UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO
POSGRADO EN CIENCIAS FÍSICAS
 INSTITUTO DE CIENCIAS NUCLEARES
MEASUREMENT OF  φ (1020) RESONANCE PRODUCTION IN p-Pb
COLLISIONS AT √sNN  = 5.02 TeV WITH THE ALICE EXPERIMENT
TESIS
QUE PARA OPTAR POR EL GRADO DE:
MAESTRO EN CIENCIAS FÍSICAS (FÍSICA)
PRESENTA:
EDGAR PÉREZ LEZAMA
TUTOR PRINCIPAL:
DR. GUY PAIC
INSTITUTO DE CIENCIAS NUCLEARES
MIEMBROS DEL COMITÉ TUTOR:
DR. ELEAZAR CUAUTLE FLORES
INSTITUTO DE CIENCIAS NUCLEARES
DR. VARLEN GRABSKI
INSTITUTO DE FÍSICA
MÉXICO, D. F. Septiembre 2014 
 
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Dedico esta tesis a mis amados padres ...
Agradecimientos
El mayor y principal agradecimiento es a mis padres, Ángeles Lezama y Jorge
Pérez, por su apoyo incondicional a lo largo de esta trayectoria y por su dedicación
para darme una formación académica. Agradezco mis t́ıos y en especial Martha
Pérez, Ramón López y Eduardo Pérez, quienes fueron parte importante de este
nuevo logro profesional y de alguna u otra manera estuvieron apoyándome y
alentándome para poder obtener este importante logro.
Al Dr. Guy Paic, mi asesor, le estaré siempre agradecido por dedicar tiempo
en mi formación como cientifico y tambien por ayudarme a que este trabajo
trascendiera internacionalmente. Gracias por todas las discusiones en el grupo
del ICN.
Le doy las gracias a mis tutores y sinodales Eleazar Cuautle, Varlen Grabski,
Lukas Nellen, Ernesto Belmont, Andrés Sandoval y Gerardo Herrera por dedicar
parte de su tiempo en leer mi tesis y aportarme valiosas sugerencias y opiniones
que finalmente ayudaron a mejorar este trabajo.
Agradezco a mis amigos de la carrera: Tonatiuh Jiménez, Ricardo Román, Iván
Toledano, Miguel López y Mart́ın Zumaya, por apoyarme y alentarme en el sinu-
oso camino de la ciencia. Espero que nuestra amistad y colaboración se mantenga
por mucho tiempo. Especial agradecimiento a Antonio Ortiz por motivarme en
la fisica de altas energias y darme consejos muy valiosos para mejorar mi trabajo
y mi entendimiento de la f́ısica. Gracias a Enrique Patiño por proporcionarme
material y equipo del laboratorio de detectores.
My completion of this thesis could not have been accomplished without the sup-
port and help of the Resonance Group and specially from Ajay Kumar Dash,
Francesca Bellini, Anders Knospe, Viktor Riabov, Mikhail Malaev and Christina
Markert. The weekly discussions helped me to improve this work. Thanks to the
ALICE collaboration for all your comments and suggestions.
La conclusion de este trabajo no hubiera sido posible sin los apoyos economicos
que financiaron mis estudios de maestria. Gracias a la beca CONACyT, los
apoyos PAEP, el convenio CERN-UNAM, al ICN y especialmente a Alejandro
Ayala y a Miguel Alcubierre por apoyarme y darme la oportunidad de realizar
estancias en CERN, donde adquiŕı mucha experiencia y conocimiento por parte
de los expertos en el area.
Contents
Contents iv
Resumen vi
0.1 Introducción . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
0.1.1 Resonancias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
0.2 Experimento ALICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
0.2.1 Detectores TPC y TOF . . . . . . . . . . . . . . . . . . . . . . . . . ix
0.3 Resultados . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
0.3.1 Selección de Eventos y de Trazas . . . . . . . . . . . . . . . . . . . . xi
0.3.2 Espectro de momento del mesón φ(1020) . . . . . . . . . . . . . . . . xii
0.3.3 Discusión de Resultados . . . . . . . . . . . . . . . . . . . . . . . . . xiii
0.4 Conclusiones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Summary xvi
List of Figures xvi
1 High Energy Physics 1
1.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Kinematic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Quantum Chromodynamics (QCD) . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Quark Gluon Plasma (QGP) . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Phases of strongly interacting matter . . . . . . . . . . . . . . . . . . 6
1.4.2 Strangeness enhancement . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.3 Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
iv
CONTENTS
2 The ALICE Experiment at LHC 11
2.1 Large Hadron Colider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 The accelerator complex . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 ALICE (A Large Ion Collider Experiment) . . . . . . . . . . . . . . . . . . . 13
2.2.1 ALICE detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Particle Identification in ALICE 21
3.1 AliRoot framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 TPC PID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 TOF PID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 φ(1020) Analysis Results 26
4.1 Event and Track Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.2 Track selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 φ(1020) Meson Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.1 Kaon identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.2 Invariant Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.3 Combinatorial Background Subtraction . . . . . . . . . . . . . . . . . 29
4.2.4 Peak and Residual Background Fits . . . . . . . . . . . . . . . . . . . 33
4.2.5 Raw Yield Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.6 Peak Correction Factor . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 Monte Carlo simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.1 Reconstruction Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 38
5 φ(1020) Spectra And Systematic Analysis 41
5.1 φ(1020) Invariant Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Mass and Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.3 Systematic Uncertainties Analysis . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3.1 Systematic Uncertainties of the Yield . . . . . . . . . . . . . . . . . . 46
5.3.1.1 Detailed description of each source . . . . . . . . . . . . . . 46
5.3.2 Fits to φ Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.3.3 Integrated Yield and Particle Ratios . . . . . . . . . . . . . . . . . . 55
5.4 Analysis Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
v
CONTENTS
6 Discussion of Results 62
7 Conclusions 68
Bibliography 70
Appdx A 73
.0.1 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
vi
Resumen
0.1 Introducción
La f́ısica de altas enerǵıas ha establecido y validado durante las últimas decadas una de-
tallada, pero incompleta, teoŕıa de part́ıculas elementales y sus interacciones fundamentales
llamada Modelo Estándar. Este modelo ha explicado exitosamente una serie de resultados
experimentales y ha predicho de manera precisa una amplia variedad de fenómenos.
De acuerdo con la teoŕıa del Modelo Estándar toda la materia está constituida de tres
tipos de part́ıculas elementales: leptones, quarks y las part́ıculas mediadoras. En total
son doce part́ıculas, seis quarks: up, down, strange, charm, bottom y top, y seis leptones:
electrón, neutrino del electrón, muón, neutrino del muón, tauón y neutrino del tau. Los
quarks y los leptones se clasifican dentro de la categoria de los fermiones, por tener esṕın
semientero.
El Modelo Estándar considera tres tipos de interacciones fundamentales y estas se pro-
ducen a través del intercambio de bosones (esṕın entero) o part́ıculas mediadoras. El fotón(γ)
es la part́ıcula mediadora de la interacción electromagnética, los bosones vectoriales(W± y
Z0) son responsables de la interacción débil, y los ocho gluones(g) son los mediadores de la
interacción fuerte.
El Modelo Estándard tiene, sin embargo, limitaciones que requieren extensiones para
mantener la teoria consistente. El aspecto más importante es las masas de los bosones de
norma electro-débiles (W± y Z0) que se predicen que debeŕıan ser nulas en la teoŕıa. Lo cual
es claramente inconsistente con la teoŕıa. Esta discrepancia puede ser resuelta agregando
un bosón de norma adicional, añadido a la teoŕıa, el bosón de Higgs. El mecanismo de
Higgs genera las masas para los W± y Z0 mientras que los fotones permanecen sin masa.
Resultados recientes del LHC han confirmado la existencia de una part́ıcula desconocida
con una masa entre 125 y 127 GeV/c2. En marzo del 2013 se probó que la part́ıcula de-
sconocida se comportaba, interactuaba y decaia en muchas de las formas predichas por el
vii
CONTENTS
Modelo Estárdar, y fue tentativamente confirmado de tener paridad positiva y esṕın cero,
dos atributos fundamentales del bosón de Higgs.
0.1.1 Resonancias
El estudio de la producción de resonancias mesónicas φ(1020) y K∗(892) tiene su particular
importancia. Estas part́ıculas tienen masas muy cercanas pero sus tiempos de vida difieren
por un factor alrededor de 10, siendo: τφ = 46 fm/c and τK∗0 = 4.0 fm/c, y su contenido de
extrañeza o número de quarks extraños difieren por una unidad. Se espera que el K∗0 sea
mas sensitivo a efectos de re-dispersión en el medio hadrónico, debido a su corto tiempo de
vida. Por otro lado, el mesón φ puede escapar del medio hadrónico casi sin re-dispersión, por
esto, esta resonancia es un buen candidato para investigar restauración parcial de simetŕıa
quiral en el tiempo de formación. Además, el φ es de gran ayuda para probar la producción
extrañeza, siendo el mesón vectorial más ligero compuesto de quarks del mar (ss).
0.2 Experimento ALICE
EL LHC1 (Gran Colisionador de Hadrones) comenzó como una idea a mediados de la década
de los 80’s. Anteriormente el CERN2 (Organización Europea para la Investigación Nuclear)
contaba con el colisionador LEP3 (Gran Colisionador Electrón-Positrón), que funcion de
1989 hasta el ao 2000. EL LHC se encuentra ubicado en la frontera Franco-Suiza cerca de
Ginebra, y enterrado a una profundidad entre 50m y 175m. El LHC es un sincrotrón que
acelera paquetes de part́ıculas en anillos separados y en sentidos contrarios, cada paquete
viaja muchas veces alrededor del anillo del acelerador hasta que se alcanza suficiente enerǵıa
para colisionarlas. La enerǵıa máxima de aceleración para protones es de 7 TeV y 2.76 TeV
por nucleón en iones de plomo. Con esto, se alcanzan enerǵıas en el centro de masa de la
colisión de
√
s=14 TeV para protón-protón,
√
sNN=5.02 TeV p-Pb y
√
sNN=5.5 TeV en
iones de plomo.
Para mantener los haces enfocados y acelerados hasta el momento de la colisión, el aceler-
ador tiene que guiarlos a lo largo del anillo. Para lograr esto, el LHC cuenta con 1232 dipolos
de 14.3 m de longitud, que desv́ıan la trayectoria de las part́ıculas. Los dipolos contienen
magnetos superconductores que operan a una temperatura de 1.9◦K, lo cual está 0.8◦K por
1Large Hadron Collider
2Centree Européenne pour la Recherche Nucléaire.
3Large Electro-Positron Collider
viii
CONTENTS
debajo de la temperatura de fondo del universo, esta temperatura se logra utilizando helio
en estado superfluido. Para enfocar los haces, se tienen 392 cuadrupolos con una longitud
entre 5 y 7 metros.
El experimento ALICE (A Large Ion Collider Experiment) tiene 16m de alto, 26 m
de largo y pesa aproximadamente 10,000 toneladas, ALICE es el cuarto de los grandes
experimentos del CERN, que explorará la nueva f́ısica que surja a partir de colisionar nucleos
de iones contra nucleos de iones (Pb-Pb) a enerǵıas del LHC, permitiendo el estudio de la
f́ısica del equilibrio y del no equilibrio de materia interaccionando fuertemente en densidades
del orden de ε ≃ 1− 1000GeVfm−3.
El objetivo de ALICE es estudiar a la materia que se encuentra bajo condiciones de
densidad extrema, formando aśı un nuevo estado de la materia llamado plasma de quarks
y gluones (QGP1). La materia en este estado se encuentra 100,000 veces más caliente que
el núcleo del sol y bajo estas condiciones los protones y neutrones se funden, liberando
aśı los quarks y gluones que conforman a estos hadrones. Debido a que ningún quark ni
gluón han sido observados de forma aislada, siempre están unidos dentro de los hadrones, el
estudio de las propiedades del QGP será clave para la Cromodinámica Cuántica en un mejor
entendimiento del fenómeno de Confinamiento2. El experimento ALICE es un experimento
de propósito general cuyos detectores miden e identifican hadrones, leptones y fotones. Esto
se ha logrado analizando un amplio rango de momento (desde ∼ 0.1GeV hasta ∼ 100GeV)
utilizando las técnicas de identificación conocidas: pérdida de enerǵıa por ionización dE/dx,
tiempo de vuelo, radiación Cherenkov y de transición, calorimetŕıa electromagnética y filtros
de muones.
0.2.1 Detectores TPC y TOF
TPC
El detector TPC o Cámara de Proyección Temporal, es el principal detector de trazas que está
optimizado para, junto con los otros detectores ciĺındricos, medir el momento de part́ıculas
cargadas, identificar el tipo de part́ıcula y determinar la posición del vértice. El volúmen de
este detector, de forma ciĺındrica, está delimitado por un radio interno de 84.8 cm y el radio
externo de 246.6 cm, cubre una longitud de 500 cm en la dirección del haz (eje z).
El espacio fase cubierto por la TPC en psudorapidez es | η |<0.9 para trazas de part́ıculas
1Por sus siglas en inglés Quark-Gluon Plasma.
2Los quarks y gluones están confinados dentro de los hadrones.
ix
CONTENTS
radiales. Por ser de forma ciĺındrica, cubre completamente el ángulo azimutal (con excepción
de las zonas muertas), aśı mismo cubre un amplio rango de pt con buena resolución, desde
0.1 GeV hasta 100 GeV.
El detector consiste principalmente de dos partes: la jaula del campo y el electrodo cen-
tral. La primera es llenada con 90 m3 de una mezcla de gases: Ne/CO2/N2 (90/10/5), las
part́ıculas cargadas que atraviesen este gas excitarán e ionizarán los átomos de la mezcla a lo
largo de la trayectoria de la part́ıcula. Como consecuencia de esta ionización, las part́ıculas
irán progresivamente perdiendo enerǵıa por unidad de longitud de la traza (dE/dx), la
pérdida de enerǵıa es espećıfica y caracteŕıstica según el tipo de part́ıcula que está atrav-
esando la TPC. Los electrones son transportados, a lo largo de 2.5 m hacia las tapas del
cilindro de la TPC a causa de un fuerte campo eléctrico generado entre las tapas exteriores
y el electrodo central, debido a que este último está a un alto voltaje negativo y las tapas
externas a un alto voltaje positivo.
Las tapas circulares de la TPC son las que detectan los electrones arrastrados desde el
punto de ionización, cada tapa está conformada de 18 sectores trapezoidales que son MWPC1
(Cámara Proporcional de Multialambres). El MWPC consiste en una serie de rejillas de
cátodos y ánodos a diferentes voltajes. Un ánodo está a un voltaje positivo de 1500V, lo
cual conlleva a una amplificación de los electrones arrastrados, pues estos incrementan su
enerǵıa debido al potencial, causando mayores ionizaciones y comenzando aśı una avalancha
de electrones. La señal que reciben los pads2 son proporcionales al número de electrones
y a la enerǵıa perdida de las part́ıculas cargadas ionizantes. Pero esta proporcionalidad se
estropeaŕıa si los fotones, que son generados en la avalancha, viajaran más distancia que
el tamaño de la avalancha, creando aśı otras nuevas avalanchas que no seŕıan provenientes
directamente de los electrones arrastrados, este efecto es minimizado por los gases CO2 y N2
que tienen un alto coeficiente de fotoabsorción sobre un amplio rango de longitud de onda.
TOF
El detector de Tiempo de Vuelo (TOF), cubre una región central de pseudorapidez de |
η |<0.9, es capaz de identificar part́ıculas de un rango de momento intermedio de 0.4 a
2.5GeV para piones y kaones o hasta 4GeV para protones, con una separación mayor a
3σ entre π/K y K/p, esto último se utilizó en esta tesis como método de identificación de
part́ıculas en el TOF y se explicará en el siguiente caṕıtulo.
1Por sus siglas en inglés Multi-Wire Proportional Chamber.
2Elementos sensibles a la detección de electrones.
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CONTENTS
El detector cubre una superficie ciĺındrica con una aceptancia en el ángulo polar entre
45◦ y 135◦. El radio interno del cascarón ciĺındrico es de 370 cm y el radio externo de 399 cm,
con una longitud de 741 cm en la dirección z. La estructura modular del TOF cuenta con
18 sectores distribuidos en el ángulo azimutal (φ) y este arreglo se repite en cinco módulos
en la dirección z.
Los módulos contienen un total de 1638 elementos detectores, llamados MRPC (Multi-gap
Resistive Plate Chamber), y cubren un área de 160 m2. La principal caracteŕıstica de estas
cámaras es su fuerte campo eléctrico y uniforme en todo el volúmen gaseoso1 del detector,
ocasionando que las ionizaciones, debidas a las part́ıculas cargadas producidas en la colisión,
generen inmediatamente avalanchas de part́ıculas que producirán señales. Debido a que no
existe tiempo de arrastre asociado a los electrones en movimiento, a diferencia de la TPC
donde si existe, el tiempo de vuelo de las part́ıculas detectadas es obtenido midiendo el
retardo entre la señal del trigger, proporcionada por el detector T0, y la señal del TOF.
0.3 Resultados
Usando las ventajas en identificación de part́ıculas de los detectores TPC y TOF, el mesón
φ puede ser reconstruido a partir de los productos de su decaimiento. Este trabajo se enfocó
en el canal de decaimiento a dos kaones: φ →K++K−.
0.3.1 Selección de Eventos y de Trazas
Se analizó en esta tesis los eventos de colisiones p-Pb a una enerǵıa de
√
sNN = 5.02 TeV.
Debido al diseño del magneto 2-en-1 del LHC, la enerǵıa de los dos haces no puede ser
ajustada de manera independiente, llevando esto a diferente enerǵıa por beam. El sistema
centro de masa está entonces desplazado con respecto al sistema de laboratorio con una
rapidez de yN = -0.465 en la dirección del haz del proton.
Los eventos seleccionados a analizar son aquellos que pasan algunos cortes estándar. Los
eventos son aceptados si tienen vértice primario reconstruido en el detector SPD y cuya
coordenada z se encuentre entre ±10 cm del punto de interacción. La multiplicidad en los
eventos es obtenida en terminos del porcentaje del estimador de multiplicidad proporcionado
por el detector V0A (lado del Pb).
1El gas contenido en el TOF es una mezcla de: C2H2F4(90%),i− C4H10(5%), SF6(5%)
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CONTENTS
Se seleccionaron trazas primarias, que son aquellas producidas en la colisión incluyendo
productos de decaimientos electromagnéticos débiles pero excluyendo productos de decaimien-
tos débiles y particulas secundarias. Una part́ıcula de decaimiento débil es una part́ıcula hija
de un decaimiento débil de un hadron ligero o de un muon.
0.3.2 Espectro de momento del mesón φ(1020)
Como ya se mencionó, los mesones φ(1020) son identificados por su canal de decaimiento a
dos kaones, los cuales son identificados mediante el uso de los detectores TPC y TOF. Como
parte de la información obtenida es la enerǵıa(E) y el momento(p) de cada kaon, con esto
se puede calcular la masa invariante de un par de kaones de la siquiente manera:
M2
inv = (p21 + p22) = (E1 + E2)
2 − (p1 + p2)
2 (1)
Las distribuciones de masa invariante obtenidas tienen una seal alrededor de 1.02 GeV/c
junto con una gran cantidad de ruido combinatorio proveniente de kaones no correlacionados.
Este ruido se elimina mediante el método de eventos mixtos. La masa invariante de eventos
mixtos se calcula a partir de kaones de carga opuesta de diferentes eventos, de tal manera
que el pico de la seal no se formará pero si el ruido combinatorio.
Después de tener la distribucion de masa invariante, en la que el ruido combinatorio se
sustrajo, es posible que ruido residual esté presente todav́ıa. Entonces se ajusta una función
Voigt para la region del pico o de la seal del φ y una función polinomial para describir el
ruido residual. A partir de integrar la función de Voigt, sobre un amplio rango de masa,
se obtiene el yield. Este procedimiento se repite para 15 rangos de momento transverso
pT, entonces se obtiene una distribución del yield de la φ en función de pT. Se tiene una
distribución semejante para cada intervalo de multiplicidad: 0-5%, 5-10%, 10-20%, 20-40%,
40-60%, 60-80% y 0-100%.
A cada espectro de producción, o yield, de la φ se tiene que corregir por algunos factores
y correcciones que se relacionan con caracteristicas del detector. El principal es la corrección
por eficiencia, en donde se toma en cuenta la imperfecta detección de todas las part́ıculas
provenientes de la colision. A partir de simulaciones Monte Carlo usando en particular el
generador DPMJET, la eficiencia se calcula como el cociente siguiente:
ǫrec =
φreconstruido,TPC−TOF
φgenerado
, donde (2)
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CONTENTS
• Generado φ: Son los mesones φ generados de eventos que cumplen los cortes ya antes
descritos, y que no tienen interacción con los sistemas de detección, en este trabajo
seria el caso de los detectores TPC y TOF.
• Reconstruido φ: Se refiere al numero de mesones φ para el cual sus dos kaones hijas
en las que decayó son recontruidas dentro de la TPC o del TOF.
Para obtener es espectro de la part́ıcula φ se usa la siguiente expresión:
d2N
dpTdy
=
d2Nraw
dpTdy
· εtrig
εrecεPC
(3)
donde
• εrec : Es la eficiencia de reconstrucción.
• εPC : Es la corrección de la seal, la cual toma en cuenta el numero de mesones φ que
caen fuera de la región de integración.
• εtrig : Corrección que toma en cuenta la eficiencia del vértice y del trigger, tiene un
valor de 97.8± 1% para mediciones Minimum Bias.
d2Nraw
dpTdy
=
Y ield
Nevt × BR× dpTdy
(4)
0.3.3 Discusión de Resultados
Los espectros del mesón φ se obtuvieron en función de pT para siete multiplicidades. Para
obtener información de estos espectros es necesario ajustar alguna función de la cual podamos
extraer parametros. En particular se buscó obtener el yield integrado(dN/dy), mediante el
ajuste de la función de Levy-Tsallis a cada uno de los espectros de las multiplicidades, de
este ajuste. También se pudo obtener el pT promedio (〈pT〉). Se encontó una tendencia
creciente para dN/dy para el φ, llendo de las colisiones mas perifericas a las mas centrales.
El 〈pT〉 se comparó con colisiones pp y con otros hadrones tales como: (K∗0,Λ, p,K±, π±).
Similar a lo que se encontró en colisiones Pb-Pb, el 〈pT〉 tiene una tendencia creciente como
función de la multiplicidad. Se esperaŕıa que el comportamiento entre los hadrones K∗0, p,
φ y Λ fuera el mismo, sin embargo, se obtuvo que siguen una gerarqúıa aparente de masas.
xiii
CONTENTS
Se comparó la producción del mesón φ con la producción de K, π, p, en función de la
multiplicidad y para collisiones pp y Pb-Pb. El comportamiento de los resultados en p-Pb
es compatible con Pb-Pb, y pp, además de que la prediccion del Modelo Termal concuerda
con los resultados más centrales.
Las diferencias en los mecanismos de producción de bariones y mesones pueden ser es-
tudiados en las razones barión-mesón. Si la producción de hadrones puede ser explicada en
terminos de hidrodinámica, entonces las masas de las particulas juega un rol importante en
determinar la forma de las distribuciones de pT. Para estudiar este aspecto, la distribución
de pT del mesón φ es comparada con la de los protones, el cual es un barion de masa similar
pero diferente contenido de quarks. En las razones p/φ como funcion de pT muestran una
tendencia decreciente tanto en colisiones perifericas y centrales. Las colisiones pp y Pb-
Pb(80-90%) tienen un excelente acuerdo con las perifericas en Pb-Pb, mientras que (0-5%)
en p-Pb es intermedio entre pp y Pb-Pb(0-10%).
En la razón φ/π una tendencia creciente y muy semejante entre colisiones perifericas(60-
80%) y centrales(0-5%). Si comparamos con la razon barión-mesón p/π en p-Pb y en Pb-Pb,
vemos que son comportamientos crecientes muy parecidos. Esto indicaŕıa que el numero de
quarks no es un factor importante que determine las distribuciones de pT de las particulas
en bajo y pT intermedio, para colisiones centrales.
0.4 Conclusiones
En este trabajo se midió la producción del mesón φ en colisiones p-Pb a una enerǵıa de
√
sNN = 5.02 TeV, en la región de rapidez −0.5 < y < 0. Se estudió el canal de decaimiento
a dos kaones, el cual tiene una probabilidad de decaimiento del 48.9%. Mediante el uso de las
capacidades de identificación de part́ıculas de los detectores TPC y TOF los kaones fueron
seleccionados y calculandose aśı la masa invariante. El ruido combinatorio es sustraido
de las distribuciones de masa invariante mediante la técnica de Eventos Mezclados. La
producción del mesón φ se obtuvo mediante el conteo de las entradas en la distribución
de masas invariantes, después se aplicaron correcciones y factores de normalización para
obtener el espectro de pT del mesón φ para eventos divididos en siete multiplicidades, la
cual es medida por el detector V0A.
Al espectro del φ se ajusta una función Levy-Tsallis para obtener la producción integrada
(dN/dy) y pT promedio. Que después se comparan con los valores de otras part́ıculas más
estables (p, K, π). Se encontró que el 〈pT〉 tiene una tendencia creciente, en función de
xiv
CONTENTS
multiplicidad, y que aparentemente se sigue una jerarqúıa de masas en los casos de p, K∗0 y
φ. El mismo comportamiento esta presente en colisiones pp.
Las razones φ/p como función de pT para colisiones p-Pb perifericas (60-80%) es com-
patible con los resultados de pp y Pb-Pb(80-90%). Para colisiones p-Pb centrales (0-5%) los
valores de la razón son intermedios entre colisiones centrales y perifericas de Pb-Pb, compor-
tamiento que era esperado. Por el otro lado, en la razón mesón-mesón φ/π prácticamente
no hay diferencia entre los valores de colisiones centrales y perifericas p-Pb. Una tendencia
creciente semejante se presenta en p/π para Pb-Pb, entonces podemos concluir que la masa
de las part́ıculas es un parametro importante y no tanto el contenido de quarks.
xv
List of Figures
1.1 Fundamental particles and the forces mediators. . . . . . . . . . . . . . . . . . . 2
1.2 a) The momentum vector in the plane x-z, b) Transverse plane, where pT is mea-
sured, c) Illustrative values for the pseudorapidity and their respective θ angle
values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Regions of the principal forms of hadronic matter are shown in the baryon-density-
temperature plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Distributions of the CERN’s accelerators that increase the energy of the pro-
tons up to 7 TeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 ALICE schematic layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Pseudorapidity (η) ranges covered by ALICE detectors. . . . . . . . . . . . . . . 16
2.4 ITS detector dimensions and sub-detectors. . . . . . . . . . . . . . . . . . . . . 17
2.5 TPC detector dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Schematic illustration of the working principle and the read-out chambers of the
TPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 TOF detector design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1 Data processing framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 dE/dx-spectra from TPC detector together with a Bethe-Bloch curve for each par-
ticle. Signals coming from p-Pb collisions. . . . . . . . . . . . . . . . . . . . . 23
3.3 TOF signal as a function of momentum. The clear bands correspond to each type
of particle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1 V0A particles multiplicity in terms of percentile ranges. . . . . . . . . . . . . . . 27
4.2 Left: TOF PID response for the kaon hypothesis. Right: TPC PID response for
the kaon hypothesis. Dashed lines correspond to 2σ, 3σ and 4σ particle selection
limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
xvi
LIST OF FIGURES
4.3 K+K− Invariant mass distributions in several pT ranges are shown as black points
and the combinatorial background(event mixing) are blue points. . . . . . . . . . 31
4.4 K+K− Invariant mass distributions for high pT values are shown as black points
and the combinatorial background(event mixing) are blue points. . . . . . . . . . 32
4.5 Invariant mass distribution after the mixed events background subtraction using
the information from TPC and TOF combined. Results correspond to 0-100%
multiplicity bin, magenta line is the total fit (ResidualBg+Voigt). . . . . . . . . . 35
4.6 Invariant mass distribution after the mixed events background subtraction using
the information from TPC and TOF combined. Results correspond to 0-100%
multiplicity bin, magenta line is the total fit (ResidualBg+Voigt). . . . . . . . . . 36
4.7 Peak correction factor for the default analysis parameters in the multiplicity bin
0− 100% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.8 Ratios of the efficiency as a function of multiplicity over the Minimum Bias efficiency
(0-100)%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.9 Efficiency used to correct the TPC-TOF data, 3σ and 4σ are shown. . . . . . . . 40
5.1 Fully corrected φ Spectra 1/2πpT×(d2N/dpTdy) obtained with TPC-TOF detectors
information, for Minimum Bias, 0-5%, 5-10%, 10-20%, 20-40%, 40-60% and 60-80%
multiplicity measurements. Only statistical errors are shown. . . . . . . . . . . . 42
5.2 Mass of the φ mesons measured in Minimum bias, 0-5% and 60-80% multiplicity
ranges. Only statistical uncertainties are shown. . . . . . . . . . . . . . . . . . 43
5.3 Width of the φ mesons measured in Minimum bias, 0-5% and 60-80% multiplicity
ranges. Only statistical uncertainties are shown. . . . . . . . . . . . . . . . . . 44
5.4 pT dependent systematic uncertainty due to material budget(MB) for the φ. . . 49
5.5 pT dependent systematic uncertainty due to hadronic interaction cross section for
the φ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.6 pT dependent systematic uncertainty due to analysis cuts variations for the φ. . . 50
5.7 Percentage of the systematic uncertainties for each source in 0-100% multiplicity
bin, using the combined TPC-TOF information. . . . . . . . . . . . . . . . . . . 51
5.8 Fractional smoothed systematic uncertainties for each multiplicity range and for
each systematic source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.9 Fully corrected spectra for φ(K+K−) using the combined TPC-TOF information,
corresponding to minimum bias. Statistical uncertainties (bars) and systematic
uncertainties (boxes). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
xvii
LIST OF FIGURES
5.10 Fully corrected spectra for φ(K+K−) using the combined TPC-TOF information as
a function of multiplicity. Statistical uncertainties are shown in bars and systematic
uncertainties are shown in boxes. . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.11 Fits to the corrected φ spectra (d2N/dpTdy) in the 5-10% multiplicity bin. . . . . 55
5.12 Fits to the corrected φ spectra (d2N/dpTdy) in the 60-80% multiplicity bin. . . . 56
5.13 Left: φ points, for 0-5%, moved down to the systematic unc. limit. Right: φ
points moved up to the systematic unc. limit. The red curve is the Levy fit to each
spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.14 Left: φ integrated yield as a function of multiplicity. dNφ/dy vs dNch/dη. Right:
φ mean pT ( 〈pT〉 ) as a function of multiplicity. Systematic uncertainties (boxes),
statistical uncertainties (lines). . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.15 Comparison between the three different methods to obtain the φ spectra. The fit
is compared to the data point at the bottom of the plot. . . . . . . . . . . . . . 60
5.16 Combined φ invariant spectra for minimum bias measurement, Levy-Tsallis fit func-
tion is shown. Statistical uncertainties (bars), Systematic uncertainties (boxes). . 61
5.17 Combined φ invariant spectra for six multiplicity ranges, and the respectively
Levy-Tsallis fit functions. Statistical uncertainties (bars), Systematic uncertain-
ties (boxes). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.1 φ integrated yield(dNφ/dy) as a function of multiplicity. Statistical uncertain-
ties(bars), systematic uncertainties(boxes) and uncorrelated systematic (shaded
boxes). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2 Mean transverse momentum of π±,K±,K0
s,K
∗0
s , p,Λ and φ for two collision systems,
pp at
√
s = 7 TeV and p-Pb at
√
sNN = 5.02 TeV. . . . . . . . . . . . . . . . . 63
6.3 Left: Ratio φ/π as a function of multiplicity (dNch/dη)
1/3 for the three collision
systems: pp, p-Pb and Pb-Pb. Right: Ratio φ/p as a function of multiplicity
(dNch/dη)
1/3 for the same collision systems described before. Statistical uncer-
tainties(bars), systematic uncertainties(boxes) and uncorrelated systematic (shaded
boxes). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
xviii
LIST OF FIGURES
6.4 Left: Ratio φ/K− as a function of multiplicity (dNch/dη)
1/3 and comparison be-
tween pp, p-Pb and Pb-Pb collision systems. Right: Ratio φ/K as a function of the
collision energy(
√
sNN ) , compared with different collision systems in other experi-
ments. The values given by a grand-canonical thermal model with a chemical freeze-
out temperature of 156 MeV are also shown [37]. Statistical uncertainties(bars),
systematic uncertainties(boxes) and uncorrelated systematic (shaded boxes) are
shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.5 Ratio p/φ as a function of pT for pp at
√
s = 7 TeV, p-Pb at
√
sNN = 5.02 TeV
and Pb-Pb at
√
sNN = 2.76 TeV, comparing central and peripheral intervals. . . 66
6.6 Ratio φ/π as a function of pT for p-Pb at
√
sNN = 5.02 TeV and comparing central
and peripheral measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.7 Ratio p/π = (p+p)/(π++π−) as a function of pT in the rapidity interval 0 < y < 0.5
(left panel). The ratios are compared to results in Pb-Pb collisions measured at
mid-rapidity, shown in right panel. The empty boxes show the total systematic
uncertainty; the shaded boxes indicate the contribution uncorrelated across multi-
plicity bins. Figure taken from [27]. . . . . . . . . . . . . . . . . . . . . . . . . 67
1 Resolution histogram (truncated Gaussian fit) in the transverse momentum 1.0 <
pT < 1.5 (left plot) and 2.5 < pT < 3.0 (right plot), both in the multiplicity bin
0− 100%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2 Reconstructed histogram with a Voigtian0 fit, where σvoi is obtained. The left
plot is shown in the transverse momentum 1.0 < pT < 1.5 and the right plot in
2.5 < pT < 3.0, both in the multiplicity bin 0− 100% . . . . . . . . . . . . . . . 74
3 Three calculations of the resolution are presented, σGauss, σh, σvoi in the 0-100%
multiplicity bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
xix
Chapter 1
High Energy Physics
1.1 Standard Model
The High Energy Physics(HEP) has established and tested since the 60’s a detailed theory
of the elementary particles and their fundamental interactions called Standard Model. The
Standard Model describes the fundamental forces and the composition of matter. It is
a gauge theory that includes the strong, weak, and electromagnetic forces and the related
interactions. Being the gravity the fourth force that is not included in this theory. According
to the Standard Model theory, all mater is constituted out of point-like particles which have
a spin 1/2 and grouped into three families, each family has two quarks and two leptons
members [1].
The SU(3) × SU(2) × U(1) Standard Model(SM) is the combination of three theories,
describing each of the forces. The Quantum Chromodynamics (QCD) is one of the com-
ponents of the SM(SU(3)), it is a gauge theory which describes the strong interactions of
colored quarks(q) and gluons(g). The color is a property similar to the charge in strong
interactions, for example, a quark of specific flavor can have three different color charge
(green, blue and red) and in order to form hadrons which are colorless(white), either with
three colored quarks or a quark and an anti-quark. Hadrons are grouped into baryons and
mesons. Baryons consist of three quarks, qqq or qqq while mesons consist of two quarks
(qq). The gluons are the mediators of the strong force. The interaction between quarks and
gluons can change the color but not the flavor. Since color (like electric charge) is always
conserved, this means that the gluon come in eight different bi-colored combinations [1].
The electro-weak interaction is based on the gauge theory group SU(2) × U(1). There
1
1. High Energy Physics
are two kinds of electro-weak interactions: charged(mediated by W±) and neutral(mediated
by Z0), the first one is the only that changes flavor. The Quantum Electrodynamics(QED)
describes the electromagnetic interactions mediated by the exchange of photons(γ). Leptons
are affected by the weak force and the charged ones in addition by electromagnetic force.
The Standard Model has also, however, limitations that require extensions to keep the
theory consistent. The most important issue is the masses of the electro-weak gauge bosons
predicted to be zero within the theory. This is clearly inconsistent with experiment. This
situation can be resolved by an additional gauge boson added to the theory, the Higgs
boson. The Higgs mechanism generates the masses for the W± and the Z0 while the γ
remains massless. Recent results from LHC have confirmed, in July 2012, the existence
of a unknown particle with a mass between 125 and 127 GeV/c2. By March 2013, the
particle has been proven to behave, interact and decay in many of the ways predicted by the
Standard Model, and was also tentatively confirmed to have positive parity and zero spin,
two fundamental attributes of a Higgs boson [2].
Figure 1.1: Fundamental particles and the forces mediators.
2
1. High Energy Physics
1.2 Kinematic Variables
In order to analyse and measure the properties of the hadrons, it is convenient to define some
variables that depend on some measurable quantities of the particles. The energy-momentum
four-vector is:
pµ = (p0, p1, p2, p3) = (E/c, px, py, pz) (1.1)
The transverse momentum is defined in terms of the px and py components of the total
momentum p.
pT =
√
p2x + p2y, (1.2)
then the energy-momentum four-vector can be written as pµ = (E, pT , pz) where c=1. In
the figure 1.2, left image, it is shown the momentum vector over the x-z plane, where θcms
is the direction of the vector with respect to z-axis (beam axis) and the right image shows
the transverse momentum vector in the x-y plane [3].
The rapidity(y) is defined as a function of the energy(E) and the longitudinal momentum(pz)
of the same particle, the expression is:
y =
1
2
ln
E + pz
E − pz
(1.3)
If one considers the case in which the momentum magnitude of a particle is much bigger
than the mass of the same particle, i.e. p ≫ m, the rapidity(y) can be approximated as
y ≈ −ln[tan(θ/2)] where θ is the vector momentum angle with respec to the beam axis (z
direction). Under this approximation the rapidity is known as pseudorapidity[3].
η = −ln[tan(θ/2)] (1.4)
The figure 1.2 shows examples of the different values of the pseudorapidity and its cor-
responding angle in the x-z plane.
3
1. High Energy Physics
protónprotón
P
x-z Plane
cm
Transverse plane x-y
pt
φ
θ=90
θ=45
θ=10
θ=0
η=0
η=0.88
η=2.44
η=
x
z
y
x
a) b) c)
Figure 1.2: a) The momentum vector in the plane x-z, b) Transverse plane, where pT is measured,
c) Illustrative values for the pseudorapidity and their respective θ angle values.
1.3 Quantum Chromodynamics (QCD)
The QCD is the theory of the strong interactions. The strong interactions have been studied
since the beginning of the 20th century soon after the discovery of the atomic nucleus. This
interaction is a fundamental force describing interactions between quarks and gluons which
make up hadrons (protons, neutron, pions, etc), similar description to the way QED does for
electrons and photons. In QCD, the interactions are invariant under a SU(3) transformation
in colour space (SU(3) colour symmetry). Thus, the quarks carry three colour charges, and
each gluon is a combination of eight different combinations of colour and anti-colour charge.
The intrinsic charge of the gauge field (the gluon) is the decisive modification in compari-
son to QED; it makes the pure gluons system self-interactive, in contrast to the ideal gas
of photons[13]. The two main strong interaction features of interest for heavy-ion physics are:
• Colour confinement: the force between quarks does not diminish as they are sep-
arate. Because of this. When one tries to separate two quarks, the energy is enough
to create another quark and then creating another quark pair; they are forever bound
into hadrons such as the proton and the neutron or the pion and kaon. Although an-
alytically unproven, confinement is widely believed to be true because it explains the
consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD.
• Asymptotic freedom: the value of the strong coupling constant, αS, depends on
the momentum transfer (Q2) at which an observed process occurs (running coupling
4
1. High Energy Physics
constant). αS decreases with increasing energy and asymptotically, at infinite energy,
tends to zero .
There is no known phase-transition line separating these two properties; confinement is
dominant in low-energy scales but, as energy increases, asymptotic freedom becomes domi-
nant. This theory predicts that strong interaction properties in a complex system may differ
from those observed in the vacuum. Quark confinement inside hadrons can disappear at
energy densities higher than those typical of normal nuclear matter [13].
The Lagrangian density of QCD is given by [4]:
L = −1
4
F a
µνF
µν
a +
∑
f
ψ
f
α(iγµD
µ)ψ
f
β (1.5)
with the non Abelian group tensor
F a
µν = (∂µA
a
ν − ∂νA
a
µ − gfa
bcA
b
µA
c
ν) (1.6)
and
Dµ = ∂µ + ig
λa
2
Aa
µ (1.7)
The fundamental degrees of freedom of the theory are the 3× 6 quarks fermionic fields ψ
and the eight gluonic fields Aµ. λa and fa
bc are the eight SU(3) group generators (the 3× 3
Gell-Mann matrices) and the structure constants.
The inclusion of quark masses would add a term
Lm =
∑
f
mfψ
f
αψ
fα (1.8)
in Eq. 1.5. Equation 1.7 contains one dimensionless coupling constant g, and hence
Eq. 1.5 provides no scale: QCD predicts only the ratios of physical quantities, not absolute
values in terms of physical units. In QCD hadrons are colour-neutral bound states of quarks
(baryons) or of quark-antiquark pairs (mesons); they are thus the chromodynamic analogue
of atoms as the electrically-neutral bound states in QED. The differences between the two
theories becomes significant at large distances: while a finite ionization energy ∆E suffices
to break up the electrodynamic bound, this is not possible in the case of quark binding.
This property of the QCD leads to the concept of “confinement”. At short distances QCD
shows another peculiar behaviour, the decrease of the colour charge with decreasing the
5
1. High Energy Physics
distance from the colour-probe to the charge itself. This leads to the concept of “asymptotic
freedom”, which implies that partons1 inside hadrons interact weakly among themselves and
can be considered as almost free.
1.4 Quark Gluon Plasma (QGP)
Ultra-relativistic heavy ion collisions offer a good opportunity to investigate highly excited
dense nuclear matter under controlled laboratory conditions. The aim for such studies is the
expectation that an entirely new form of matter may be created from such reactions. That
form of matter, called Quark Gluon Plasma (QGP), is the QCD analogue of the plasma
phase of ordinary atomic matter. Nevertheless, the deconfined quanta of a QGP are not
directly observable because of the fundamental confining property of the physical QCD vac-
uum. What is observable are hadronic and leptonic residues of the transient QGP state.
Among some probes there are the Leptonic probes, γ, e+e−, µ+µ−, they carry information
about the spectrum of electromagnetic current fluctuations in the QGP stat; the abundance
of quarkonia Ψ,Ψ′,Υ,Υ′ (also observed via l+l−) carry information about the chromoelectric
field fluctuations in the QGP. The large number of hadronic probes, π,K, p, p,Λ,Ξ,Ω, φ, ρ, ...
provide information on the quark flavor chemistry and baryon number transport. Theory
suggest that with decays such as ρ → e+e− the properties of the hadronization and chi-
ral symmetry breaking can be indirectly studied. Quantum statistical interference patterns
in ππ,KK, pp,ΛΛ correlations provide somewhat cloudy lenses with which the space-time
geometry of hadronic ashes of the QGP can be investigated. The detailed rapidity and trans-
verse momentum spectra of hadrons provide barometric information of pressure gradients
during the explosive expansion of the QGP medium[5].
The main problem with all the above probes is precisely that they are all indirect mes-
sengers. Since we can not see free quarks and gluons it is not trivial to verify the QCD
predictions of the QGP state. However, nature choses to hide those constituents within the
confines of colour neutral composite many body systems hadrons.
1.4.1 Phases of strongly interacting matter
It is expected that in heavy ion collisions, one reaches conditions under which the structured
confining vacuum is dissolved, forming a domain of thermally equilibrated hadronic matter
1The basic constituents of hadrons, quarks and gluons.
6
1. High Energy Physics
comprising freely moving quarks and gluons. A schematic plot of the the phase diagram of
dense hadronic matter is shown in figure 1.3 The different phases populate different domains
of temperature T and baryon density. For high temperatures and/or high baryon density,
we have the deconfined phase. If deconfinement is reached in the nuclear-collision, it freezes
back into the state containing hadrons during the temporal evolution of the small fireball.
The most difficult domain to reach experimentally is the one of low baryon number density,
at high T , corresponding to the conditions that were in the early Universe. This demands
extreme collision energies, which would permit the baryon number to escape from the central
rapidity region, where only the collision energy is deposited.
Now we want to qualitatively understand the magnitude of the temperature at which
the deconfined quark-gluon phase will freeze into hadrons. The order of magnitude of this
transition temperature (if a phase change occurs) or cross temperature (if no phase transition
occurs) is obtained by evaluating where a benchmark value for energy density occurs, εH ≈
3PH = 1 GeV fm−3 [6]. The generalized Stefan-Boltzmann law describes the energy density
ε and pressure P as functions of the temperature T of a massless relativistic gas:
P SB =
1
3
εSB =
π2
90
gT 4 (1.9)
where the quantity g is the number of different (relativistic) particle states available and is
often called the ‘number of degrees of freedom’ or ‘degeneracy’. In the deconfined phase,
g ≡ gg +
7
4
gq, (1.10)
which comprises the contribution of massless gluons(bosons) and quarks(fermions). The
relative factor 2× 7
8
= 7
4
expresses the presence of particles and antiparticles (factor 2) and
the smaller fermion phase space, compared with the boson case, given the exclusion principle.
Gluons and quarks carry color and spin, but quarks in addition come in two(nf = 2) flavors
u and d. Since at high temperatures the flavor count may include the strange quark, we
leave (nf = 2) as a variable. Then we obtain the following degeneracy in a QGP:
gluons : gg = 2(spin)× (N2
c )(color) = 2× 8 = 16,
quarks : gq = 2(spin)×Nc(color)× nf (flavor) = 2× 3× nf .
When the semi-massive strange quarks are present, the effective number of ‘light’ flavors is
7
1. High Energy Physics
≈ 2.5. Thus, g ≈ 40 in equation 1.9, to be compared with just two directions of polarization
for photons[6].
For a massless ideal quark-gluon gas, we find
TH = 160MeV, for εH = 1.1 GeVfm−3
Hagedorn introduced this critical temperature in his study of the boiling point of hadronic
matter[29].
Figure 1.3: Regions of the principal forms of hadronic matter are shown in the baryon-density-
temperature plane.
1.4.2 Strangeness enhancement
The quarks u and d from which the stable matter is made are easily produced as quark-
antiquark pair because they have small masses. Another abundantly added quark flavor is
strangeness, particularly if the deconfined QGP phase of matter is formed. Strangeness was
one of the first proposed signatures of the deconfined phase. The mass of strange quarks
and antiquarks is of the same magnitude as the temperature T at which protons, neutrons,
and other hadrons are expected to dissolve into quarks. This means that the abundance
of strange quarks is sensitive to the conditions, structure, and dynamics of the deconfined-
matter phase.
In proton proton collisions, the production of particles containing strange quarks is
strongly suppressed as compared to the production of particles with u and d quarks [7].
8
1. High Energy Physics
It has been argued that this suppression is due to the higher mass of the ss quark pair.
The suppression increases with the strangeness content of the particles produced in proton
proton collisions.
In case of QGP formation, ss pairs can either be produced via the interactions of two
gluons or of qq pairs. Leading order αs pQCD calculation suggest that the second pro-
cess dominates only for
√
s ≤ 0.6 GeV. The time-scale of chemical equilibration of (anti-)
strangeness due to gluon gluon interaction is estimated to be about 3 to 6 fm/c, depending on
the temperature of the plasma[8]. Following this line, the yield of strange and multi-strange
mesons and baryons has been predicted to be strongly enhanced in the presence of a QGP as
compared to a purely hadronic scenario at the same temperature. However, the estimated
equilibration times may not be sufficient rapid to cause a saturation in the production of
strange hadrons before QGP freeze-out. Some examples of strange particles are listed below:
• Cascades Ξ(qss): The doubly strange cascades, Ξ0(uss) and Ξ−(dss), are below the
mass threshold for hadronic decays into hyperons and kaons. Consequently, there is
only one decay in each case, Ξ0 → Λ+π− (cτ = 4.9cm) and Ξ0 → Λ+π0 (cτ = 8.7cm).
There are also several Ξ∗ resonances known, which normally feed down in a hadronic
decay into the hyperon and kaon abundances: Ξ∗(qss) → Y (qqs) +K(qs).
• Omegas Ω−(qss): There are several primary weak-interaction decay channels leading
to the relatively short proper decay path, (cτ = 2.46cm): Ω−(1672) → Λ+K− (68%),
Ω−(1672) → Ξ0 + π− (24%) and Ω−(1672) → Ξ− + π0 (9%). The first of these decay
channels is similar to the decay of the Ξ−, except that the pion is replaced by a kaon in
the final state. In the other two options, after cascading has finished, there is a neutral
pion in the final state, which makes the detection of these channels impractical.
• Phi φ(ss): The species addressed in this thesis, the vector (J=1) meson φ is believed
to be a ‘pure’ bound state of the strange-quark pair φ = ss. With mass 1019.45 MeV,
it has a relatively narrow full width Γφ = 4.26 MeV. The main two decay channels are:
φ→ K+ +K−, 48.9%
φ→ K0
L +K0
S, 34.2%
9
1. High Energy Physics
1.4.3 Resonances
Hadronic resonances have their importance in high energy collisions analyses because they
can provide experimental evidence for partial chiral symmetry restoration in the deconfined
Quark-Gluon phase produced in this energetic collisions. The production of resonances
occurs both during the transition (at a critical temperature T ≈ 160 MeV) from the quark-
gluon plasma (QGP) to the hadronic phase and in the hadronic phase itself by regeneration.
Since the resonances lifetimes are comparable to the lifetime of the partonic plasma phase (a
few fm/c) they are an important tool to investigate medium modifications to the resonant
state due to chiral transition[9]. It is expected that chiral symmetry is restored at around
the same critical temperature as the deconfined phase transition, with the quark-antiquark
condensate decreasing towards 0 with increasing temperature. Resonances that interact
with the medium in the mixed or early hadronic phase, when chiral symmetry is at least
partially restored, may be shifted of their mass and exhibit broader widths than observed in
vacuum[10].
The temperature evolution and lifetime of the hadronic phase affect the relative strengths
of resonance-generation processes and re-scattering, and therefore ratios of resonance yields
to non-resonance yields. Particle ratios have been predicted as functions of the chemical
freeze-out temperature and the elapsed time between chemical and thermal freeze-out using
thermal models[10]. In principle, measurements of two different particle ratios are needed to
tune the thermal models and determine uniquely the chemical freeze-out temperature and
the lifetime of the hadronic medium.
The study of the mesonic resonances φ(1020) and K∗0(892) production is of particular
interest. They have mass close to the proton mass but their lifetimes differ of about a factor
of 10, being τφ = 46 fm/c and τK∗0 = 4.0 fm/c, and their strangeness content differ by one
unity. The K∗0 is expected to be more sensitive to the re-scattering effects in the hadronic
medium because of the much shorter lifetime. The φ is other story because it can escape the
medium with almost no re-scattering, then this resonance is a good candidate to investigate
partial restoration of chyral symmetry at the formation time. In addition, the φ can help to
probe strangeness production, being the lightest vector meson composed of sea quarks (ss).
In pp collisions, ss pair production was found to be significantly suppressed with respect to
uu and dd[15].
10
Chapter 2
The ALICE Experiment at LHC
2.1 Large Hadron Colider
The LHC is, at the moment, the biggest particle accelerator in the world. The idea of the
project started in 1984, was approved in 1994 and the construction work in the underground
tunnel started in 2001. Before the LHC, CERN1 had the LEP2 that was working from 1989
to 2000. Then after dismantling of the LEP, the LHC used the same underground tunnel of
27 km of circumference. The LHC is located under the the Swiss-French border area close
to Geneva at a depth of 50 to 175 m.
The LHC is a synchrotron that accelerates two counter-rotating beams in separate beam
pipes. Each beam rotates several times around the ring until it reach enough energy to
collide. The largest achievable acceleration energies are 7 TeV for protons and 2.76 TeV per
nucleon for lead ions, therefore providing collisions at
√
s = 14 TeV and
√
s = 5.5 TeV,
respectively.
To keep the beam focused and to bend the beam through the ring, the LHC has 1232
dipoles of 14.3 m length and contains superconducting magnets which operate at a tem-
perature of 1.9 K. And 392 quadrupoles maintain the beam focused, each quadrupole has
a length between 5 and 7 m. Powered by a maximum current of 11.7 kA the dipoles can
provide a magnetic field from 0.535 T during the injection (beam energy of 450 GeV) up to
8.33 during the collisions(energy of 7 TeV) [11].
1Centre Européen pour la Recherche Nucléaire.
2Large Electron Positron Collider
11
2. The ALICE Experiment at LHC
2.1.1 The accelerator complex
The accelerator complex at CERN is a succession of machines that accelerate particles to
increasingly higher energies. Each machine boosts the energy of a beam of particles, before
injecting the beam into the next machine in the sequence. In the Large Hadron Collider
(LHC) the last element in this chain particle beams are accelerated up to an energy of
4 TeV per beam. Most of the other accelerators in the chain have their own experimental
halls where beams are used for experiments at lower energies. The proton source is a simple
bottle of hydrogen gas. An electric field is used to strip hydrogen atoms of their electrons
to yield protons. Linac 2, the first accelerator in the chain, accelerates the protons to the
energy of 50 MeV. The beam is then injected into the Proton Synchrotron Booster (PSB),
which accelerates the protons to 1.4 GeV, followed by the Proton Synchrotron (PS), which
pushes the beam to 25 GeV. Protons are then sent to the Super Proton Synchrotron (SPS)
where they are accelerated to 450 GeV. The protons are finally transferred to the two beam
pipes of the LHC. The beam in one pipe circulates clockwise while the beam in the other
pipe circulates anticlockwise. It takes 4 minutes and 20 seconds to fill each LHC ring, and
20 minutes for the protons to reach their maximum energy of 4 TeV. Beams circulate for
many hours inside the LHC beam pipes under normal operating conditions. The two beams
are brought into collision inside four detectors ALICE, ATLAS, CMS and LHCb where the
total energy at the collision point is equal to 8 TeV. The accelerator complex includes the
Antiproton Decelerator and the Online Isotope Mass Separator (ISOLDE) facility, and feeds
the CERN Neutrinos to Gran Sasso (CNGS) project and the Compact Linear Collider test
area, as well as the neutron time-of-flight facility (nTOF). Protons are not the only particles
accelerated in the LHC. Lead ions for the LHC start from a source of vaporized lead and
enter Linac 3 before being collected and accelerated in the Low Energy Ion Ring (LEIR).
They then follow the same route to maximum energy as the protons.
12
2. The ALICE Experiment at LHC
AD
S- Booster
ISLODE
n- ToF
LINAC2
LINAC3
(ions)
Leir
PS
SPS
LHC
Gran Sasso
7 30 km
ALICE
CMS
LHCb
ATLAS
East Area
North Area
78m
628m
157m
182m
7 km
27 km
proton ióno antiproton neutron neutrino
neutrino
protón
protón
neutrón
antiprotón
Figure 2.1: Distributions of the CERN’s accelerators that increase the energy of the protons
up to 7 TeV.
2.2 ALICE (A Large Ion Collider Experiment)
The ALICE, one of the four big experiments at CERN and the one in which this thesis is
focused, is 16 m high, 26 m length and has a total weight around 10,000 t. It is designed
to address the physics of strong interacting matter and the quark-gluon plasma at extreme
values of energy density and temperature in nucleus-nucleus collisions. ALICE will allow the
comprehension of hadrons, electrons, muons, and photons produced in the collision of heavy
nuclei (Pb-Pb). The physics programme also includes collision with lighter ions and at lower
energy, in order to vary energy density and interaction volume, as well as dedicated proton-
nucleus runs[18]. Proton-proton runs recorded in ALICE will provide reference data for the
heavy-ion programme and address a number of specific strong-interaction topics for which
ALICE is complementary to the other LHC detectors. The ALICE physics programme is
summarized below:
• pp collisions at
√
s = 900 GeV and 7 TeV during 2010
13
2. The ALICE Experiment at LHC
• PbPb collisions at
√
s = 2.76 TeV in November 2010
• pp collisions at
√
s = 7 TeV during 2011
• PbPb collisions at
√
s = 2.76 TeV in Autumn 2011
• LHC technical stop in 2012
• pp collision at
√
s = 14 TeV starting from 2013 and then regular runs
• Subsequent heavy-ion program:
1-2 years PbPb
1 year pPb-like collision (pPb,dPb or αPb)
1-2 years Ar-Ar
Among some physics observables that ALICE can study are the global event structure
such as multiplicity and transverse or zero-degree energy flow. With this is possible to define
the geometry, i.e. impact parameter, shape and orientation of the collision volume, and
number of interacting nucleons. Nuclear modification to the parton distribution function can
be extracted by comparing global event features and, more directly, specific hard processes
like direct photons, heavy flavours in pp, pA and A-A collisions.
14
2. The ALICE Experiment at LHC
Figure 2.2: ALICE schematic layout.
2.2.1 ALICE detectors
ALICE consists of an ensemble of several detectors, it has the central barrel part which mea-
sures hadrons, electrons, and photons, and a forward muon spectrometer. The central part
cover polar angles from 45◦ to 135◦ and is embedded in a large solenoid magnet. From inside
out, the barrel contains an Inner Tracking System (ITS) of six planes of high-resolution
silicon pixel (SPD), drift (SDD), and strip (SSD) detectors, a cylindrical Time-Projection
Chamber (TPC), three particle identification arrays of Time-of-Flight (TOF), Ring Imag-
ing Cherenkov (HMPID) and Transition Radiation (TRD) detectors, and two calorimeters
(PHOS and EMCal). Excepting HMPID, PHOS, and EMCal all the other detectors cover
the full azimuthal angle.
VZERO
The V0 detector [16] is a small angle detector consisting of two arrays of scintillator counters,
called V0A and V0C, which are installed on either side of the ALICE interaction point.
15
2. The ALICE Experiment at LHC
Figure 2.3: Pseudorapidity (η) ranges covered by ALICE detectors.
This detector has several functions. It provides minimum-bias triggers for the central
barrel detectors in pp, pA and A-A collisions. These triggers are given by particles originating
from initial collision and from secondary interactions in the vacuum chamber elements. As
the dependence between the number of registered particles on the V0 arrays and the number
of primary emitted particles is monotone, the V0 serves as an indicator of the centrality of
the collision via the multiplicity recorded in the event.
The V0A detector is located 340 cm from the vertex on the side opposite to the muon
spectrometer whereas V0C is fixed to the front face of the hadronic absorber, 90 cm from
the vertex. They cover the pseudo-rapidity ranges 2.8 < η < 5.1 (V0A) and 2.8 < η < 5.1
(V0C) and are segmented into 32 individual counters each distributed in four rings.
Inner Tracking System (ITS)
The ITS is the closest detector to the beam axis. As shown schematically in figure 2.4 the
ITS consist of six cylindrical layers of silicon detectors, located at a radii between 4 and
43 cm. ITS covers the rapidity range of |η| < 0.9 for al vertices located within the length
of the interaction diamond (±1σ, i.e. ±5.3 cm along the beam direction). The number,
position and segmentation of the layers were optimized for efficient track finding and high
impact-parameter resolution. The two first layers correspond to the SPD1 located at r = 4
and 7.2 cm respectively and a length of 28.2 cm along z axis. The next two layers correspond
1Silicon Pixel Detector
16
2. The ALICE Experiment at LHC
to SDD1 with radii of r = 15 and 23.9 cm being the inner cylinder shorter than the outer
one, 44.4 cm and 59.4 cm respectively. The last two layers, the SSD2 with r = 38.5 and 43.6
cm [17].
The main tasks of the ITS are to localize the primary vertex with a resolution better
than 100 µm, to reconstruct secondary vertices from the decays of hyperons and D and B
mesons, to track and identify particles with momentum below 200 MeV/c, to improve the
momentum and angle resolution for particles reconstructed by the Time Projection Chamber
(TPC) and to reconstruct particles traversing dead regions of the TPC [19].
Figure 2.4: ITS detector dimensions and sub-detectors.
Time Projection Chamber (TPC)
The Time Projection Chamber is the main tracking detector of the central barrel and is op-
timised to provide, together with other central barrel detectors, charged particle momentum
measurements with good two-track separation, particle identification, and vertex determi-
nation. In addition, data from central barrel detectors are used to generate a fast online
High-Level Trigger (HLT) for the selection of low cross section signals. The TPC is a cylin-
drical detector with an inner radii of 84.8 cm and outer radii of 246.6 cm, covering 500 cm
along the beam axis. The phase space covered by the TPC is |η| < 0.9 for tracks with full
radial track length(matches in ITS, TRD, and TOF detectors). The TPC covers the full
azimuth (with exception of the dead zones). A large pT range is covered from about 0.1
GeV/c up to 100 GeV/c with good momentum resolution [19].
1Silicon Drift Detector
2Silicon micro-Strip Detector
17
2. The ALICE Experiment at LHC
This detector consist of two main parts: the field cage and the readout chambers. Both
are filled with a gas mixture of Neon, Nitrogen and CO2. If a charged particle travels through
the gas volume, it excites and ionizes has atoms along its track. As a consequence, it loses
an amount of energy per unit track length (dE/dx) which is specific for every particle type.
Inside the field cage, a homogeneous electric field perpendicular to the readout chambers is
generated: The cathode plane of the readout chambers is at a potential of 0V and, in the
middle of the TPC, the parallel central electrode is set to a negative voltage of 100kV. At
the borders of the field, the homogeneity of the field is achieved by special equipotential
strips which are connected by a voltage divider. Thus, every strip is put to a potential that
its center would have in a homogeneous field [23].
Figure 2.5: TPC detector dimensions.
The readout chamber is a multi-wire proportional chamber (MWPC) shown in figure 2.6.
It is consisting of a segmented cathode pad plane and the anode, cathode and gating wire
planes. The anode wires are set to a positive voltage of 1500V which leads to an amplification
of the drifted electrons: In the vicinity of the wire the electric field grows proportional to
1/r. The electron energy rises which leads to ionization and the released electrons themselves
cause an avalanche process [23].
TPC allows the three-dimensional reconstruction of the tracks. The pads provide the re-
construction of the coordinates (x,y) via the distribution of the induced signal. The position
18
2. The ALICE Experiment at LHC
Figure 2.6: Schematic illustration of the working principle and the read-out chambers of the TPC.
of the particle in the drift direction is obtained with the measurement of the drift time (∆t)
till the readout planes. The drift velocity of the electrons (ve) in the gas is well known; then
the coordinate z is calculated with z = ve∆t. The three dimensional signal is called cluster.
Time Of Flight (TOF)
The Time-Of-Flight (TOF) detector is a large area array that covers the central pseudo-
rapidity region (|η| < 0.9) for Particle IDentification (PID) in the intermediate momentum
range, below about 2.5 GeV/c for pions and kaons, up to 4 GeV/c for protons, with a π/K
and K/p separation better than 3σ. The TOF, coupled with the ITS and TPC for tracks
and vertex reconstruction and for dE/dx measurements in the low-momentum range (up to
about 1GeV/c), provides even-by-event identification of large samples of pions, kaons, and
protons. In addition, at the inclusive level, identified kaons allow invariant mass studies, in
particular detection of open heavy-flavoured states and vector-meson resonances such as the
φ mesons, on which this thesis is about [17].
The detector covers a cylindrical surface of polar acceptance |θ − 90◦| < 45◦. It has a
modular structure corresponding to 18 sectors in ϕ and to 5 segments in z direction. The
19
2. The ALICE Experiment at LHC
Figure 2.7: TOF detector design.
whole device is inscribed in a cylindrical shell with an internal radius of 370cm and an
external one of 399cm. The basic unit of the TOF system is a 10-gap double-stack MRPC1
strip 122 cm long and 13 cm wide, the key aspects of these chambers is that the electric field
is high and uniform over the full sensitive gaseous volume of the detector. Any ionization
produced by a traversing charged particle immediately starts a gas avalanche process which
generates the observed signals on the pick-up electrodes. Unlike other types of gaseous
detectors, there is no drift time associated with the movement of the electrons to a region
of high electric field. Thus the time jitter of these devices is caused by the fluctuations in
the growth of the avalanche [26].
1Multi-gap Resistive-Plate Chamber
20
Chapter 3
Particle Identification in ALICE
3.1 AliRoot framework
The ALICE offline framework, AliRoot[25], is shown schematically in figure 3.1. Its imple-
mentation is based on Object-Oriented techniques for programming and, as a supporting
framework, on the ROOT system, complemented by AliEn system which gives access to
the computing Grid. These fundamental technical choices result in one single framework,
entirely written in C++.
The AliRoot framework is used for simulation, alignment, calibration, reconstruction,
visualization and analysis of the experimental data. AliRoot has been in continuous de-
velopment since 1998. In the figure 3.1 the kinematics tree containing, for example, the
physics processes at the parton level and the results of the fragmentation(primary particles)
is created by event generators. The data produced by the event generators contain full
information about the generated particles: type, momentum, charge, and mother-daughter
relationship. The hits (energy deposition at a given point and time) are stored for each
detector. The information is complemented by the so called track references corresponding
to the location where the particles are crossing user defined reference planes. The hits are
converted into digits taking into account the detector and associated electronics response
function. Finally, the digits are stored in the specific hardware format of each detector as
raw data. At this point the reconstruction chain is activated.
21
3. The ALICE Experiment at LHC
Figure 3.1: Data processing framework
3.2 TPC PID
From the TPC, the number of clusters assigned ncl to each track the energy loss (dE/dx)
information can be extracted, having in each cluster a total charge Qtot, representing the
sum over the pads in the row. In the measured energy loss there is a tail towards higher
energy losses, this leads to a problem because the average energy loss would not be a good
estimator for the mean energy loss as it would be for a Gaussian distribution. Therefore the
truncated mean method is used to overcome this problem. It is characterized by a cut-off
parameter η between 0 and 1. The truncated mean 〈S〉η is then defined as the average over
the m=ηn lowest values among the ncl samples:
〈S〉η =
1
m
m
∑
i=0
Qi (3.1)
where i = 0,...,n and Qi−1 ≤ Qi for all i. If one simulates with the Monte Carlo method
based on typical ionization distributions the measurement of many tracks in order to deter-
mine an optimal value for η, one finds a value between 0.35 and 0.75. For the ALICE TPC
this value is currently set to η = 0.5.
The signals in the TPC can be identified as a certain type of particles (electrons, pions,
kaons, protons, etc) by the Bethe-Bloch formula. This formula can describe the energy loss
22
3. The ALICE Experiment at LHC
curve of a particle with mass m traversing certain medium, this parametrization has been
previously used by the ALEPH experiment[24] as follows:
f(βγ) =
P1
βP4
(P2 − βP4 − ln(P3 +
1
(βγ)P5
)) (3.2)
where the parameters Pi depend on the data sample being analysed. The figure 3.2 shows
the TPC energy loss as a function of momentum as well as the Bethe-Bloch parametrization
curves for each type of particle.
)c (GeV/p
0.2 0.3 0.4 1 2 3 4 5 6 7 8 910
 (
a
rb
. 
u
n
it
s
)
x
/d
E
T
P
C
 d
0
100
200
300
400
500
600
700
π
e
K
p d t
05/03/2013
TeV 5.02 = NNsp-Pb 
Figure 3.2: dE/dx-spectra from TPC detector together with a Bethe-Bloch curve for each particle.
Signals coming from p-Pb collisions.
The particles are identified by selecting certain range (2σ, 3σ, etc) from the Bethe-Bloch
curve parametrized to each type of particle.
3.3 TOF PID
The TOF detector, differently from TPC, does not identify particles by the energy loss.
Instead it uses the time the particle travels from the primary vertex to one of the TOF
sensitive pads. In ALICE, the TOF particle identification is based on the comparison between
23
3. The ALICE Experiment at LHC
the time-of-flight measured by TOF (tTOF) and the expected time (texp,i)). The latest is
calculated in terms of the momentum, length L and mass hypothesis i of each type of
particle as follows:
(texp,i) =
∑
k
∆ti,k =
∑
k
√
p2k +m2
i
pk
∆lk (3.3)
In order to take into account the energy loss and the consequent variation in the track
momentum, (texp,i)) is calculated as the sum over k of the small time increments ∆ti,k;
the time a particle of mass mi and momentum pk takes to travel along each propagation
step k (of ∆lk length) during the track reconstruction procedure. To perform TOF particle
identification it is necessary to define tTOF−t0−texp,i, where t0 is subtracted. The resolution
for the mass hypothesis i (σPID,i), is the combination of the TOF detector time resolution
(σTOF), the time-zero resolution (σt0) and the tracking resolution (σtexp), and the expression
is given as follows:
σPID,i =
√
σ2
TOF + σ2
t0 + σ2
texp (3.4)
where σtexp is defined as:
σ2
texp =


∆p · texp,i
1 + p2
m2
i


2
(3.5)
and assuming that the resolution on the length of the track is negligible with respect to the
one on the momentum and ∆p.
The PID separation relies on the difference between the observed time-of-flight (tTOF−t0),
and the expected time texp,i for all the particles types (π, K, p). The particle separation is
in terms of nσ as:
nσi =
tTOF − t0− texp,i
σPID,i
(3.6)
where σPID,i is shown in eq. 3.4. The specific nσ cuts for kaons are explained in the next
chapter; where the analysis details are discussed.
24
3. The ALICE Experiment at LHC
p-Pb minimum bias
p
K
π
p
K
π
 = 5.02 TeV
NN
sp-Pb 
5/03/2013
 (GeV/c)p
0 1 2 3 4 5
β
T
O
F
 
0.2
0.4
0.6
0.8
1
 = 5.02 TeV
N
sp-Pb 
Figure 3.3: TOF signal as a function of momentum. The clear bands correspond to each type of
particle.
25
Chapter 4
φ(1020) Analysis Results
4.1 Event and Track Selection
In this section the characteristics of the event selection and the corresponding tracks used
to measure the φ(1020) mesons will be described in detail.
4.1.1 Event Selection
The collision system p-Pb at
√
sNN = 5.02 TeV collected by ALICE in the beginning of
2013, is analyzed in the present work. Because of the 2-in-1 magnet design of the LHC[28],
the energy of the two beams cannot be adjusted independently, leading this to a different
energies per beam due to the different Z/A. The nucleon-nucleon center-of-mass system,
therefore, is moved in the laboratory frame with a rapidity of yN = −0.465 in the proton
beam direction.
The events selected are those that passed some standard cuts. Events are accepted if
they have a primary vertex, reconstructed in the SPD, whose z coordinate is within ±10 cm
from the interaction point. The multiplicity classes in the events are selected in terms of
percentiles of the raw multiplicity estimator, being the V0A (in Pb direction) the detector
that provides the multiplicity information. The cuts applied to the events are the following:
• Physics Selection Task, which selects events according to the ALICE triggers defini-
tions. In this work the trigger used was kINT7.
• Events required to have a reconstructed primary vertex.
26
4. φ(1020) Analysis Results
• Events with vertex-z cut of | vz |< 10 cm.
• Multiplicity ranges (V0A): 0-5%,5-10%,10-20%,20-40%,40-60%, 60-80% and 0-100% .
After the trigger and vertex selection described before, the total number of Minimum Bias
events analyzed is 9.4 × 107. In the figure 4.1 the multiplicity distribution of the accepted
events, divided in ranges of multiplicity percentage, is shown.
VZERO-A amplitude (a.u.)
0 100 200 300 400 500 600 700 800 900
E
v
e
n
ts
 (
a
.u
.)
1
10
210
310
410
0
-5
%
5
-1
0
%
1
0
-2
0
%
2
0
-4
0
%
4
0
-6
0
%
6
0
-8
0
%
8
0
-1
0
0
%
 = 5.02 TeV
NN
sALICE p-Pb at 
0-5%
5-10%
10-20%
20-40%
40-60%
60-80%
80-100%
03/05/2013
Figure 4.1: V0A particles multiplicity in terms of percentile ranges.
4.1.2 Track selection
The primary particles are those produced in the collision including weak and electromag-
netic decays products, but excluding products from strange weak decays and particles from
secondary interactions. In ALICE we have a set of track cuts that are optimized to select
the primary particles, this set is known within the Collaboration as the 2011 Standard Track
Cuts and they are summarized in the list below.
• Tracks are required to have at least 70 crossed rows in the TPC, and a χ2 of the
momentum fit smaller than 4 per cluster.
27
4. φ(1020) Analysis Results
• The Distance-of-Closest Approach (DCA) in the Z direction to the reconstructed event
vertex is required to be less than 2 cm and in the XY plane less than 0.0105+0.0350/p1.1T
cm.
• At least two clusters in the ITS must be associated to the track.
• χ2 per ITS cluster less than 36.
• TPC and ITS refit.
• Pions and kaons daughter rejection.
The φ mesons are identified via two charged kaons (φ → K−K+), which is the most
probable decay channel (branching ratio of 0.489± 0.005). Also, for a pair of kaons to be
considered as a φ candidate, its rapidity was asked to be within the range 0 < ycms < 0.5
[27].
4.2 φ(1020) Meson Identification
4.2.1 Kaon identification
After applying the track selection cuts mentioned in the previous section, the kaons are
identified through their time of flight signal in the TOF (Time of Flight) detector and their
energy loss in the TPC (Time Projection Channel). The advantage of using both detector
combined procedure is that TPC can provide track information at low transverse momentum
pT < 1.0 GeV/c and TOF contribute to reduce the background at high transverse momentum
pT > 5.0. Whenever a track has TOF information it is taken in the analysis and when this
is not the case the TPC information is used. Two different cuts in Nσ for kaons are used,
|nσK,TPCTOF | < 3 and |nσK,TPCTOF | < 4. The figure 4.2 shows the PID response (n− σ) as
a function of pT for TOF and TPC detectors, taking the kaon hypothesis.
4.2.2 Invariant Mass
Having the kaons identified by the n-sigma method described before, then the φ invariant
mass has to be calculated in function of energy and momentum from each kaon daugh-
28
4. φ(1020) Analysis Results
TOF PID response, kaon hypothesis TPC PID response, kaon hypothesis
Figure 4.2: Left: TOF PID response for the kaon hypothesis. Right: TPC PID response for the
kaon hypothesis. Dashed lines correspond to 2σ, 3σ and 4σ particle selection limits.
ter. If the first and second kaon daughters are denoted by the subscript numbers 1 and 2
respectively, then the invariant mass equation is given as follows:
M2
inv = (p21 + p22) = (E1 + E2)
2 − (p1 + p2)
2 (4.1)
The figures 4.3 and 4.4 show the φ invariant mass (eq. 4.1) distribution in all the pT
ranges analyzed. A prominent peak is located at Mk+k− ≈ 1.02 GeV/c2, corresponding to
the φ mass range. From the plots a large background below the signal is notorious and needs
to be subtracted in order to extract the φ meson yield.
4.2.3 Combinatorial Background Subtraction
Depending on the underlying physics and on the event multiplicity, the background originates
from uncorrelated particles and/or from correlated particles i.e. of common origin. In
principle if one choses appropriate functions, the signal can be extracted by fitting the
signal+background distributions, but this technique, however, does not work if signal and
background have a similar shape. Then, the only way to overcome this problem is to estimate
independently the background distribution and to subtract it from the signal+background
spectrum. Two methods are used to estimate the combinatorial background, the Event
Mixing and Like Charge. In this analysis the default method is Event Mixing, being Like
Charge used only as a cross check because it does not have a good reproduction of the
29
4. φ(1020) Analysis Results
background shape.
1. Event Mixing (default choice): Invariant-mass distribution are calculated for pairs
of oppositely charged kaons from different events. Each event analyzed is mixed with
5 other events in which for a pair of events, the difference in vertex-z is required to
be less than 1 cm and the multiplicity percentile difference is required to be less than
10%.
2. Like Charge: Invariant-mass distribution are calculated using pairs of kaons with the
same charge from the same event. In each invariant mass bin, the value of the like-
charge background is 2
√
N−−N++, where N−−(N++) is the number of K−K−(K+K+)
pairs in the bin.
The figures 4.3 and 4.4 show the invariant mass distributions of the unlike-charge and
mixed events in all pT bins analyzed. Where the mixed event background is normalized in
such a way that it has the same integral as the unlike-charge distribution in a given invariant
mass range. The normalization region chosen as default is: 1.04 < m < 1.06 GeV/c2.
30
4. φ(1020) Analysis Results
)2c(GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
200
400
600
800
1000
1200
Unlike sign
Mixed Events
<0.8 (GeV/c)
T
0.4<p
)2c(GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
1000
2000
3000
4000
5000
6000
Unlike sign
Mixed Events
<0.8 (GeV/c)
T
0.6<p
)2c(GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
2000
4000
6000
8000
10000
12000
14000
Unlike sign
Mixed Events
<1.0 (GeV/c)
T
0.8<p
)2c(GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
Unlike sign
Mixed Events
<1.2 (GeV/c)
T
1.0<p
)2c(GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
5000
10000
15000
20000
25000
Unlike sign
Mixed Events
<1.4 (GeV/c)
T
1.2<p
)2c(GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
5000
10000
15000
20000
25000
Unlike sign
Mixed Events
<1.6 (GeV/c)
T
1.4<p
)2c(GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
5000
10000
15000
20000
25000
Unlike sign
Mixed Events
<1.8 (GeV/c)
T
1.6<p
)2c(GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
5000
10000
15000
20000
25000
Unlike sign
Mixed Events
<2.0 (GeV/c)
T
1.8<p
)2c(GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
5000
10000
15000
20000
25000
30000
35000
Unlike sign
Mixed Events
<2.5 (GeV/c)
T
2.0<p
Figure 4.3: K+K− Invariant mass distributions in several pT ranges are shown as black points
and the combinatorial background(event mixing) are blue points.
31
4. φ(1020) Analysis Results
)2c (GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
Unlike sign
Mixed Events
<3.0 (GeV/c)
T
2.5<p
)2c (GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
2000
4000
6000
8000
10000
12000
Unlike sign
Mixed Events
<4.0 (GeV/c)
T
3.0<p
)2c (GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
500
1000
1500
2000
2500
3000
3500
4000
Unlike sign
Mixed Events
<5.0 (GeV/c)
T
4.0<p
)2c (GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/1
 M
e
V
/
0
200
400
600
800
1000
1200
1400
1600
Unlike sign
Mixed Events
<6.0 (GeV/c)
T
5.0<p
)2c (GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/2
 M
e
V
/
0
100
200
300
400
500
600
Unlike sign
Mixed Events
<7.0 (GeV/c)
T
6.0<p
)2c (GeV/φM
0.98 1 1.02 1.04 1.06 1.08 1.1
2
c
C
o
u
n
ts
/2
 M
e
V
/
0
100
200
300
400
500
Unlike sign
Mixed Events
<10.0 (GeV/c)
T
7.0<p
Figure 4.4: K+K− Invariant mass distributions for high pT values are shown as black points and
the combinatorial background(event mixing) are blue points.
32
4. φ(1020) Analysis Results
4.2.4 Peak and Residual Background Fits
After the combinatorial background is subtracted, by the Mixed Event method, some residual
background might be still present and has to be subtracted. It is estimated by fitting
the invariant-mass distribution (combinatorial background subtracted) with a polynomial
function. Two functions are used to estimate the residual background: linear and quadratic
functions, the last one being the default choice. After the background subtractions the
peak is fitted by two basic functions: the relativistic Breit-Wigner function and a Voigtian
function.
• Breit-Wigner: The relativistic Breit-Wigner distribution (after the 1936 nuclear res-
onance formula[20] of Gregory Breit and Eugene Wigner) is a continuous probability
distribution with the following probability density function,
f(E) =
k
(E2 −M2)2 +M2Γ2
, (4.2)
where k is a constant of proportionality, equal to
k =
2
√
2MΓγ
π
√
M2 + γ
with γ =
√
M2(M2 + Γ2). (4.3)
It is widely used to model resonances in high energy physics. In this case, E is the
center of mass energy that produces the resonance, M is the mass of the resonance,
and Γ is the resonance width(or decay width), related to its mean lifetime according to
τ = 1/Γ. For values of E off the maximum at M such that |E2 −M2| = MΓ, (hence
|E −M | = Γ/2 for M ≫ Γ), the distribution f has attenuated to half its maximum
value, which justifies the name for Γ sharpens infinitely to 2Mδ(E2 −M2). The form
of the relativistic Breit-Wigner distribution arises from the propagator of an unstable
particle, which has a denominator of the form p2 −M2 + iMΓ. The propagator in its
rest frame then is proportional to the quantum-mechanical amplitude for the decay
utilized to reconstruct that resonance,
√
k
(E2 −M2) + iMΓ
(4.4)
The resulting probability distribution is proportional to the absolute square of the
amplitude, so then the above relativistic Breit-Wigner distribution for the probability
33
4. φ(1020) Analysis Results
density function. This function was only used just as a cross-check for the φ yield, so
it was not included in the systematic analysis.
• Voigtian: The Voigt profile (named after Woldemar Voigt) is a line profile resulting
from the convolution of two broadening mechanisms, one of which alone would pro-
duce a Gaussian profile, and the other would produce a Lorentzian profile[21]. The
Lorentzian describe the ideal resonance signal and the Gaussian accounts for the de-
tector resolution. It is implemented using the following function:
dN
dmKK
=
AΓ
(2π)3/2σ
×
∫ ∞
−∞
exp
[
−(mKK −m′)2
2σ2
]
1
(m′ −M0)2 + Γ2
0/4
dm′ (4.5)
where σ is the mass resolution parameter which is pT-dependent and is fixed to the
value found from simulated data, this procedure is described in Appendix .0.1.
Both, the peak and residual background, are fitted in the invariant mass region: 0.99 <
Mφ < 1.09 GeV/c2. The resolution is allowed to vary freely and the width parameter (Γ) is
fixed to the PDG value 4.26 MeV/c2. In the figures 4.5 and 4.6 is shown the combinatorial
background subtracted invariant mass, along with the Voigtian and residual background fits,
for several pT ranges of the φ meson. Then after subtracting the combinatorial background
and after fitting the residual background the raw yield is determined as:
N raw = N counts − Integralpol2,
where N counts is the total number of counts in the mass region of 1.01 < m < 1.03 GeV/c2
in the combinatorial background subtracted histogram. And Integralpol2 is the integral
over the same mass region of the second order polynomial function that is fitted to the
residual background. Absolute statistical uncertainty for the raw yield is determined as
√
A2 + Integral2stat, where A =
√
∑
n=i δ
2
n and δn is the statistical error of the n-th bin after
mixed background subtraction. And Integral2stat is the statistical error of the polynomial
integral.
34
4. φ(1020) Analysis Results
]2) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
-100
0
100
200
300
400
500
600
Voigtian fit
Residual Bg fit
<0.6 (GeV/C)
T
0.4<p
]2) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
0
500
1000
1500
2000
2500
3000
3500
Voigtian fit
Residual Bg fit
<0.8 (GeV/C)
T
0.6<p
]2) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
0
1000
2000
3000
4000
5000
6000
7000 Voigtian fit
Residual Bg fit
<1.0 (GeV/C)
T
0.8<p
]2) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
0
2000
4000
6000
8000
10000
Voigtian fit
Residual Bg fit
<1.2 (GeV/C)
T
1.0<p
]2) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
0
2000
4000
6000
8000
10000 Voigtian fit
Residual Bg fit
<1.4 (GeV/C)
T
1.2<p
]2) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
0
2000
4000
6000
8000
10000
Voigtian fit
Residual Bg fit
<1.6 (GeV/C)
T
1.4<p
]2) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
0
2000
4000
6000
8000
Voigtian fit
Residual Bg fit
<1.8 (GeV/C)
T
1.6<p
]2) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
0
1000
2000
3000
4000
5000
6000
7000 Voigtian fit
Residual Bg fit
<2.0 (GeV/C)
T
1.8<p
]2) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
0
2000
4000
6000
8000
10000
12000
14000
Voigtian fit
Residual Bg fit
<2.5 (GeV/C)
T
2.0<p
Figure 4.5: Invariant mass distribution after the mixed events background subtraction using the
information from TPC and TOF combined. Results correspond to 0-100% multiplicity bin, magenta
line is the total fit (ResidualBg+Voigt).
35
4. φ(1020) Analysis Results
]
2
) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
-1000
0
1000
2000
3000
4000
5000
6000
7000
8000
Voigtian fit
Residual Bg fit
<3.0 (GeV/C)
T
2.5<p
]
2
) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
-1000
0
1000
2000
3000
4000
5000
6000
7000
Voigtian fit
Residual Bg fit
<4.0 (GeV/C)
T
3.0<p
]
2
) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
0
500
1000
1500
2000 Voigtian fit
Residual Bg fit
<5.0 (GeV/C)
T
4.0<p
]
2
) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
-200
0
200
400
600
800
Voigtian fit
Residual Bg fit
<6.0 (GeV/C)
T
5.0<p
]
2
) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
-100
0
100
200
300 Voigtian fit
Residual Bg fit
<7.0 (GeV/C)
T
6.0<p
]
2
) [GeV/c
-
K
+
(K
inv
M
0.98 1 1.02 1.04 1.06 1.08 1.1
C
o
u
n
ts
-200
-100
0
100
200
300
<10.0 (GeV/C)
T
7.0<p
Figure 4.6: Invariant mass distribution after the mixed events background subtraction using the
information from TPC and TOF combined. Results correspond to 0-100% multiplicity bin, magenta
line is the total fit (ResidualBg+Voigt).
36
4. φ(1020) Analysis Results
4.2.5 Raw Yield Calculation
The φ yield is calculated using two methods. In the default method, the yield is extracted
by integrating the invariant mass histogram over the region 1.01 < m < 1.03 GeV/c2 and
subtracting the integral of the residual background that is fitted in the same region, as
described previously.
The second method consist in integrating the fit function which is a Voigtian function
with fixed width Γ =4.26 MeV, value obtained from the PDG. The function is integrated in
the mass region 2M(K±) < m < ∞, the mass region below 2M(K±) = 0.987334 GeV/c2 is
kinematically forbidden[30]. Therefore, the yield is given by
Y ield =
∞
∫
2M(K±)
peak(m)dm (4.6)
4.2.6 Peak Correction Factor
Since the default method used in this analysis is integrating the invariant-mass distribution
over the range 1.01 < m < 1.03 GeV/c2 to get the φ yield, a correction factor is necessary to
account for the portion of the yield that lies outside the range of integration. This correction
is the peak factor, and it is calculated as follows:
ǫPC =
1.03
∫
1.01
fit(m)dm
∞
∫
2M(K±)
fit(m)dm
. (4.7)
Here, the numerator in ǫPC is the integral in the default range (1.01¡m¡1.03 GeV/c2) of the fit
to the background-subtracted invariant mass distribution. The denominator is the integral
of the same function over a wider range, starting from 2M(K±) = 0.9873 GeV/c2 up to
infinity. The peak correction (ǫPC) is applied only when the default method (integrating the
histogram) is used to obtain the yield. In the case when the yield is extracted by integrating
the peak fit function, this correction is not applied. The figure 4.7 shows an example of the
peak correction factor in the 0− 100% multiplicity bin.
37
4. φ(1020) Analysis Results
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
P
C
ε
0.8
0.82
0.84
0.86
0.88
0.9
Peak Correction Factor, 0-100%
Figure 4.7: Peak correction factor for the default analysis parameters in the multiplicity bin
0− 100%
4.3 Monte Carlo simulations
A simulation data set is analyzed in order to get information, needed to complete the real
data analysis, such as: φ reconstruction efficiency× acceptance, the φ mass resolution (used
as a Voigtian parameter in the real data fits), mass and width.
The simulation data set analyzed is the production (ESDs): LHC13b2 efix p1, LHC13b2 efix p2,
LHC13b2 efix p3, LHC13b2 efix p4, produced by the DPMJET event generator, the parti-
cle interaction with the ALICE detectors are simulated using GEANT3. After all the event
selection cuts and track quality cuts, which are the same used in real data (see 4.1), the
number of selected events is 99 million.
4.3.1 Reconstruction Efficiency
In the context of this section the ‘generated’ particles are referred as the ones produced by
the event generator(DPMJET) for p-Pb collisions without any detector effects. The ‘recon-
structed’ tracks are those that passed through the reconstruction algorithms, the selected
reconstructed particles are primary kaons that passed the same track cuts as in data (see
4.1) including the PID cuts in the detectors. A reconstructed φ meson is a φ for which
both daughter tracks (K+, K−) have been reconstructed by the algorithms. The total φ
38
4. φ(1020) Analysis Results
 (GeV/c)
T
p
0 1 2 3 4 5 6 7 8 9 10
R
a
ti
o
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
Multiplicity/(0-100)%
0-5%
5-10%
10-20%
20-40%
40-60%
60-80%
Figure 4.8: Ratios of the efficiency as a function of multiplicity over the Minimum Bias efficiency
(0-100)%.
reconstruction efficiency is given by:
ǫrec =
φreconstructed,TPC−TOF
φgenerated
, where (4.8)
• Generated φ: Are the generated φmesons from the events that fulfil the requirements
of the Event Selection Cuts, described in section 4.1. The φ particles are asked to be
within a rapidity region 0 < ycms < 0.5.
• Reconstructed φ: The number of φ mesons within a rapidity region 0 < ycms < 0.5
for which both kaons decay daughters are reconstructed and passed the track selection
cuts and either TPC or TOF PID nσ-cuts.
In the figure 4.9 ǫrec is shown as a function of pT, for each nσ cut applied, where a strong
variation in the low part of the transverse momentum is observed but no strong dependence
on multiplicity. This can be seen by doing ratio of the multiplicity dependent efficiency over
the minimum bias(0-100%) one, the figure 4.8 shows this ratio from which we see clear that
the variations are less than 5%.
39
4. φ(1020) Analysis Results
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
E
ff
ic
ie
n
c
y
*A
c
c
e
p
ta
n
c
e
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
TPC-TOF: 0-100% (V0A)
 (tune on data)σ3
 (tune on data)σ4
 Efficiency TPC-TOFφ
Figure 4.9: Efficiency used to correct the TPC-TOF data, 3σ and 4σ are shown.
40
Chapter 5
φ(1020) Spectra And Systematic
Analysis
5.1 φ(1020) Invariant Spectra
After obtaining the φ uncorrected yield in each multiplicity and pT bin, some factors and
corrections need to be applied to the Raw Yield these corrections are summarized in the
equations 5.1 and 5.2:
d2Nraw
dpTdy
=
Raw Y ield
Nevt ×BR× dpTdy
(5.1)
where Raw Yield is the integral of the entries in the φ invariant mass distribution (see
4.2.5), Nevt is the number of analyzed events in each multiplicity range, BR = 0.489 is the
φ → K+K− branching ratio, dpT is the width of the pT bin analyzed and dy = 0.5 is the
rapidity bin.
The corrections to the φ spectra are:
• ǫrec : Reconstruction efficiency × acceptance for the TPC-TOF detector combination,
in this efficiency is included the nσ cut (see Section 4.3.1).
• ǫPC : Peak correction factor(see Section 4.2.6).
• ǫtrig : Correction that accounts for trigger and vertex efficiency for NSD collisions, it
has a value of 97.8± 1% for Minimum Bias measurements.
41
5. φ(1020) Spectra And Systematic Analysis
Taking into account the normalization and the corrections listed above, the corrected φ
meson spectra is calculated as follows:
d2N
dpTdy
=
d2Nraw
dpTdy
· ǫtrig
ǫrecǫPC
(5.2)
The figure 5.1 shows the fully corrected φ spectra (eq. 5.2) as a function of pT for all the
multiplicity ranges analyzed.
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
 (
c
/G
e
V
)
d
y
T
d
p
N
2
d
×
T
pπ
2
e
v
t
N
1
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
1 TPC-TOF combined
(0-100%)x60
(0-5%)x10
(5-10%)x5
(10-20%)x2
(20-40%)x1
(40-60%)x0.5
(60-80%)x0.2
Figure 5.1: Fully corrected φ Spectra 1/2πpT × (d2N/dpTdy) obtained with TPC-TOF detectors
information, for Minimum Bias, 0-5%, 5-10%, 10-20%, 20-40%, 40-60% and 60-80% multiplicity
measurements. Only statistical errors are shown.
5.2 Mass and Width
The mass and width values are obtained from the Voigtian fit parameters for each pT bin.
For the mass case, the width parameter in the Voigtian function was fixed to the PDG value
(4.26 MeV/c2) while for the width measurement only the resolution parameter is fixed to the
42
5. φ(1020) Spectra And Systematic Analysis
σvoi value (see Appendix .0.1). The figure 5.2 shows the mass as a function of pT, for three
measured multiplicities: central, peripheral and Minimum Bias. In the low-intermediate pT
the points agree within the statistical uncertainties, except for the first point, that is clearly
bellow the PDG value and needs further investigations. At high pT large statistical errors
are present mainly due to the low statistics in the multiplicity measurements.
)c(GeV/
T
p
1 2 3 4 5 6 7 8 9 10
)2
c
M
a
s
s
 (
G
e
V
/
1.018
1.0185
1.019
1.0195
1.02
1.0205
1.021
= 5.02 TeV
NN
spPb,
-
+K
+
K→φ-0.5< y <0,
Uncertainties: stat. (bars)
V0A Multiplicity Event Class (Pb-Side)
0-100%
0-5%
60-80%
PDG Mass
Mass, TPC-TOFφ
Figure 5.2: Mass of the φ mesons measured in Minimum bias, 0-5% and 60-80% multiplicity
ranges. Only statistical uncertainties are shown.
The figure 5.3 shows the full width values in three multiplicity ranges. Some statistical
fluctuations are observed in the first pT bin and in high pT range. Above 1 GeV/c the
data points agree with the PDG width value, but below that momentum, the data point
are above the PDG value. This last feature was also observed in Pb-Pb collisions[35] and
in generated events based in a multiphase transport model (AMPT) at
√
sNN = 39 GeV for
Au-Au collisions[36]. This deviation of the full width at low momentum can be explained
from the point of view that the φ meson scatter before their decay into kaons inside the
medium, affecting the full width as well as the mass of the resonance particle.
43
5. φ(1020) Spectra And Systematic Analysis
)c(GeV/
T
p
1 2 3 4 5 6 7 8 9 10
)
2
c
F
u
ll 
W
id
th
 (
G
e
V
/
0
0.002
0.004
0.006
0.008
= 5.02 TeV
NN
spPb,
-
+K
+
K→φ-0.5< y <0,
Uncertainties: stat. (bars)
V0A Multiplicity Class (Pb-Side)
0-100%
0-5%
60-80%
PDG Width
Full Width, TPC-TOFφ
Figure 5.3: Width of the φ mesons measured in Minimum bias, 0-5% and 60-80% multiplicity
ranges. Only statistical uncertainties are shown.
5.3 Systematic Uncertainties Analysis
Often, systematic uncertainties are neither very clearly defined nor well separated from
statistical uncertainties. Sometimes the two uncertainties even become mixed, for example
in trigger efficiencies, which may be partially determined from data statistics. Moreover, in
many analyses, so-called ‘external errors’ from external input values, ‘theory errors’ from
theoretical input or other error sources are separated from the ‘experimental’ systematic
uncertainty. A standard definition of systematic uncertainties is the following[22]:
Systematic uncertainties are all uncertainties that are not directly due to the
statistics of the data
With this definition, also statistical uncertainties of trigger efficiencies, measured from
data, and detector acceptances, determined from Monte Carlos(MC) simulation, are consid-
ered as systematic errors. This may seem strange, but it appears justified when considering
that these uncertainties may still be reduced after the data-taking by further Monte Carlo
44
5. φ(1020) Spectra And Systematic Analysis
production or by smarter methods of determining a trigger efficiency. I will use a pragmatic
definition of systematic uncertainties, which better fits the purpose of this work[22]:
Systematic uncertainties are measurement errors which are not due to statistical
fluctuations in real or simulated data samples
With this definition, a list of typical sources of systematic errors and biases in high energy
physics can be written:
• badly known detector acceptances or trigger efficiencies;
• incorrect detector calibrations;
• badly known detector resolutions;
• badly known background;
• uncertainties in the simulation or underlying theoretical models;
• uncertainties on input parameters like cross sections, branching fractions, lifetimes, the
luminosity, and so on(often called ‘external uncertainties’);
• computational and software errors;
• personal biases towards a specific outcome of an analysis;
• other usually unknown effects on the measurement.
Obviously, in particular the last three sources of systematic are difficult to asses, but also
the other items on the list are sometimes difficult to find and to estimate. In this section
the procedure followed to obtain the systematic uncertainties will be described. It consist
basically in varying many times the possible permutations of the analysis parameters such
as: fit region, combinatorial and residual background, PID cuts, etc. The same analysis is
repeated for each pT and multiplicity range, giving several measurements for the φ yield.
The general strategy for evaluating systematic uncertainties is described in the next points:
1. Choose one set of parameters for the analysis as “default”.
2. Observe deviation in the yield between the default system and the system when one
of the parameters is changed.
45
5. φ(1020) Spectra And Systematic Analysis
3. The systematic uncertainty is calculated for a given source as the RMS1 deviation of
the available sources.
4. The total systematic uncertainty, taking into account all the different sources, is the
sum in quadrature of each source.
5.3.1 Systematic Uncertainties of the Yield
Before starting to review all the permutation in the parameters of the systematic uncertain-
ties analysis it is good to recall the default parameters used to obtain the φ spectra.
Default Parameters:
• PID cut: 3σTPC−TOF .
• Combinatorial Background and Normalization Region: Mixed event normal-
ized to the invariant-mass region 1.04 < Mφ < 1.06 GeV/c2.
• Fit Region: 0.99 < Mφ < 1.09 GeV/c2.
• Peak Fit: Voigtian function, where the width parameter is fixed to the vacuum(PDG)
value 4.26 MeV/c2.
• Yield Extraction Method: Integrating the invariant-mass histogram (bin counting).
5.3.1.1 Detailed description of each source
In order to obtain a more reliable estimation of the uncertainties, the systematic errors have
been computed as the Root Mean Square (RMS) of the measurements set, where RMS is
defined as
σx =
√
√
√
√
1
N
N
∑
i=1
x2i , (5.3)
where xi is the measurement, N is the number of measurements in the sample. In this
section, the uncertainties will be denoted with “U” and a subscript describing the type of
systematic.
1Root Mean Square
46
5. φ(1020) Spectra And Systematic Analysis
PID Cuts (UPID): The systematic uncertainty UPID accounts for a non-ideal PID response
of the detector, which would result in a deviation in the φ yield when different PID
cuts are applied. The TPC and TOF analysis is based on 3σ − cut for the kaons
selection. In order to check the systematic effects related to the PID selection, 4σ cut
has been compared to the default value.
Normalization Region (UNR): The systematic uncertainty of the normalization region, is
related to the invariant mass region where the mixed events distribution is scaled to
subtract the combinatorial background. It is obtained by taking the RMS deviation
from the default measurement(Normalization Region 0) and the Normalization Regions
1 and 2 listed below:
• Normalization Region 0: 1.04 < MK+K− < 1.06 GeV/c2.
• Normalization Region 1: 0.995 < MK+K− < 1.01 GeV/c2.
• Normalization Region 2: 0.995 < MK+K− < 1.006 and
1.04 < MK+K− < 1.06 GeV/c2.
Fit Region (UFR): The UFR uncertainty is the difference in the yields when different re-
gions for the residual background fit are used. The default Region 0 is compared with
Region 1, 2 and 3. The Voigtian function (Γ fixed) together with the residual back-
ground (pol2) are fitted in each region giving variations to the yields, then the RMS
of the available values gives the systematic uncertainty.
• Fit Region 0: 0.99 < MK+K− < 1.09 GeV/c2.
• Fit Region 1: 0.995 < MK+K− < 1.06 GeV/c2.
• Fit Region 2: 1.0 < MK+K− < 1.07 GeV/c2.
• Fit Region 3: 0.99 < MK+K− < 1.07 GeV/c2.
Residual Background Fit (URB): The use of a different polynomial function to fit the
residual background gives the (URB) uncertainty. The default yield is extracted using
a quadratic fit function and then the systematic uncertainty is calculated when a linear
function fit is used.
47
5. φ(1020) Spectra And Systematic Analysis
Peak Fit (UPF ): This uncertainty accounts for differences observed in the yield when differ-
ent peak fit functions are used, it mainly consist in varying the fit function parameters.
The default measurement Voigt0 fit is compared to the Voigt1, Voigt2 and Voigt3, as
listed below:
• Voigtian 0: The resolution is allowed to vary freely and the width parameter is
fixed to the vacuum value 4.26 MeV/c2.
• Voigtian 1: The resolution is fixed to the value σhisto.
• Voigtian 2: The resolution is fixed to the value σvoi.
• Voigtian 3: The resolution is fixed to the value σgauss.
The calculation of σhisto, σvoi and σgauss is described in Appendix.0.1.
Peak Yield Extraction Method (UY i): The RMS in the yield due to the extraction method
between integrating the histogram (bin counting) used as default, and integrating the
fit function gives the systematic uncertainty (UY i).
Tracking (Utrack): The value of the Global Tracking Efficiency uncertainty is borrowed from
the identified charged particles analysis [27], where it is assigned 3% for a single track
and for the case of φ the value is Utrack = 6%.
Material Budget (UMB): The material supporting the detectors and their misalignment
constitute the ‘dead zones’ in which the detector is not sensitive to the particle passage.
This is taken into account by the UMB systematic uncertainty which is a pT dependent.
And the value assigned to the φ depends on the pT of each kaon, the kaon individual MB
uncertainty is obtained from the identified charged particles analysis in p-Pb collisions
at
√
sNN = 5.02 TeV [27]. The left plot in the figure 5.4 shows the systematic percentile
values as a function of pT.
Hadronic Interactions (UHI): The uncertainty on the hadronic interaction cross section
is a pT dependent uncertainty where, as the (UMB), the contribution of each kaon to
the total pT of the φ is taken into account to calculate this uncertainty. The histograms
from figure 5.5 are calculated using the information from each of the kaon daughters,
by using Monte Carlo simulations.
48
5. φ(1020) Spectra And Systematic Analysis
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
0.01
0.02
0.03
0.04
0.05
 Material Budgetφ
Figure 5.4: pT dependent systematic uncertainty due to material budget(MB) for the φ.
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
0.005
0.01
0.015
0.02
0.025
0.03
 Hadronic Interactionφ
Figure 5.5: pT dependent systematic uncertainty due to hadronic interaction cross section for the
φ.
49
5. φ(1020) Spectra And Systematic Analysis
Analysis Cuts UTrkC: The systematic uncertainty related to the analysis cuts is calculated
by varying some of the StandardITSTPCTrackCuts2011, it is a pT dependent uncer-
tainty that in average is around 2%, the figure 5.6 shows the percentage value of this
systematic as a function of pT. The variations used to calculate the UTrkC uncertainty
are listed below:
• Chi 2 in ITS: 30 and 45 (36 is default)
• Chi 2 in TPC: 3 and 5 (4 is default)
• MinNCrossedRowsTPC: 60 and 80 (70 is default)
• DCA-Z: 1 and 3 (2 is default)
• DCA-XY: 5 and 9 (7 is default)
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
0.005
0.01
0.015
0.02
0.025
0.03
 Analysis Cuts Systematicsφ
Figure 5.6: pT dependent systematic uncertainty due to analysis cuts variations for the φ.
Total Systematic Uncertainty (Utotal): The total systematic uncertainty is the sum in
quadrature of all the sources listed above. All these quantities, except for U2
HI , U
2
MB
and U2
TrkC , are calculated in each multiplicity range.
UT =
√
U2
PID
+ U2
NR
+ U2
FR
+ U2
RB
+ U2
PF
+ U2
Y i
+ U2
TE
+ U2
MB
+ U2
HI
+ U2
TC
(5.4)
50
5. φ(1020) Spectra And Systematic Analysis
Smoothing
Some of the raw systematic uncertainties exhibit fluctuations from pT bin to another, but we
are expecting that the uncertainties behave more uniform. Then the spikes and dips in the
systematic uncertainties have to be smoothed. This is done by comparing the problematic
pT bins to the values from the Minimum Bias (0-100)% systematic uncertainty, which is
expected to be uniform. Then the (0-100)% value is changed to the problematic one in
the multiplicity range, turning the dips and spikes to a more realistic value. The figure
5.7 shows the smoothed systematic uncertainties percentage values for the Minimum Bias
measurements and the figure 5.8 shows the same for all multiplicity bins.
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
5
10
15
20
25
Multiplicity: 0-100%
Total Integral Fit
Resifual BG(poly1) Norm. Region
PID Fit Region
Peak fit function Global tracking
Material Budget Hadronic int.
Figure 5.7: Percentage of the systematic uncertainties for each source in 0-100% multiplicity bin,
using the combined TPC-TOF information.
51
5. φ(1020) Spectra And Systematic Analysis
(GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
5
10
15
20
25
Multiplicity: 0-5%
Total Integral Fit
Resifual BG(poly1) Norm. Region
PID Fit Region
Peak fit function Global tracking
Material Budget Hadronic int.
(GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
5
10
15
20
25
Multiplicity: 5-10%
Total Integral Fit
Resifual BG(poly1) Norm. Region
PID Fit Region
Peak fit function Global tracking
Material Budget Hadronic int.
(GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
5
10
15
20
25
Multiplicity: 10-20%
Total Integral Fit
Resifual BG(poly1) Norm. Region
PID Fit Region
Peak fit function Global tracking
Material Budget Hadronic int.
(GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
5
10
15
20
25
Multiplicity: 20-40%
Total Integral Fit
Resifual BG(poly1) Norm. Region
PID Fit Region
Peak fit function Global tracking
Material Budget Hadronic int.
(GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
5
10
15
20
25
Multiplicity: 40-60%
Total Integral Fit
Resifual BG(poly1) Norm. Region
PID Fit Region
Peak fit function Global tracking
Material Budget Hadronic int.
(GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
re
la
ti
v
e
 u
n
c
e
rt
a
in
ty
0
5
10
15
20
25
Multiplicity: 60-80%
Total Integral Fit
Resifual BG(poly1) Norm. Region
PID Fit Region
Peak fit function Global tracking
Material Budget Hadronic int.
Figure 5.8: Fractional smoothed systematic uncertainties for each multiplicity range and for each
systematic source.
52
5. φ(1020) Spectra And Systematic Analysis
After having the fractional systematic uncertainty for all the multiplicity and pT bins,
then the φ spectra for minimum bias (0-100%) is showed in figure 5.9 and as a function of
multiplicity is shown in figure 5.10.
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
 (
c
/G
e
V
)
d
y
T
d
p
N
2
d
×
T
pπ
2
e
v
t
N
1
-6
10
-5
10
-4
10
-3
10
-2
10
Figure 5.9: Fully corrected spectra for φ(K+K−) using the combined TPC-TOF information, cor-
responding to minimum bias. Statistical uncertainties (bars) and systematic uncertainties (boxes).
5.3.2 Fits to φ Spectra
In order to obtain additional information from the φ meson production in p-Pb collision,
the φ spectra (d2N/dpTdy) is fitted by some functions that give us details such as the φ
integrated yield (dN/dy). Three functions are used, the first one is a power law, sometimes
called Hagedorn or modified Hagedorn [29]:
x× A×
(
1 +
x
pt0
)−n
(5.5)
The histogram is only fit in the region 0.4 < pT < 10.0 GeV/c, giving better fit at high
53
5. φ(1020) Spectra And Systematic Analysis
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
 (
c
/G
e
V
)
d
y
T
d
p
N
2
d
×
T
pπ
2
e
v
t
N
1
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
1 TPC-TOF combined
(0-5%)x10
(5-10%)x5
(10-20%)x2
20-40%
40-60%
60-80%
Figure 5.10: Fully corrected spectra for φ(K+K−) using the combined TPC-TOF information as
a function of multiplicity. Statistical uncertainties are shown in bars and systematic uncertainties
are shown in boxes.
pT but at low pT the fit is not good. Thus the power law function is only used as a cross
check, and not for getting information.
Second, a Boltzmann-Gibbs blast wave function [31] is used to fit the data:
pT × AmT
∫ 1
0
xI0
(pT
T
sinh tanh−1 [βsx
n]
)
K1
(mT
T
cosh tanh−1[βsx
n]
)
dx, (5.6)
where I0 and K1 are modified Bessel functions of the first and second kind, respectively. The
histogram is fit over the data range, 0.4 < pT < 10.0 GeV/c. This function gives a good
description of the data in all momentum range, thus this will be compared with the third
function; a Lévy-Tsallis function [32]-[33]:
pT × A(n− 1)(n− 2)
nT [nT +M(n− 2)]
[
1 + mT−M
nT
]−n (5.7)
54
5. φ(1020) Spectra And Systematic Analysis
where A is a parameter that gives the integral of the function. Again, the function is fit
over the data range and extrapolated above and below the data. The Lévy-Tsallis function
is used as default fit function. The figures 5.11 and 5.12 show the three function fitted to
the data points for (5-10)% and (60-80)% multiplicity ranges.
/ ndf2χ 7.933 / 11
beta_max 0.0114±0.7937
T 0.0050±0.4621
n 1.5±10
norm 0.307±6.182
(GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
(c
/G
e
V
)
d
y
T
d
p
N
2
d
-4
10
-3
10
-2
10
-1
10
Data points
Levy-Tsallis
Blast Wave
Power Law
) in TPC-TOF (5-10)%
+
K
-
(Kφ
Figure 5.11: Fits to the corrected φ spectra (d2N/dpTdy) in the 5-10% multiplicity bin.
5.3.3 Integrated Yield and Particle Ratios
The method used to obtain the total dNφ/dy depends on the pT region and is summarized
in the next points:
• Below Data: Low pT region, 0 < pT < 0.4 GeV/c, from the extrapolation of the
Lévy-Tsallis fit the dN/dy is obtained by integrating the function.
• Data: Region where data points are present, 0.4 < pT < 10.0 GeV/c, dN/dy is
obtained by integrating the data.
• Above Data: High pT region, 10.0 < pT < 30.0 GeV/c, dN/dy obtained by integrat-
ing the extrapolation of Lévy-Tsallis fit.
55
5. φ(1020) Spectra And Systematic Analysis
 / ndf 2χ  27.04 / 11
beta_max  0.0087± 0.8377 
T         0.0084± 0.3473 
n         0.900± 7.992 
norm      0.646± 5.444 
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
 (
c
/G
e
V
)
d
y
T
d
p
N
2
d
×
T
pπ
2
e
v
t
N
1
-4
10
-3
10
-2
10
Data points
Levy-Tsallis
Blast Wave
Power Law
) in TPC-TOF (60-80)%
+
K
-
(Kφ
Figure 5.12: Fits to the corrected φ spectra (d2N/dpTdy) in the 60-80% multiplicity bin.
The total dN/dy is then the sum of the three regions described before. The statistical
and systematic uncertainties are calculated by re-fitting the data when the data point are
moved up and down to the errors limits, as it is shown in the figure 5.13. Then the maximum
difference between (dN/dy)high − (dN/dy)data and (dN/dy)data − (dN/dy)low is taken as the
statistical or systematic uncertainty for the (dN/dy)data, depending the case. The same
procedure is repeated for all the multiplicities.
Since the global tracking efficiency is correlated among pT bins it was taken out from
the φ spectra and then the integrated yield is calculated with this spectra. Then the 6%
from the global tracking efficiency is added in quadrature, as 0.06 × (dN/dy), to all the
systematic uncertainties. The systematic due to the fit function is obtained by comparing
the (dN/dy)fit from Lévy-Tsallis and blast wave function, and the difference is added in
quadrature to the data systematic uncertainty (dN/dy)data .
56
5. φ(1020) Spectra And Systematic Analysis
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
d
y
T
d
pd
N
0
0.05
0.1
0.15
0.2
0.25
Low Extrapolation
High Extrapolation
 spectra 0-5%φ
Levy fit
 (GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
d
y
T
d
p
N
2
d
0
0.05
0.1
0.15
0.2
0.25
Low Extrapolation
High Extrapolation
 spectra 0-5%φ
Levy fit
Figure 5.13: Left: φ points, for 0-5%, moved down to the systematic unc. limit. Right: φ points
moved up to the systematic unc. limit. The red curve is the Levy fit to each spectra.
The mean transverse momentum is obtained as:
〈pT〉 =
〈pT〉Iext + ΣibinpT,ibindpT,ibinIibin
Idata + Iext
(5.8)
where 〈pT〉 and Iext are respectively the mean transverse momentum for the extrapolation
region(from fitted function) and the integral of the fitted function in the extrapolation region,
pT is the pT bin center of the ibin-th, dpT,ibin is the bin with and Iibin is the yield of the
ibin-th. For the systematic uncertainty on the 〈pT〉 similar procedure as described before for
the dN/dy is followed. The figure 5.14 show the φ integrated yield(left) and the mean pT.
In the next chapter this results will be discussed.
In order to study the multiplicity dependence, the selected events are divided into six
event classes, based on cuts on the total charge deposited in the VZERO-A detector (V0A).
The corresponding fractions of the data sample in each class are summarized in Table 5.1.
The mean charged-particle multiplicity densities (〈dNch/dη〉) within |ηlab| < 0.5 correspond-
ing to the different event classes are also listed in the table. These are obtained using the
method presented in [34] and are corrected for acceptance as well as for contamination by
secondary particles.
57
5. φ(1020) Spectra And Systematic Analysis
Event Class V0A range(arb. unit) 〈dNch/dη〉|ηlab|<0.5
0-5% >227 45±1
5-10% 187-227 36.2±0.8
10-20% 142-187 30.5±0.7
20-40% 89-142 23.2±0.5
40-60% 52-89 16.1±0.4
60-80% 22-52 9.8±0.2
80-100% <22 4.4±0.1
Table 5.1: Definition of the event classes as fractions of the analyzed event sample and their
corresponding 〈dNch/dη〉 within |ηlab| < 0.5 (systematic uncertainties only, statistical uncertainties
are negligible). Table values taken from [27].
|<0.5
lab
η|
〉
lab
η/d
ch
dN〈
10 15 20 25 30 35 40 45
/d
Y
φ
d
N
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
=5.02 TeV
NN
spPb,
<0.5
cms
, 0<y
-
+K
+
K→φ
Uncertainties: stat. (bars), syst. (boxes)
|<0.5
lab
η|
〉
lab
η/d
ch
dN〈
10 15 20 25 30 35 40 45
(G
e
V
/c
)
〉
T
p
〈
0.8
1
1.2
1.4
1.6
1.8
2
=5.02 TeV
NN
spPb,
<0.5
cms
, 0<y
-
+K
+
K→φ
Uncertainties: stat. (bars), syst. (boxes)
Figure 5.14: Left: φ integrated yield as a function of multiplicity. dNφ/dy vs dNch/dη. Right:
φ mean pT ( 〈pT〉 ) as a function of multiplicity. Systematic uncertainties (boxes), statistical
uncertainties (lines).
58
5. φ(1020) Spectra And Systematic Analysis
5.4 Analysis Combination
In the ALICE experiment several people work on the same analysis using different techniques,
in this manner the analyses have to converge to the same results. This φ analysis is not
the exception, besides this TPC-TOF analysis presented in this thesis, two other analysis
were performed simultaneously and in this section the merge procedure of the three analysis
results is presented.
The three analysis to obtain the φ meson spectra and the people involve in each analysis
are listed below, together with the respectively ALICE analysis note link:
• TPC analysis: By Ajay K. Dash,
https://aliceinfo.cern.ch/Notes/node/264.
• TPC-TOF analysis: By Edgar P. Lezama, described in this thesis.
https://aliceinfo.cern.ch/Notes/node/222
• No PID analysis: By Viktor Riabov, M. Malaev and Y. Ryabov,
https://aliceinfo.cern.ch/Notes/node/214.
The three analysis have a good agreement between each other, the figure 5.15 shows the
comparison of the global fit1 with each different measurement method for the minimum bias
case (all multiplicity comparison have a good agreement too). Since the No-PID method
can provide better description at high pT compared to the TPC-TOF method, the final φ
spectra is composed by TPC-TOF points up to pT = 3 GeV/c and above that momentum the
No-PID results are used, the figures 5.16 and 5.17 show the combined spectra for minimum
bias and all multiplicity cases respectively.
1Fit to all the data points
59
5. φ(1020) Spectra And Systematic Analysis
)
-2 )c
) 
((
G
e
V
/
y
d
T
p
/(
d
N
2
) 
d
T
pπ
 1
/(
2
e
v
N
1
/ -9
10
-8
10
-710
-6
10
-5
10
-410
-3
10
-210
-110
ALICE NSD
TPC
TPC-TOF
No PID
n/C)
T
+PT-B*P
A/(e
ALICE Preliminary
 = 5.02 TeV
NN
sp-Pb 
-
+K+ K→φ<0, y-0.5<
2+sys.2stat.uncertainties: 
3.1% normalization uncertainty not included
)c (GeV/
T
p
0 2 4 6 8 10 12 14 16 18 20
D
a
ta
/F
it
0.8
1
1.2
Figure 5.15: Comparison between the three different methods to obtain the φ spectra. The fit is
compared to the data point at the bottom of the plot.
60
5. φ(1020) Spectra And Systematic Analysis
)c (GeV/
T
p
0 2 4 6 8 10 12 14 16 18 20
)
-2 )c
) 
((
G
e
V
/
y
d
T
p
/(
d
N
2
) 
d
T
pπ
 1
/(
2
e
v
N
1
/ -910
-810
-710
-610
-510
-410
-310
-210
-110
ALICE, NSD
Levy-Tsallis fit
ALICE Preliminary
 = 5.02 TeV
NN
sp-Pb 
-
+K
+
 K→φ<0, y-0.5<
uncertainties :stat(bars),sys.(boxes)
3.1% normalization uncertainty not included
Figure 5.16: Combined φ invariant spectra for minimum bias measurement, Levy-Tsallis fit func-
tion is shown. Statistical uncertainties (bars), Systematic uncertainties (boxes).
)c (GeV/
T
p
0 2 4 6 8 10 12 14 16
)
-2 )c
) 
((
G
e
V
/
y
d
T
p
/(
d
N
2
) 
d
T
pπ
 1
/(
2
e
v
N
1
/ -910
-810
-710
-610
-510
-410
-310
-210
-110
1
ALICE Preliminary
 = 5.02 TeV
NN
sp-Pb 
-
+K
+
 K→φ<0, y-0.5<
V0A Multiplicity Event Class (Pb-side)
uncertainties :stat(bars),sys.(boxes)
10.0×(0 - 5)%
5.0×(5 - 10)%
2.0×(10 - 20)%
1.0×(20 - 40)%
0.5×(40 - 60)%
0.2×(60 - 80)%
Levy-Tsallis fit
Figure 5.17: Combined φ invariant spectra for six multiplicity ranges, and the respectively Levy-
Tsallis fit functions. Statistical uncertainties (bars), Systematic uncertainties (boxes).
61
Chapter 6
Discussion of Results
Using the φ combined spectra shown in figure 5.16 and 5.17, we can obtain the φ(1020)
integrated yield as a function of multiplicity, it means the yield obtained from the fit and
the data points of each spectra. The figure 6.1 shows this information. From that figure is
clear that the φ meson production has an increasing trend when one goes from peripheral
to central collisions.
| < 0.5
lab
η|
V0A〉
lab
η/d
ch
Nd〈
10 20 30 40
d
y
φ
N
d
0.2
0.4
ALICE Preliminary
 = 5.02 TeV
NN
sp-Pb 
 < 0y, -0.5 < 
-
 + K
+
 K→ φ
Uncertainties: stat. (bars), sys. (boxes)
uncor. sys. (shaded boxes)
Figure 6.1: φ integrated yield(dNφ/dy) as a function of multiplicity. Statistical uncertain-
ties(bars), systematic uncertainties(boxes) and uncorrelated systematic (shaded boxes).
62
6. Discussion of Results
The mean transverse momentum 〈pT〉 for the φ resonance, as well as for other particles,
are presented in the figure 6.2 for two collision systems; pp at
√
s = 7 TeV and p-Pb at
√
sNN = 5.02 TeV. Similar to what was observed in Pb-Pb[35], the p-Pb collisions exhibit
the same increasing trend for the φ as well as for other hadrons (K∗0,Λ, p,K±, π±). While
the 〈pT〉 of stable particles seem to follow a mass ordering, the resonances (φ,K∗0) do not, is
clear that their mean transverse momentum is larger than p and Λ mean pT . Similar mass
ordering deviation for resonances is observed in pp collisions. From the mean pT plot one
can note that the baryon mean pT (p and Λ) is higher than the meson mean pT (K±, K0
s and
π±), but for the φ(1020) and K∗0 the mean pT values are similar to the baryon ones. Since
the masses of p(mp = 938 MeV/c2), K∗0(mK∗0 = 891 MeV/c2), φ(mφ = 1019 MeV/c2) and
Λ(mΛ=1115 MeV/c2) are similar one would expect that the 〈pT〉 values should be consistent
with each other but this was not found.
The 〈pT〉 values for pp collision are consistent with peripheral p-Pb collisions, following
the same mass ordering as observed in p-Pb collisions. In the case of K∗0 the pp value is
in between the multiplicity ranges (60-80)% and (80-100)% but in the case of φ the most
peripheral multiplicity range analysed1 is (60-80)%.
| < 0.5
lab
η|
V0A〉
lab
η/d
ch
Nd〈
10 210
)c
 (
G
e
V
/
〉
T
p〈
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
±π
±K
p
S
0K
Λ
V0A Multiplicity classes (Pb side)
 = 5.02 TeV
NN
sALICE preliminary, p-Pb  
φ 0
K*
ALICE pp 7 TeV
φ 0
K*
p
Figure 6.2: Mean transverse momentum of π±,K±,K0
s,K
∗0
s , p,Λ and φ for two collision systems,
pp at
√
s = 7 TeV and p-Pb at
√
sNN = 5.02 TeV.
1The future work will add the (80-100)% value.
63
6. Discussion of Results
1/3
)η/dchN(d
2 4 6 8 10 12 14
)-
π
+
+
π
/(
φ
2
0.01
0.015
0.02
0.025
0.03
ALICE Preliminary
-
+ K
+
K→φp-Pb
V0A Multiplicity Event Classes (Pb-side)
Uncertainties: stat. (bars), sys. (boxes)
uncor. sys. (shaded boxes)
< 0y= 5.02 TeV, -0.5 <
NN
sp-Pb
| < 0.5y= 2.76 TeV, |
NN
sPb-Pb
| < 0.5y= 7 TeV, |spp
1/3
)η/dchN(d
2 4 6 8 10 12 14
)
p
/(
p
+
φ
2
0.2
0.3
0.4
0.5
0.6
ALICE Preliminary
-
+ K
+
K→φp-Pb
V0A Multiplicity Event Classes (Pb-side)
Uncertainties: stat. (bars), sys. (boxes)
uncor. sys. (shaded boxes)
< 0y= 5.02 TeV, -0.5 <
NN
sp-Pb
| < 0.5y= 2.76 TeV, |
NN
sPb-Pb
| < 0.5y= 7 TeV, |spp
GC Thermal Model (T=156 MeV) GC Thermal Model
 (T=156 MeV)
Figure 6.3: Left: Ratio φ/π as a function of multiplicity (dNch/dη)
1/3 for the three collision
systems: pp, p-Pb and Pb-Pb. Right: Ratio φ/p as a function of multiplicity (dNch/dη)
1/3 for
the same collision systems described before. Statistical uncertainties(bars), systematic uncertain-
ties(boxes) and uncorrelated systematic (shaded boxes).
To study particle production mechanisms one should compare the pT distributions and
the total yields of φ mesons to theoretical models and other particle species (with different
baryon number, mass, or strange quark content). The φ meson is used for these studies
because it lives long enough that its yields and pT distributions do not appear to be affected
by re-scattering or regeneration in the hadronic phase. The figure 6.3 shows the ratios φ/π
(Left) and φ/p (Right). These ratios are presented as a function of (dNch/dη)
1/3 (the cube
root of the charged-particle multiplicity density), where the p-Pb results are compared with
pp and Pb-Pb ones and also compared with the theoretical value given by a grand-canonical
thermal model (based in Pb-Pb collisions) with a chemical freeze-out temperature of 156
MeV [37]. From the particle ratios it is clear that the p-Pb collision system follows the same
increasing trend as the Pb-Pb results, while the pp point is consistent with the peripheral
(60-80%) p-Pb point, feature that was expected because p-Pb is the intermediate collision
system between pp and Pb-Pb. One observes a good agreement between p-Pb and Pb-Pb
in the region of similar multiplicities.
The left plot in figure 6.4 shows the ratio φ/K− as a function of multiplicity where the
64
6. Discussion of Results
results appear to follow a single trend, independent of collision system and energy. The three
systems are consistent within the uncertainties and agree with the thermal model calculation.
The right plot of the figure shows that the φ/K− ratio is independent of collision energy
and system, from RHIC to LHC energies and the thermal model also agrees within the
uncertainties with the Pb-Pb, p-Pb and pp collision systems.
1/3
)η/dchN(d
2 4 6 8 10 12 14
/K
φ
0.05
0.1
0.15
0.2
)
-
+K
+
/(Kφ< 0, 2y= 5.02 TeV, -0.5 <
NN
sp-Pb
-
/Kφ| < 0.5,y= 2.76 TeV, |
NN
sPb-Pb
-
/Kφ| < 0.5,y= 7 TeV, |spp
ALICE Preliminary
-
+ K
+
K→φp-Pb
V0A Multiplicity Event Classes (Pb-side)
Uncertainties: stat. (bars), sys. (boxes)
uncor. sys. (shaded boxes)
(GeV)NNs
10 210
3
10 410
-
/K
φ
0
0.05
0.1
0.15
0.2
0.25
0.3 NA49, Pb-Pb, 8.8 GeV, 0-7.2%
NA49, Pb-Pb, 12.3 GeV, 0-7.2%
NA49, Pb-Pb, 17.3 GeV, 0-10%
NA49, pp, INEL
PHENIX, Au-Au, 0-10%
PHENIX, pp, INEL
GC Thermal Model
= 156 MeV)T(
STAR, d-Au, 0-20%
STAR, Cu-Cu, 0-10%
STAR, Au-Au, 62.4 GeV, 0-20%
STAR, Au-Au, 130 GeV, 0-10%
STAR, Au-Au, 200 GeV, 0-5 %
STAR, pp, NSD
ALICE, Pb-Pb, 0-5 %
ALICE, pp, INEL
ALICE Preliminary
V0A Multiplicity Event Classes (Pb-side)
)
-
+K
+
/(KφALICE, p-Pb, 0-5%, 2
GC Thermal Model
(T=156 MeV)
Figure 6.4: Left: Ratio φ/K− as a function of multiplicity (dNch/dη)
1/3 and comparison be-
tween pp, p-Pb and Pb-Pb collision systems. Right: Ratio φ/K as a function of the collision
energy(
√
sNN ) , compared with different collision systems in other experiments. The values given
by a grand-canonical thermal model with a chemical freeze-out temperature of 156 MeV are also
shown [37]. Statistical uncertainties(bars), systematic uncertainties(boxes) and uncorrelated sys-
tematic (shaded boxes) are shown.
Differences in the production mechanisms of baryons and mesons can be studied through
baryon-to-meson ratios. If the hadrons produced are subject to hydrodynamical flow, the
particle mass plays an important role in determining the shape of the pT distribution. To
study this aspect of particle production, the pT distribution of φ mesons are compared to
protons which is a baryon with a similar mass to the φ but different quark content. Figure
6.5 shows p/φ ≡ (p + p) as a function of pT for pp, p-Pb and Pb-Pb collision systems.
The most central and the most peripheral collisions are presented for p-Pb and Pb-Pb. For
the peripheral results, the three collision systems have a good agreement. This similarity is
expected because at these multiplicities (centralities) the particle production in p-Pb (Pb-
65
6. Discussion of Results
Pb) should resemble the pp collisions. The 0-5% multiplicity range for p-Pb remains between
pp and Pb-Pb (0-10%) up to 2 GeV/c, above that momentum both the pp and p-Pb continue
the decreasing trend while the Pb-Pb (0-10%) remains practically flat.
)c (GeV/
T
p
0 1 2 3 4 5 6
φ
)/
p
(p
+
0
2
4
6
8
10
12
14
| < 0.5y = 2.76 TeV, |
NN
sPb-Pb 
arXiv:1404.0495
0-10%
80-90%
| < 0.5y = 7 TeV, |spp 
Eur. Phys. J. C 72, 2183
Uncertainties: stat. (bars), sys. (boxes)
ALICE Preliminary
 < 0y = 5.02 TeV, -0.5 < 
NN
sp-Pb 
V0A Multiplicity Event Classes (Pb-Side)
0-5%
60-80%
Figure 6.5: Ratio p/φ as a function of pT for pp at
√
s = 7 TeV, p-Pb at
√
sNN = 5.02 TeV and
Pb-Pb at
√
sNN = 2.76 TeV, comparing central and peripheral intervals.
The figure 6.6 shows the meson-to-meson ratio φ/π = φ/(π+ + π−) as a function of pT.
A very similar increasing trend is observed either is peripheral or central collisions. As it is
shown in figure 6.7, the baryon-to-meson ratios p/π in p-Pb(left) and Pb-Pb(right) collisions
have a very similar shape compared to the φ/π for pT < 3 GeV/c, feature observed also
using Pythia at generation level[38]. This indicates that the number of quarks is not an
important factor that determines the pT distributions of particles at low and intermediate
pT in central collisions.
66
6. Discussion of Results
)c (GeV/
T
p
0.5 1 1.5 2 2.5 3
)- π
+
+ π
/(φ
0
0.05
0.1 ALICE Preliminary
 = 5.02 TeV
NN
sp-Pb 
-
+K
+
 K→φ<0, y-0.5<
V0A Multiplicity Classes (Pb-Side)
uncertainties: stat.(bars), sys.(boxes)
(0 - 5)%
(60 - 80)%
Figure 6.6: Ratio φ/π as a function of pT for p-Pb at
√
sNN = 5.02 TeV and comparing central
and peripheral measurements.
)c (GeV/
T
p
)- π
 +
 
+ π
) 
/ 
(
p
(p
 +
 
0
0.2
0.4
0.6
0.8
1
0 1 2 3
0-5%
60-80%
 = 5.02 TeVNNsALICE, p-Pb, 
V0A Multiplicity Classes (Pb-side)
0 1 2 3
0-5%
80-90%
 = 2.76 TeVNNsALICE, Pb-Pb, 
Figure 6.7: Ratio p/π = (p+p)/(π++π−) as a function of pT in the rapidity interval 0 < y < 0.5
(left panel). The ratios are compared to results in Pb-Pb collisions measured at mid-rapidity, shown
in right panel. The empty boxes show the total systematic uncertainty; the shaded boxes indicate
the contribution uncorrelated across multiplicity bins. Figure taken from [27].
67
Chapter 7
Conclusions
In this work the production of the φ(1020) meson has been measured in p-Pb collision at
√
sNN = 5.02 TeV, in the rapidity region −0.5 < y < 0 (Pb side). It was measured through
the φ → K+ +K− decay channel with a branching ratio of 48.9%. The kaons were selected
using the PID capabilities of the TPC and TOF detectors. With the kaons information
the φ invariant mass is obtained, from which the signal was extracted. The combinatorial
background was subtracted from the uneven sign distributions by the Event Mixing tech-
nique. The raw yield was extracted by integrating the invariant mass distributions. After
the normalizations and corrections to the raw yield, the invariant φ spectra are obtained in
fifteen pT intervals and for seven multiplicity ranges; measured by the V0A detector. The
systematic uncertainties on the yield were calculated by varying a set of parameters such as:
fit settings, residual background function, event mixing normalization region, among others.
The φ spectra are fitted by the Levy-Tsallis function in order to obtain information on
the integrated yield(dN/dy), which is later compared to other charged particles yields (p, K
and π). The 〈pT〉 shows an increasing trend for the φ as well as for other particles, but for
particles of similar masses(K∗0, p, φ and Λ ) the 〈pT〉 is not compatible between them which
is opposite to the prediction of hydrodynamics. The pp values are found to have the same
mass behaviour and consistent with the peripheral p-Pb ones.
Results of particle ratios (φ/π, φ/p, φ/K) as a function of mean charged-particles mul-
tiplicity density (〈dNch/dy〉) are compared with pp and Pb-Pb collisions and they are found
to be compatible with a common increasing trend. The ratio φ/p as a function of pT for
peripheral p-Pb collision(60-80%) is compatible with pp and Pb-Pb(80-90%) and for central
p-Pb collision(0-5%) the ratio remains in between peripheral and central Pb-Pb collisions,
characteristic that was expected. On the other hand, in meson-to-meson ratio (φ/π) there
68
is practically not difference between central and peripheral p-Pb collisions. Since the be-
haviour of the φ/π is very similar to that of p/π for both p-Pb and Pb-Pb systems we
conclude that the important parameter are the masses of the respective particles and not
their quark content.
69
Bibliography
[1] Griffiths, David. Introduction to Elementary Particles, 2nd Edition,Wiley-VCH,2004. 1
[2] http://home.web.cern.ch/about/updates/2013/03/new-results-indicate-new-particle-
higgs-boson 2
[3] Introduction to High-Energy Heavy-Ion Collisions, C.Y. Wong, World Scientic, 1994 3
[4] F. Halzen and A.D. Martin, Quarks and Leptons, John Wiley and Sons (1984) 5
[5] S. A. Bass et al., Signatures of Quark-Gluon-Plasma formation in high energy heavy-ion
collisions:A critical review, J.Phys.G25:R1-R57, 1999. 6
[6] Letessier, Jean and Rafelski, Johann. Hadrons and Quark-Gluon Plasma, Cambridge
Univesity Press, 2002. 7, 8
[7] J. P. Bailly et al.. Phys. Lett. B195 (1987) 609. 8
[8] J. Rafelski and B. Müller. Phys. Rev. Lett. 48 (1982) 1066 [Erratum: ibid. 56 (1986)
2334]. 9
[9] C. Markert, R.Bellwied, I.Vitev, Phys.Lett. B669:92 (2008) 10
[10] A. G. Knospe (ALICE Collaboration), J. Phys. Conf. Ser. 420, 012018 (2013). 10
[11] Biolcati, Emanuele. Distribution of hadrons identified with the Inner Tracking System
of the ALICE experiment for p-p data, Ph.D Thesis, Università degli Studi di Torino,
Italia, 2011. 11
[12] Tavernier, Stefaan. Experimental Techniques in Nuclear and Particle Physics, 1a
edición, Springer, 2010.
70
BIBLIOGRAPHY
[13] Perkins, Donald H. Introduction to High Energy Physics, 4a edición, Cambridge Uni-
vesity Press, 2000. 4, 5
[14] R. Hagedorn, 1965. Statistical thermodynamics of strong interactions at high energies.
I. Suppl. Nuovo Cimento, 3, 147. 8, 53
[15] Aguilar-Benitez M. et al. (LEBC-EHS Collaboration), Z. Phys. C 50, 405 (1991). 10
[16] ALICE collaboration, ALICE forward detectors: FMD, T0 and V0: Technical Desing
Report, CERN-LHCC-2004-025, http://cdsweb.cern.ch/record/781854 15
[17] ALICE Collaboration et al 2004 J. Phys. G: Nucl. Part. Phys. 30 1517. 17, 19
[18] ALICE Collaboration et al. The ALICE Experiment at the CERN LHC, 2008, JINST
3 S08002 13
[19] ALICE Experiment, Detectors of the ALICE experiment,
http://aliceinfo.cern.ch/Public/en/Chapter2/Page3-subdetectors-en.html 17
[20] Breit, G.; Wigner, E. (1936). ”Capture of Slow Neutrons”. Physical Review 49 (7): 519.
doi:10.1103/PhysRev.49.519 33
[21] Olivero, J.J.; R.L. Longbothum (February 1977). ”Empirical fits to the Voigt line width:
A brief review”. Journal of Quantitative Spectroscopy and Radiative Transfer 17 (2):
233236. 34
[22] O. Behnke et al, Data Analysis in High Energy Physics, 2012, WILEY-VCH. 44, 45
[23] Kalweit, Alexander Philipp. Energy Loos Calibration of the ALICE Time Projection
Chamber, Master Thesis, Technischen Universität Darmstadt, Alemania, 2008. 18
[24] W. Blum and L. Rolandi, Particle Detection with Drift Chambers. Springer, Berlin,
1998. 23
[25] The ALICE experiment offline project,
www.cern.ch/ALICE/Projects/offline/aliroot/Welcome.html. 21
[26] ALICE collaboration (K. Aamodt et al.), The European Physical Journal, C71, Number
6, 1655, 2010. 20
71
BIBLIOGRAPHY
[27] Abelev B I et al. (ALICE Collaboration), Physics Letters B 728, 20, 2014. xix, 28, 48,
58, 67
[28] L. Evans and P. Bryant, JINST 3, S08001 (2008). 26
[29] Nuclear Physics B, Vol. 335, No. 2. (7 May 1990), pp. 261-287 8, 53
[30] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010). 37
[31] Schnedermann E, Sollfrank J and Heinz U 1993 Phys. Rev. C 48 246275 54
[32] Tsallis C 1988 J. Stat. Phys. 52 479 54
[33] Abelev B I et al. (STAR Collaboration) 2007 Phys. Rev. C 75 064901 54
[34] ALICE Collaboration, B. Abelev, et al., Pseudorapidity density of charged particles
pPb collisions at
√
sNN = 5.02 TeV, Phys. Rev. Lett. 110 (2013) 032301. 57
[35] Abelev B I et al. (ALICE Collaboration) 2014 K∗(892)0 and φ(1020) production in
Pb-Pb collision at
√
sNN = 2.76 TeV, http://arxiv.org/abs/1404.0495 43, 63
[36] Harsh Shah, Detection of φ(1020) meson by the decay φ → K+K− in AMPT model,
http://www.niser.ac.in/ bedanga/Detection phi harsh.pdf 43
[37] J. Stachel, A. Andronic, P. Braun-Munzinger, K. Redlich, 2014, J. Phys.: Conf. Ser.
509, 012019 xix, 64, 65
[38] E. Cuautle, R. Jimenez, I. Maldonado, A. Ortiz, G. Paic and E. Perez, arXiv:1404.2372
[hep-ph].
66
72
Appdx A
.0.1 Resolution
In this appendix section will be described the way the different variations of resolutions
are obtained, but first it is useful to note that Mgen is not necessarily the PDG mass: the
generated φ mesons are assigned masses with a realistic (Breit-Wigner) distribution. And
this generated mass is obtained by fitting a Breit-Wigner to the generated histogram in the
0-100% multiplicity bin giving the value: Mgen(BW ) = 1.019543 ± 0.000005 GeV/c2 and
Γgen = 4.399±0.019 MeV/c2, and these values are pT independent. The generated mass and
the mean mass shift 〈∆M〉 will be used to correct the real mass distribution. The mean mass
shift and the resolution histogram are extracted from the “resolution histogram” (∆M) in
the following manners:
• A Gaussian is used to fit the ∆M histogram, where the mean mass shift 〈∆M〉 is the
mean parameter of this Gaussian, and the resolution parameter is labeled as σGauss.
• The resolution and the mean mass shift are taken directly from the ∆M histogram,
without any fitting, then the 〈∆M〉h and σh are obtained.
• The other option used to get the resolution is to fit the reconstructed histogram with
a Voigtian function (width fixed to 4.4 MeV/c2) where the σvoi is obtained.
73
)2(●❡❱✴❝✁♥✲M❘✁✂M
✄✵✳✵✶ ✄✵✳✵✵✺ ✵ ✵✳✵✵✺ ✵✳✵✶
C
♦
✉
☎
ts
✵
2✵✵
✹✵✵
✻✵✵
✽✵✵
✶✵✵✵
✶2✵✵
✶✹✵✵
✶✻✵✵
✶✽✵✵
T
φ lution, Mult: 0-100%, 1.0<p
)2(GeV/c
Gen
-M
Rec
M
-0.01 -0.005 0 0.005 0.01
C
o
u
n
ts
0
200
400
600
800
1000
<3.0
T
φ Resolution, Mult: 0-100%, 2.5<p
Figure 1: Resolution histogram (truncated Gaussian fit) in the transverse momentum 1.0 < pT <
1.5 (left plot) and 2.5 < pT < 3.0 (right plot), both in the multiplicity bin 0− 100%.
)2(GeV/c
inv
M
0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06
C
o
u
n
ts
0
500
1000
1500
2000
2500
<1.5
T
1.0<p
)2(GeV/c
inv
M
0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06
C
o
u
n
ts
0
200
400
600
800
1000
1200
1400
1600
<3.0
T
2.5<p
Figure 2: Reconstructed histogram with a Voigtian0 fit, where σvoi is obtained. The left plot is
shown in the transverse momentum 1.0 < pT < 1.5 and the right plot in 2.5 < pT < 3.0, both in
the multiplicity bin 0− 100%
74
(GeV/c)
T
p
1 2 3 4 5 6 7 8 9 10
)
2
(M
e
V
/c
σ
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
: Resolution Voigt
voi
σ
: Resolution Gaussian
Gauss
σ
: Resolution Histogram
h
σ
: 0-100%Multiplicity
Figure 3: Three calculations of the resolution are presented, σGauss, σh, σvoi in the 0-100% multi-
plicity bin.
75