simulations predict 0.25 events/day from reactor-produced backgrounds, comprising various contributions,
including reactor neutrons, reactions in water, and (γ, n) reactions in lead. The shielding design reduces the
gamma ŕux from the reactor core to approximately 1 Hz in the LAr target volume, making electron recoil
backgrounds negligible. Thomson scattering contributes a minor fraction of the backgrounds.
The simulations estimate 0.85 events/day from backgrounds for cosmic rays, including contributions from
cosmogenic and muon-induced neutrons in water and concrete. For setups B and B(1.5), the backgrounds from
the reactor core are considered negligible due to the greater distance (30 m) from the core, typically outside the
reactor building. The proposed shielding for these setups includes 3 meters of water and 50 cm of polyethylene,
reducing cosmic ray backgrounds to 180 events/day.
Internal radioactivity backgrounds are negligible for all conőgurations, accounting for less than 1% of the signal,
assuming purity levels similar to those in materials used by the PICO Collaboration [1, 56].
Overall, the estimated background contribution to the signal is approximately 5% (from the reactor) and 11%
(from cosmic rays) for setup A, and 12% (from cosmic rays) for setups B and B(1.5). The reported physics
reach assumes these background levels. A systematic uncertainty of 10% is applied to reactor backgrounds,
which can be characterized in situ from non-signal regions. Cosmic ray backgrounds are statistically subtracted
with no systematic uncertainty.
8.2.2 Calibration
The bubble chamber’s response to nuclear recoils is characterized by a nucleation efficiency function, represent-
ing the likelihood of recoil with energy T to nucleate a bubble. This probability rises from 0 to 100% around an
energy threshold ET . For the physics reach outlined in this work, a Normal Cumulative Distribution Function
(Gaussian CDF) is assumed:
38
Figure 8.2: Signal and neutron background rates above threshold for setups A (top) and B (bottom). Setup
A’s background comes from the reactor and cosmogenic neutrons. In contrast, only cosmogenic neutrons are
shown in setup B since the backgrounds produced from the core are negligible at 30 m (usually outside of the
reactor building). A cumulative distribution function (CDF) was assumed for the threshold efficiency [44].
39
Pr(T ) =
1
2
(
1 + erf
(
T − ET
σ
√
2
))
, (8.1)
where ET is set to 100 eV and the width σ is 10 eV. This sharp turn-on is similar to that observed in C3F8
[65]. The chosen functional form is for convenience, with the exact shape needing experimental measurement.
Systematic uncertainties in ET of 5% (setups A and B) and 2% (setup B(1.5)) are assumed, covering both
threshold and general shape uncertainties following calibration.
To produce low energy, nearly mono-energetic neutrons for calibration, (γ,n) reactions in beryllium are utilized.
Three photo-neutron sources, each yielding different recoil energy spectra, are proposed: 207Bi-Be (94 keV
neutrons), 124Sb-Be (23 and 380 keV neutrons), and 58Co-Be (9 keV neutrons) (Fig. 8.3). These were simulated
in the GEANT4 framework for the 10-kg chamber. Simulations show that sources with activities ranging from
1 to 100 µCi can provide high-statistics recoil energy spectra below 8 keV, 3 keV, and 1 keV, respectively. This
calibration approach can constrain the nucleation efficiency function under different thermodynamic conditions,
similar to techniques used by the PICO Collaboration [65].
0 0.5 1 1.5 2 2.5 3
Energy threshold (keV)
1
10
210
S
in
gl
e 
bu
bb
le
 e
ve
nt
s/
ho
ur Neutron calibration sources
Ci, 154.4 evts/hr µ124Sb-Be, 1 
Ci, 142.5 evts/hr µ207Bi-Be, 10 
Ci, 75.5 evts/hrµ58Co-Be, 100 
0 0.5 1 1.5 2 2.5 3
Energy threshold [keV]
3−10
2−10
1−10
M
ul
tip
le
s/
S
in
gl
es
Event ratio n=2/n=1
Ci µ124Sb-Be, 1 
Ciµ207Bi-Be, 10 
Ciµ58Co-Be, 100 
Event ratio n>=3/n=1
Ciµ124Sb-Be, 1 
Ciµ207Bi-Be, 10 
Ciµ58Co-Be, 100 
Figure 8.3: Recoil energy spectra for the three photo-neutron sources proposed (right) and bubble multiplicity
ratio spectra (left) for two and more than three bubbles concerning single bubble events.
The insensitivity to electron recoils allows for an innovative calibration method using nuclear recoils from
Thomson scattering. For instance, 1.33, 1.41, and 1.46 MeV γ-rays from 60Co, 152Eu, and 40K, respectively,
produce nuclear recoil spectra with distinct cut-offs at 95, 107, and 115 eV. These can strongly constrain the
nucleation efficiency for recoils around 100 eV. Additionally, a tagged recoil calibration using thermal neutrons
might be feasible. The de-excitation γ-rays from neutron capture on 40Ar lead to a recoiling 41Ar nucleus with
energy around 320 eV.
8.3 Physics Reach
The experimental setups’ physics reach is explored for a one-year exposure period. The investigation focuses
on the Standard Model (SM) cross-section for Coherent Elastic Neutrino-Nucleus Scattering in the context of
a low-threshold scintillating argon bubble chamber.
40
8.3.1 Standard Model Cross-Section for CEνNS
The SM cross-section for CEνNS, neglecting the axial contribution, is described by the following equation:
dσ
dT
=
G2
F
2π
MNQ2
w
(
2− MNT
E2
ν
)
F 2(q2), (8.2)
Where T is the nuclear recoil energy, Eν the neutrino energy, F (q2) the nuclear form factor, Qw = ZgVp +NgVn
the weak nuclear charge, and MN , Z, N are the nuclear mass, proton, and neutron number, respectively. The
cross-section is convolved with the reactor anti-neutrino spectrum and the detector efficiency to calculate the
expected number of events. The Huber+Mueller model’s theoretical prediction is employed [66, 67], which
offers a 2.4% uncertainty in the total neutrino ŕux for setups A and B for neutrino energies between 2 and 8
MeV, while neutrinos below 2 MeV use Ref. [68]. Setup B(1.5) adopts the Daya Bay experiment’s uncertainty
measure of 1.5% for the anti-neutrino ŕux from their reactors [45].
8.3.2 Sensitivity Analysis
The sensitivity of the experiment is assessed using a χ2 function deőned as:
χ2 = min
α,β,γ
[
(Nmeas − (1 + α)Nth(X, γ)− (1 + β)Breac)
2
σ2
stat
+
α2
σ2
α
+
β2
σ2
β
+
γ2
σ2
γ
]
, (8.3)
Where Nmeas is the measured number of events after subtracting the background from cosmogenic and muon-
induced neutrons (Bcosm), Nth(X, γ) the theoretical prediction with the nuclear recoil threshold set to (1 +
γ) · 100 eV, and Breac the background from the reactor. The statistical uncertainty σstat is calculated as
√
Nmeas + (R+ 1)Bcosm, where R is the ratio of reactor-on time to reactor-off time. The systematic uncer-
tainties σα, σβ , and σγ pertain to the signal, background, and threshold, respectively. For setups A and B,
the systematic uncertainties are σα = 0.024, σβ = 0.1, and σγ = 0.05. In setups B and B(1.5), the reactor
background component is negligible; thus, β and σβ are not considered. Setup B(1.5) adopts σα = 0.015 and
σγ = 0.02.
In the subsequent analysis, the measured number of events Nmeas is assumed to be as predicted by the SM.
8.3.3 The Weak Mixing Angle
Focusing solely on the Standard Model (SM) signal in the experiment, a comprehensive analysis is conducted
to ascertain the value of the weak mixing angle at lower energy scales, accompanied by its associated uncer-
tainty. This angle is crucial for understanding weak interactions and is derived from the CEνNS differential
cross-section, which is directly linked to the SM weak coupling gVp = 1/2 − 2 sin2 θW . Applying Eq.(8.3),
where X = sin2 θW , the angle’s value is őnely tuned. Fig.8.4 illustrates the evolution of the weak mixing
angle across different energy scales, following the Renormalization Group Equation (RGE) within the Minimal
Subtraction (MS) scheme, as discussed in references [69, 70]. This őgure also showcases the anticipated results
and uncertainties for the discussed experimental setups. Remarkably, the projection for the setup with a 1.5%
reactor spectrum uncertainty complements the low-energy Atomic Parity Violation (APV) measurements [71],
surpassing the sensitivity of other CEνNS experiments with assumed systematic uncertainties in the reactor
spectrum between 1.0% and 1.3% [72].
8.3.4 Investigating a Light Gauge Boson Mediator
The exploration of additional U(1) gauge symmetries beyond the SM framework, particularly light Z ′ mediators,
is an active area of research, supported by an array of phenomenological studies and experimental evidence
41
from beam dump experiments and collider data [73, 74, 75, 76, 77, 78]. This work delves into a scenario where
an extra gauge boson is coupled to quarks and leptons within a gauged B − L symmetry. Here, quarks carry
a U(1)B − L charge Qq = 1/3, while leptons have a charge Ql = −1, aligning with models such as gauged
B − 3Le and others [79, 80, 50]. This introduces a Beyond the SM interaction between neutrinos and quarks,
as shown in the following equation:
Leff = − g′2QlQq
q2 +MZ ′2
[
∑
α
ν̄αγµPLνα
][
∑
q
q̄γµq
]
, (8.4)
where q denotes the transferred momentum, and this interaction leads to interference with the SM cross-section.
Fig. 8.5 demonstrates the predicted sensitivities from the experimental setups in the g′ − MZ′ plane. The
one-year exposure limits set by this research are expected to be more stringent than those from other current
CEνNS experiments for all proposed setups. The scintillating bubble chamber technology is poised to be a
frontrunner in the search for new vector bosons across a wide mass range, from 20 MeV to ∼1 GeV and from
70 to 230 GeV.
8.3.5 Assessing the Neutrino Magnetic Moment
Neutrino magnetic moments, emerging from interactions with the electromagnetic őeld, represent a pivotal
aspect of both Majorana and Dirac neutrino studies [98, 99]. This novel interaction distinctively contributes
to the CEνNS cross-section, as depicted by the following formula:
dσ
dT
= π
α2
EMZ2µ2
ν
m2
e
(
1
T
− 1
Eν
+
T
4E2
ν
)
F 2(q2), (8.5)
where αEM symbolizes the electromagnetic coupling, and me represents the electron mass. Here, the neutrino
magnetic moment µν is normalized to the Bohr magneton µB .
The ensuing limits from the χ2 analysis for the three experimental setups are outlined in Fig.8.6. These
bounds are comparable in scale to those from the GEMMA and Borexino experiments, reŕecting the signiőcant
advancement and potential of the technology employed in these experiments[100, 101].
8.3.6 Light Scalar Mediator
This section delves into the theoretical framework and experimental implications of a light scalar mediator
universally coupled to quarks and leptons. This framework extends the Standard Model by introducing an
effective dimension-six operator. The unique nature of this operator lies in its proportionality to the square of
the ratio of the mediator’s coupling to its mass.
The scalar mediator’s contribution to the CEνNS cross-section is an addition to the Standard Model (SM)
contribution, yet it does not interfere with it. This contribution is quantiőed using the following equation:
dσ
dT
=
M2
N
4π
g4φQ
2
φT
E2
ν(2MNT +M2
φ)
2
, (8.6)
Here, MN represents the nuclear mass, T is the nuclear recoil energy, Eν is the neutrino energy, Mφ is the mass
of the scalar mediator, and gφ and Qφ are coupling constants. Notably, Qφ is intricately linked to hadronic
form factors, as described in [102].
A key aspect of this investigation is the analysis of the experimental setups A and B, aiming to explore the
parameter space of this new physics scenario. The analysis focuses on the gφ-Mφ plane, seeking to establish
42
exclusion regions based on a 95% conődence level. These regions are meticulously illustrated in Fig. 8.7. A
comparative analysis with existing data from COHERENT-CsI and COHERENT-LAr measurements is also
conducted. The őndings suggest that setups A and B are poised to impose more stringent constraints than cur-
rent COHERENT data, primarily due to the anticipated higher event yield in these setups. This enhancement
in sensitivity could provide pivotal insights into the role and characteristics of light scalar mediators within the
realm of neutrino physics.
8.3.7 Sterile Neutrino Search
The theoretical landscape of neutrino oscillations has been robustly validated by a series of critical exper-
iments, conforming to the Standard Model’s assertion of three massive neutrinos. Pioneering research by
Super-Kamiokande, SNO, and KamLAND has played a signiőcant role in establishing this paradigm [22, 23, 24].
Despite this coherent narrative, several experimental outcomes, notably from LSND, SAGE, and MiniBooNE,
suggest a potential extension beyond the current three-ŕavor neutrino model, hinting at the existence of addi-
tional sterile neutrinos. These putative sterile neutrinos are characterized by their interaction solely through
mixing with active neutrino states [25, 104, 105].
CEνNS is a powerful tool to probe these elusive sterile neutrinos, presenting a unique opportunity to set
constraints in various scenarios. This study delves into the 3 + 1 neutrino model hypothesis, harnessing the
capabilities of the scintillating bubble chamber situated near a reactor. The aim is to measure CEνNS across
three proposed experimental setups precisely. The survival probability of electron anti-neutrinos (ν̄e) is modeled
as a function of the propagation length (L), the neutrino energy (Eν), and a 4 × 4 neutrino mixing matrix.
This analysis is instrumental in advancing our understanding of sterile neutrinos and their potential role in the
broader neutrino oscillation framework:
Pν̄e→ν̄e
(
L
Eν
)
= 1− 4
∑
k>j
|Uek|2|Uej |2 sin2
(
∆m2
kjL
4Eν
)
,
= 1− sin2 2θ13 sin
2 ∆13
− sin2 2θ14 sin
2 ∆41,
(8.7)
where Uαi is the neutrino mixing matrix element for ŕavor να (α = e, µ, τ) and mass eigenstate νi (i = 1, 2, 3).
The neutrino squared-mass differences are represented as ∆m2
ij = m2
i −m2
j and ∆ij is a function of the ratio
L/Eν , expressed as follows
∆ij = 1.267∆m2
ij
(
L
Eν
)
. (8.8)
Figure 8.8 presents the exclusion limits deduced from individual analyses across the three experimental setups.
A distinctive analysis employing the far/near ratio is also illustrated for setup A. This unique approach is
feasible owing to the mobility of the reactor used in setup A, housed within a water pool, enabling variable
baseline distances ranging from 3 to 10 meters. Speciőcally, the analysis contrasts a ’far’ position at 7 meters
with a ’near’ position at 3 meters.
Setup B(1.5) will cover all the reactor anomaly and it will give stronger constraints than any other experiment
for 10 < |∆m2
41| < 80 eV2. KARMEN+LSND [27] alternate the best limits with setup B(1.5) in the region
3 < |∆m2
41| < 10 eV2. These results reŕect the importance of reducing the uncertainty in the anti-neutrino
ŕux since that is the only difference between setups B and B(1.5).
43
8.3.8 Unitarity Violation
Investigating Coherent Elastic neutrino-nucleus Scattering in reactor environments is pivotal for studying uni-
tarity violation (UV) in the neutrino mixing matrix, a phenomenon suggested by numerous New Physics
theories, including scenarios involving heavy sterile neutrinos [49, 109, 47, 110]. These theories propose alter-
ations to the standard 3 × 3 light neutrino mixing matrix due to adding extra heavy fermions. This leads to
non-unitarity in the generalized charged current weak interaction mixing matrix. This matrix is represented
as:
N = NUV · U3×3, (8.9)
Where NUV denotes the matrix accounting for UV effects related to New Physics [111], and U3×3 symbolizes
the customary 3× 3 unitary mixing matrix [111]. The matrix NUV is parameterized as:
NUV =


α11 0 0
α21 α22 0
α31 α32 α33

 , (8.10)
With diagonal elements as real numbers and off-diagonal ones as complex. In short-baseline experiments, such
as those examined in this study, UV contributions mainly emerge from zero-distance effects. Therefore, survival
and transition probabilities for an electron anti-neutrino source can be formulated as:
Pee = α4
11,
Pµµ = (|α21|2 + α2
22)
2,
Peµ = α2
11|α21|2,
Peτ = α2
11|α31|2.
Pµτ = α2
22|α32|2.
(8.11)
Parameters α11, α21, and α31 are derived via a χ2 function to pinpoint optimal values for setups A, B, and
B(1.5). Given CEνNS’s ŕavor blindness, the theoretical event count, Nth, encompasses UV contributions from
all three neutrino ŕavors:
Nth = α2
11(α
2
11 + |α21|2 + |α31|2)Nmeas, (8.12)
The minimization of the χ2 function is detailed in Equation (8.3).
Figs.8.9 and 8.10 illustrate the expected sensitivities for the proposed setups regarding diagonal and non-
diagonal parameters, respectively, contrasting with existing bounds from global neutrino oscillation data őts
[112]. Moreover, Fig. 8.11 demonstrates the anticipated constraints in the |α21|2−|α11|2 parameter space, sug-
gesting that the scintillating bubble chamber could impose more stringent limits than oscillation experiments,
particularly for α11.
8.3.9 Non-standard Interactions
In discovering phenomena beyond the Standard Model (SM) in particle physics, deviations from the predicted
SM cross-sections are of signiőcant interest. The study of coherent elastic neutrino-nucleus scattering pro-
vides an avenue for this exploration, particularly through the lens of non-standard interactions (NSI). These
interactions, which extend the SM’s neutral current component, are encapsulated in the NSI formalism. The
modiőcation to the Lagrangian by NSI is represented mathematically as:
44
LNSI
NC = −2
√
2GF
∑
f,P,α,β
ϵfPαβ (ν̄αγ
µPLνβ)(f̄γµPXf), (8.13)
In this formula, f denotes the up and down quarks, and the variables α and β signify the neutrino ŕavors (e, µ,
τ). PX refers to the chirality projectors for both left and right-handedness, while ϵfPαβ quantiőes the strength of
the NSI couplings. This modiőcation to the neutral current component offers a path to probing new physical
phenomena through neutrino interactions.
One of the key experiments in this endeavor is setup A of the scintillating bubble chamber, designed to measure
CEνNS in a reactor. This setup focuses on constraining the NSI parameter ϵfVee . The constraints from this
setup can be compared to those obtained from COHERENT’s LAr and CsI detectors. While COHERENT-LAr
limits might be depicted as a single gray band and COHERENT-CsI as two light-blue striped bands, setup A
provides a unique perspective, often represented as two distinct and narrow red bands in the parameter space.
Figure 8.12 showcases these constraints at 90% C.L. This representation illustrates setup A’s sensitivity and
potential for pushing the boundaries of understanding in neutrino physics and NSI.
8.4 Conclusions
This investigation underscores the substantial potential of a low threshold LAr scintillating bubble chamber
in analyzing CEνNS within a reactor setting. Monte Carlo simulations affirm the feasibility of achieving a
background level of about 10% of the signal, with in-situ measurements poised to further reőne the associ-
ated systematic uncertainties. These simulations substantiate the devised plan for determining nuclear recoil
efficiency at a 100 eV energy threshold, indicating the viability of calibration to sub-keV thresholds using
photo-neutron and Thomson scattering sources.
The research’s sensitivity to an array of physics scenarios, namely electroweak precision tests, new vector
mediators, and the neutrino magnetic moment, is highly competitive under realistic assumptions of background
levels and systematic uncertainties. In particular, the weak mixing angle precision of 1% aligns closely with
APV uncertainty levels. The experiment conőgurations set forth herein are positioned to establish the most
stringent bounds for new gauge vector bosons across broad mass ranges and offer competitive bounds for the
neutrino magnetic moment. This detector technology is a beacon in various coherent elastic neutrino-nucleus
scattering experiment scenarios. With just a year’s exposure, it demonstrates its leadership potential in high
and low-power reactor facilities.
The ability of this bubble chamber technology to explore new physics, improving sensitivity compared to
existing results by the COHERENT collaboration, is highlighted; with particular emphasis on light scalar
mediators, where it could achieve signiőcantly low coupling values around 10−6 for masses approximately 10−3
GeV. Furthermore, the combination of different experimental setupsÐa 10 kg detector at 3 m from a 1 MWth
reactor and a 100 kg detector at 30 m from a 2000 MWth power reactorÐcould extensively cover the |∆m2
41|
parameter space, currently of interest due to the reactor anti-neutrino anomaly. The study also delves into
stringent limits on non-unitarity in the 3×3 neutrino mixing matrix. It evaluates non-standard interactions by
altering the neutral current component with new couplings, offering insights complementary to the CHARM
experiment. The versatility of the scintillating bubble chamber is underscored by its capability to engage in a
diverse and competitive physics program in both research and commercial reactor settings.
45
Tevatron
Setup	B(1.5)
Setup	B
Setup	A
APV
Qweak
SLAC-E158
eDIS
NuTeV
SLC
LEP
LHC
0.225
0.230
0.235
0.240
0.245
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
µ(GeV)
si
n
2
θ̂ W
(µ
)
Figure 8.4: This őgure illustrates the Renormalization Group Equation (RGE) [44] progression of the weak
mixing angle within the context of the Minimal Subtraction (MS) renormalization scheme, as elaborated in
references [69, 70]. The variation of the weak mixing angle is presented as a function of the energy scale, denoted
by µ. It includes the forecasted measurements and the associated 1σ uncertainties for the experimental setups
A, B, and B(1.5), represented by solid purple, solid orange, and dashed orange lines, respectively. Additionally,
the őgure juxtaposes these projections with measurements from various other relevant experiments. The
underlying basis of the őgure is adapted from the work detailed in reference [69].
46
Setup	A
Setup	B
Setup	B(1.5)
CONNIE	(Lindhard)
CO
HE
RE
NT
-C
sI
COHERENT-LAr
Beam	dump
A
T
L
A
SBaBar LHCb
10
-7
10
-6
10
-5
10
-4
10
-3
0.01
0.1
1
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
MZ ′(GeV)
g
′
Figure 8.5: This graph delineates the 95% Conődence Level (C.L.) exclusion limits in the coupling constant
g′ versus Z ′ boson mass (MZ′) parameter space [44]. The solid purple, solid-orange, and dashed orange
lines depict these limits for the experimental setups A, B, and B(1.5). Additionally, the dash-dotted gray
curve represents exclusion constraints as determined by the CONNIE experiment [81]. The shaded brown
and yellow areas signify the exclusion limits established by the COHERENT experiment using CsI [5] and
LAr [6, 82] detectors, respectively. Exclusion regions pertinent to dark photon searches from the BaBar [83]
and LHCb [84] experiments are represented in light gray. Similarly, exclusions from various beam dump
experiments [85, 86, 87, 88, 89, 90, 91, 92, 93, 94], as synthesized in Ref.[95], are illustrated in blue. The
exclusion zone from the ATLAS search for dilepton resonances[96], based on software developed in Ref. [97], is
also presented in light gray.
47
G
E
M
M
A
	(
9
0
%
	C
.L
.)
B
o
re
x
in
o
	(
9
0
%
	C
.L
.)
C
O
H
E
R
E
N
T
-C
sI
C
O
H
E
R
E
N
T
-L
A
r
Setup	A
Setup	B
Setup	B(1.5)
0
2
4
6
8
10
10
-11
10
-10
10
-9
10
-8
µν (µB)
∆
χ
2
90%C.L.
Figure 8.6: This őgure illustrates the constraints on the neutrino magnetic moment [44]. The solid purple,
solid-orange, and dashed orange lines indicate the bounds established for experimental setups A, B, and B(1.5).
The brown and yellow shaded areas represent the exclusion limits determined by the COHERENT experiment,
utilizing CsI [5] and LAr [6, 82] detectors, correspondingly.
48
3−10 2−10 1−10 1 10 210 310 410
 (GeV)φ M
7−10
6−10
5−10
4−10
3−10
2−10
1−10
1
φ
 g
Setup A
Setup B
COHERENT CsI
COHERENT LAr
 
Figure 8.7: This őgure illustrates the 95% conődence level exclusion regions in the gφ −Mφ parameter space
[103]. The solid purple and orange lines delineate the constraints imposed by setups A and B, respectively.
Also depicted are the exclusion regions established by the COHERENT collaboration, utilizing CsI and LAr
detectors, as denoted by the shaded brown and yellow areas. These COHERENT collaboration limits are
derived from their published data sources [5, 6, 82].
49
2−10 1−10 1
 14θ22 sin
4−10
3−10
2−10
1−10
1
10
210
310
)2
|(
eV
412
m∆ |
RAA
Daya Bay
KARMEN+LSND
NEOS
KATRIN
ININ Setup A(3m)
ININ Setup A(Far/near ratio)
LV Setup B(30m)
LV Setup B(1.5)(30m)
 
Figure 8.8: Expected exclusion regions at 95% conődence level from sterile neutrino searches [103]. The black
dashed, and dotted lines represent projected limits for setup A at a baseline of 3 meters and using a far/near
ratio, respectively, with far (near) positions at 7 (3) meters. The orange dashed and dotted lines indicate
exclusion sensitivities for setups B and B(1.5). Comparative sensitivity limits with other experiments are also
depicted: Daya Bay [106] at 95% C.L. (green), KARMEN+LSND [27] at 95% C.L. (light blue), NEOS [107] at
90% C.L. (red), and KATRIN [108] at 95% C.L. (dark blue). The shaded area corresponds to the reactor anti-
neutrino anomaly (RAA) őt [26, 107], encompassing favored solutions, while other contours indicate disfavored
solutions to their right.
50
0.96 0.968 0.976 0.984 0.992 1
11α
1
2
3
4
5
6
 2 χ∆
 at 3 m, Setup A thININ: 1 MW
 at 30 m, Setup B thLV: 2 GW
 at 30 m, Setup B(1.5) thLV: 2 GW
Oscillation experiments
90% C.L 
Figure 8.9: This őgure displays the 90% Conődence Level sensitivity to the diagonal parameter α11 for setups A
(red), B (blue), and B(1.5) (black) [103]. Included for comparison is the sensitivity derived from oscillation data
[49], highlighted by the blue-shaded region. The analysis varied α11 while marginalizing α21 and α31. Notably,
the sensitivities from the three experimental setups offer more stringent constraints at the 90% Conődence
Level than those obtained from oscillation data. Areas to the left of the blue-shaded region are considered
beyond the permissible range.
51
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
21α
0
1
2
3
4
5
6
 2 χ∆
 at 3 m, Setup A thININ: 1 MW
 at 30 m, Setup B thLV: 2 GW
 at 30 m, Setup B(1.5) thLV: 2 GW
Oscillation experiments
90% C.L 
Figure 8.10: The diagram illustrates the 90% Conődence Level sensitivity to the non-diagonal parameter α21
[103]. It compares the forecasts for setups A (red), B (blue), and B(1.5) (black) against the upper limits derived
from global oscillation őts [49] (highlighted by the blue shaded area). In this analysis, α21 was the primary
variable under consideration, while α11 and α31 were minimized. The diagram underscores the oscillation data,
providing more stringent constraints at the 90% Conődence Level. Regions to the right of the blue-shaded area
are considered outside the permissible range.
52
0 0.02 0.04 0.06 0.08 0.1
2|11α1 - |
0.7
0.75
0.8
0.85
0.9
0.95
1
2 |
21α
1 
- 
|
 at 3 m, Setup A thININ: 1 MW
 at 30 m, Setup B thLV: 2 GW
 at 30 m, Setup B(1.5) thLV: 2 GW
Oscillation experiments
Figure 8.11: Exclusion contours at 90% Conődence Level for the non-unitarity parameters |α21|2−|α11|2 [103].
The constraints set by setups A, B, and B(1.5) are illustrated with red, blue, and black lines. Included is
the sensitivity from neutrino oscillation experiments [49], depicted by the blue shaded area. In this particular
analysis, the parameters α11 and α21 were adjusted, while minimizing α31. Regions outside the boundary
deőned by the lines are deemed inconsistent with the observed data.
53
1− 0.5− 0 0.5 1
 ee
dV∈ 
1−
0.8−
0.6−
0.4−
0.2−
0
0.2
0.4
0.6
0.8
1
eeuV ∈ 
CHARM
COHERENT LAr
COHERENT CSI
ININ, Setup A
 
Figure 8.12: Projected 90% Conődence Level sensitivity of setup A for non-standard interaction parameters
ϵfVee , delineated by two narrow red bands [103]. The constraints for setups B and B(1.5) overlap signiőcantly
with setup A and are thus not displayed separately. This chart also incorporates the parameter limits deőned by
the CHARM experiment [113] (green region) and the COHERENT experiment using LAr (blue) and CsI (grey)
detectors [29]. The graphic contrasts the anticipated sensitivities of these setups with existing experimental
data.
54
9. Conclusions
The investigations conducted throughout this doctoral research have substantially advanced the understanding
of particle interactions within a scintillating bubble chamber detector őlled with liquid argon. The integration of
meticulous Monte Carlo simulations and the practical assembly of the detector have been pivotal in deciphering
the subtle interplays between various physical processes and the detector’s environment. The overarching
conclusion is that the scintillating bubble chamber has demonstrated remarkable potential through innovative
design and strategic methodology in the study of neutrino physics.
An essential outcome of this research is the detector’s adeptness in limiting the impact of non-standard in-
teractions and probing the non-unitarity of the neutrino mixing matrix and a precise measurement of sin2 θW
at low energies. The empirical data have established that the chamber can set competitive bounds in these
domains, thus expanding the frontier for new physics scenarios. Such achievements fortify our grasp of the
Standard Model of particle physics and aid in identifying and constraining phenomena beyond the SM.
The adaptability of the bubble chamber’s design has been demonstrated through extensive simulations across
varied reactor settings, encompassing both research and commercial environments. This adaptability under-
scores the chamber’s robustness in accommodating various experimental needs and environmental factors.
Although no real-world experiments have been conducted yet, simulations spanning a year of exposure have
established stringent bounds for the sterile neutrino search. This enhances the chamber’s potential contribution
to global neutrino research efforts.
In conclusion, this thesis marks a signiőcant milestone in neutrino research. The extensive simulations, rigorous
data analysis, and experimental validation work have cemented the scintillating bubble chamber’s role as a
cutting-edge tool in particle physics. The chamber’s proőciency in deciphering interactions at low energy
thresholds embodies the progress critical for exploring the intricacies of neutrino properties.
The prospects for future work are promising. It involves reőning simulation models with real-world calibration
data, improving the chamber’s material radiopurity, and further miniaturizing electronic components to reduce
backgrounds. Continuous advancements in these areas are anticipated to bolster the detector’s capabilities,
potentially ushering in a new era of particle physics and cosmology discoveries.
9.1 Background Suppression and Sensitivity
The design and construction of the LAr scintillating bubble chamber have been informed by a rigorous simu-
lation framework, which has been pivotal in predicting background levels. The optimization of this detector
has successfully targeted background levels to be approximately 10% of the signal, which is an impressive
benchmark for the őeld. This background suppression has been achieved through innovative material selec-
tion, geometrical optimization, and a deep understanding of background sources, including radon emanation,
intrinsic radioactivity of detector materials, and cosmic ray-induced backgrounds.
55
9.2 Detector Refinement and Calibration
Continuous efforts in detector reőnement, guided by Monte Carlo simulations and in-situ calibrations, have
led to a level of precision in background understanding that underpins the robustness of the experimental
őndings. The accuracy of these simulations has been paramount in developing calibration strategies critical for
validating the detector’s performance, ensuring that it operates within the stipulated parameters of sensitivity
and speciőcity.
9.3 Exploration of New Physics
The research has been instrumental in new physics in setting bounds for new vector bosons. The chamber’s
sensitivity has allowed for probing unexplored parameter spaces, which could be integral in revealing beyond
Standard Model physics. Moreover, the study of non-standard interactions and the non-unitarity of the neutrino
mixing matrix presents a compelling case for the chamber’s potential to uncover phenomena that could challenge
current theoretical frameworks.
9.4 Operational Versatility
One of the most promising aspects of the scintillating bubble chamber is its operational versatility. Research has
demonstrated that the chamber can be effectively deployed in both research and commercial reactor settings,
which is indicative of its robust design and adaptability. This versatility extends to the chamber’s ability
to measure neutrino magnetic moments and contribute valuable data to resolving the reactor anti-neutrino
anomaly.
9.5 Future Prospects
Looking forward, implementing this detector technology offers a valuable tool in the global effort to understand
the nature of neutrinos and their role in the cosmos. With extended exposure and further reőnement based
on in-situ measurements, the detector is poised to advance the frontiers of neutrino physics signiőcantly.
The methodological advancements and operational experiences gleaned from this research will also serve as a
cornerstone for future neutrino experiments.
56
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