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Master Thesis in High-Energy Physics

Performance checks and comparison of ' J / − and ' branching ratios in the BES-III experiment

Charles Dietz

Spring semester 2009

Supervisors :

Prof. Yuanning GAO, TUHEP, Tsinghua UniversityProf. Aurelio BAY, LPHE, Ecole Polytechnique Fédérale de Lausanne

Performance checks and comparison of ψ′ → J/ψ π+π− andψ′ → ρ π branching ratios in the BES-III experiment

Charles Dietz

Spring 2009

Contents

1 Introduction 3

2 The IHEP facility 42.1 The BEPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 The BES-III detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Main Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.2 Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . 62.2.3 Time-Of-Flight System . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.4 Muon Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 The BES-III Offline Software . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 The Charmonium physics 93.1 The cc̄ system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Theoritical framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.2 Charmonium spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 J/ψ and ψ′ resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.1 Basic facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.2 Physics at BES-III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 The “ρ π puzzle” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Reconstruction checks 144.1 Charged tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.1.1 Kalman filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.1.2 Pions true and reconstructed momentum . . . . . . . . . . . . . . . . 15

4.2 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2.1 Energy distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2.2 π0 resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.3 Dalitz plot for J/ψ → ρ π . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5 Event selection and background study 205.1 Decay channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.1.1 J/ψ → ρ π . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.1.2 ψ′ → J/ψ π+π− . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.1.3 ψ′ → ρ π . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.2 Selection of events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2.1 Charged tracks selection . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2.2 Photons selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1

2

5.2.3 Additional criteria and kinematic fits . . . . . . . . . . . . . . . . . . . 225.2.4 Selection process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.3 Sources of noise and background rejection . . . . . . . . . . . . . . . . . . . . 225.3.1 KK? channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.3.2 Non-resonant decays to pions . . . . . . . . . . . . . . . . . . . . . . . 245.3.3 Other backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6 Results 286.1 Detection performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6.1.1 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286.1.2 Mass resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6.2 Branching ratio comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296.3 Improvements and future perspectives . . . . . . . . . . . . . . . . . . . . . . 32

7 Conclusion 34

Acknowledgments 35

References 36

Chapter 1

Introduction

This master thesis was accomplished during the Spring semester 2009 under the directsupervision of Prof. Yuanning Gao from TUHEP1 at Tsinghua University and Prof. AurelioBay from LPHE2 at the Swiss Institute of Technology Lausanne (EPFL). It uses the veryfirst set of data collected by the BES-III experiment, described in Chapter 2, to check somereconstruction features and perform a first raw estimation of the ratio of ψ′ → ρ π andψ′ → J/ψ π+π− branching fractions3. A general introduction on charmonnium physics isgiven in Chapter 3 to set the theoritical and experimental framework of this work.

Performance checks are a crucial step in the early life of a particle detector as the qualityof all the physical results depends on it. These checks allow to apply corrections to thehardware devices and software in order to achieve a better calibration and measurementaccuracy. The checks presented in this work are far to be exhautive and have to be takenin a didactic way as they are rich in informations about how the whole detection, recording,reconstruction and analysis process works. They consist in two parts : pure reconstructionchecks about charged tracks and photons using the Monte-Carlo truth and reconstructedevents presented in Chapter 4, and resolution of π0, J/ψ and ψ′ in Chapter 6. Especiallysince the Electromagnetic Calorimeter of BES-III has a much better energy resolution thanin BES-II.

The comparison of ψ′ → ρ π and ψ′ → J/ψ π+π− branching fractions is directly relatedto the so called “ρ π puzzle” and its “12%-rule” violation, which is presently one of the mostchallenging questions in charmonium physics and appeals for some enhancements. Selectionof these channels and rejection of background are studied in details in Chapter 5 and all thefinal results are presented in Chapter 6.

1Center for High Energy Physics, Tsinghua University, Beijing, http://hep.tsinghua.edu.cn/2Laboratoire de Physique des Hautes Energies, Ecole Polytechnique Fédérale de Lausanne,

http://lphe.epfl.ch/3all informations about particle decay modes and branching fractions are taken from Ref.[1]

3

Chapter 2

The IHEP facility

The goal of this section is to present the main characteristics of the Beijing Electron-Positron Collider (BEPC) and the Beijing Spectrometer (BES) with a more detailed descrip-tion of BES-III subdetectors as well as the physics that aimed to be explored in this exper-iment. These facilities are located at the Institute of High Energy Physics (IHEP)1 of theChinese Academy of Science in West Beijing which is the biggest comprehensive fundamentalresearch center in China.

2.1 The BEPC

The old BEPC facility, which ran from 1989 to 2004, was composed of a linear injector,a storage ring, the Beijing Spectrometer (BES) and the Beijing Synchrotron Radiation Fa-clity (BSRF) . The positron injection energy is 1.3-1.5 GeV. The beam energy range of thestorage ring is up to 2.8 GeV with an average luminosity of 1031cm−2s−1 at 1.89 GeV. Thecircumference of the storage ring is 240 meters. The beam energy for dedicated synchrotronradiation running is 2.2 GeV with a beam current of 140 mA.

BEPCII is a double-ring collider (see Figure 2.1) built within the existing BEPC tunneland was launched in 2007. The designed luminosity of BEPCII is 1033cm−2s−1 at the beamenergy of 1.89 GeV, which is about two orders of magnitudes higher that the one of BEPC.Each ring can be filled with up to 93 bunches with the maximum beam current of 0.9 A perring. The beams collide at the south interaction region with horizontal crossing angle of 11mrad.. Superconducting RF system of 500 MHz, superconducting Micro−β quadruples, lowimpedance vaccum chambers are used. The positron injection rate of linac will be increasedto 50 mA per minute with full energy injection up to 1.89 GeV.

2.2 The BES-III detector

The BES-III2 detector is the second update of the Beijing Electron Spectrometer, its con-struction was finished in Summer 2008. It consists of the following major components :

• a drift chamber ;1http://www.ihep.ac.cn/2BES-III collaboration webpage : http://bes3.ihep.ac.cn/

4

CHAPTER 2. THE IHEP FACILITY 5

Figure 2.1: BEPCII double ring and BES-III detector

• an electromagnetic calorimeter ;

• a time-of-flight system ;

• a muon chamber ;

• a 1 Tesla super-conducting solenoid magnet.

More details on the sub-detectors are given below but complete description of the devices andtheir performances can be found in Ref. [2] and [3].

2.2.1 Main Drift Chamber

The Main Drift Chamber (MDC) is the most important sub-detector of BES-III as it is usedto measure precisely the momentum of charged particles and determine their type by theirspecific energy deposits (dE/dx ). It is composed of an inner chamber that can be replacedif damaged by radiations and an outer chamber, and this without a chamber wall whicheliminates a potential source of multiple scattering. The inner diameter of the drift chamberis 118 mm for easy assembly of the beam pipe. The physical outer diameter is designed to be1600 mm to achieve good momentum resolution. The maximum lenght is 2400 mm.

It uses a Helium-based gas mixture He/C3H8(60/40), together with the use of other low-mass materials, so as to minimize the effect of multiple scattering. All the cells are arrangedin 43 circular layers. The radial extent is from 73 to 771 mm occupied successively by 8stereo layers, 12 axial layers, 16 stereo layers and 7 axial layers. Each layer contains a field


Figure 2.2: View of the Main Drift Chamber

wire layer (with all field wires) and a sense wire layer (with alternating sense and field wires).Aluminium wires (φ = 110µm) are used for firld shaping and gold-plated tungsten wires(φ = 25µm) for signals.

The MDC has a maximum possible solid angle coverage of about 90% of 4π for chargedtrack measurement. It covers the polar angle | cos θ | < 0.93 and is designed to have a spatialresolution better than 130 µm averaged over the cell, a dE/dx resolution better than 6% forπ/K separation up to a momentum of 700 MeV/c, and a transverse momentum resolution ofabout 0.5% at 1 GeV/c.

2.2.2 Electromagnetic Calorimeter

The Electro-Magnetic Calorimeter (EMC) measures the energies and positions of photonsand electrons precisely. The calorimeter is composed of one barrel and two endcap sections,covering 93% of 4π. There are a total of 44 rings of crystals along the z direction in the barrel,each with 120 crystals, and 6 layers in the endcap, with different number of crystals in eachlayer. The entire calorimeter has 6272 CsI(Tl) crystals with a total weight of about 24 tons.

Figure 2.3: Orientation of CsI(Tl) crytals in the Electromagnetic Calorimeter

The barrel has an inner radius of 940 mm and a length of 2750 mm and covers the polarangle | cos θ | < 0.83. The endcaps have an inner radius of 500 mm and are placed at z = ±


1380 mm from the interaction point. They cover the polar angle range 0.85 < | cosθ | < 0.93.See Figure 2.3 for better idea.

The EMC is designed to have an energy measurement range for electrons and photonsfrom 20 MeV to 2 GeV with an energy resolution of about 2.3%/

√E(GeV ) ⊕ 1% . The

design position resolution for an electromagnetic shower is σxy ≤ 6 mm /√E(GeV ) and the

electronics noise for each crytal is required to be less than 222 keV.

2.2.3 Time-Of-Flight System

The Time-Of-Flight System (TOF) sub-detector is placed between the drift chamber andthe electromagnetic (see Figure 2.4) calorimeter and measures the flight time of chargedparticles in order to identify the particle type. It also provides a fast trigger and helps toreject cosmic-rays background.

It consists of barrel and endcap. The polar angle coverage of the barrel is | cos θ | < 0.82,and that of the endcap is from 0.85 < | cos θ | < 0.95. The inner radius of the barrel is 810mm and outer radius 925 mm, its effective length is 2320 mm. The barrel is made of twolayers of 88 plastic scintillators arranged in a cylinder. Each scintillator bar has a length of2380 mm, a thickness of 50 mm and a width of 50 mm also. Fine-mesh PMTs read out thesignal at each end of the scintillator bar. Endcap arrays consist of 48 fan-shaped scintillationelements with an inner radius of 410 mm and an outer radius of 890 mm. They are read outfrom external end by a single fine-mesh PMT.

Figure 2.4: Time-Of-Flight System location

The key-point of the TOF is its time resolution which depends of the intrisic resolutionof the many sub-components and various effects. The design intrisic resolution of a barrelcounter is 90 ps and 70 ps for an endcap counter. The total time resolution is expected to bein the range of 100-110 ps.

2.2.4 Muon Chamber

The BESIII Muon Counter (MUC) is a gaseous detector based on Resistive Plate Chambers(RPCs) sandwiched by iron absorbers. Its main manufactural material is one type of bakelite


specially developped. The muon detector consists of two endcaps and a barrel. There are 8detecting layers in each endcap and 9 in the barrel. The total amount of RPC units is 978,and the yielding area is up to 1272 m2. It covers the polar angle | cos θ | < 0.83. The gasmixture used is made of Argon (50%), F134a (42%) and iso-butane (8%).

The most important ability of the MUC is to distinguish muons from hadrons by thecharacterisitc hit patterns they produce. Generally speaking the recontruction algorithm isable to reject pions to a level of about 4% while keeping 90% of real muons. But theseinformations won’t be used in this work as no muon is involved in the studied decays.

2.3 The BES-III Offline Software

The BES-III Offline Software3 (BOSS) uses the object-oriented C++ language and runson the Scientific Linux CERN (SLC) operating system. It is based on the Gaudi framework4

which provides all the standard interfaces and tools for event simulation, data processingand physics analysis. Three types of persistent data have been defined for BOSS : raw data,reconstructed data and Data-Summary-Tape (DST). The last two types are in ROOT formatfor more convenient management and usage. The whole software is managed by CMT5, whichcan create packages, maintain dependencies and produce librairies and executables.

The simulation part is based on the GEANT4 package6. It uses two event generators :KKMC for the Electroweak Standard Model and BesEvtGen (based on EvtGen) for tau-charm physics. A unique description of the detector geometry and materials, used by bothsimulation and reconstruction packages, has been developed based on XML. Particle trackingand the interactions with the detector materials are all handled by GEANT4. Detectorresponses are modeled by the so-called “digitization code”.

The BES-III reconstruction code is a full set of algorithms consisting mainly of the followingparts :

• a track-finding algorithm and a Kalman-Filter-based track-fitting algorithm to deter-mine momentum of charged particles ;

• a particle identification algorithm based on dE/dx and TOF measurments ;

• a shower- and cluster-finding algorithm EMC energy and position measurements ;

• a muon track finder.

Some other algorithms have been developed for beam bunch crossing timing, secondary vertexand track refitting, etc.

3all the results presented in this thesis have been obtained using BOSS 6.4.44http://www.cern.ch/gaudi/5http://www.cmtsite.org/6http://geant4.cern.ch/

Chapter 3

The Charmonium physics

This section provides some general informations about the known experimental and theo-ritical reults on Charmonium physics. It focuses especially on J/ψ and ψ′ states as they willbe widely produced in BES-III and the “ρπ puzzle” which is one of the main issues concerningthese resonances. It is based mainly on Ref.[3] which contains all the informations on BES-IIIphysics theory and directions.

3.1 The cc̄ system

3.1.1 Theoritical framework

This section is not giving a full overview on all the theoritical frameworks of charmoniumphysics but a sample of basic informations. It is important to mention that mesons made ofheavy quarks (or heavy quarkonia) still play a major role in investigations of QCD dynamics.Charmonium mesons are made of cc̄ quark pairs that are bound by the strong interaction.The non-relativistic QCD (NRQCD, see Ref.[4, 5, 6]) effective theory is based on the fact thatthe charmed quark mass mc is sufficiently large so that the motion of a charmed quark insideits bound state is slow and thus can be regarded as a non-relativistic. In fact the motion ofquarks should be slow enough so that their momentum is much smaller than mc and the orderof the binding energy much smaller than their momentum. NQCD is very useful in dealingwith charmonium spectroscopy, annihilation decays and inclusive production.

The QCD Lagrangian for heavy quarks is as follows :

Lq = Ψ̄(x)(i /Dµ −mc)Ψ(x)

where i /Dµ = i∂µ + gAaµT a is the covariant derivative. It turns out te be complicated asit includes all energy scales. It can be simplified considering the relativistic limit v �c andhaving cut-off energy scale to be less than mc. This suppresses the quark pair creation andannihilation and decouples the quark and antiquark. The effective NRQCD Lagrangian canbe expressed in a sum of powers of v with coefficients called Wilson short-distance coefficientsthat are calculated to match NRQCD and QCD. Fields are described by two-componentsPauli spinor fields ψ and χ for the quark and antiquark respectively. Up to order v4 NRQCDLagrangian reads :

LNRQCD = Ll + L0 + δL

9

CHAPTER 3. THE CHARMONIUM PHYSICS 10

where Ll is the ordinary Lagrangian for gluons and light quarks and

L0 = ψ†(iD0 +

D2

2mc

)ψ + χ†

(iD0 −

D2

2mc

)χ

δL = c18m3c

ψ†(D2)2ψ +c2

8m2cψ†g(D ·E−E ·D)ψ

+c3

2mcψ†gσ ·Bψ + i c4

8mcψ†gσ · (D×E−E×D)ψ + c.c.

δL contains the corrections terms to L0

NRQCD can be extended to the level of binding energy to obtain the theory called potentialNRQCD (pNRQCD) which introduces some interaction potential between the two quarks (seeRef.[7, 8, 9]). Other models exist that provide a complementary description but they won’tbe discussed here. Reference [3] gives a full summary of the theoritical enhancements oncharmonium physics with all the corresponding references.

3.1.2 Charmonium spectroscopy

It appears that the known spectrum of conventional charmonium states can be well de-scribed by using quite simple cc̄ potential model. These models assume a spin-indepent po-tential that combines a one gluon exchange (OGE) color Coulomb term and a linear confininginteraction term :

V(cc̄)0 = −

43αsr

+ br.

This is completed by the spin-dependent Breit-Fermi Hamiltonian due to OGE and aninverted spin-orbit term that arises from the assumed scalar nature of the confining interaction:

Vspin−dep =32παs9m2c

~Sc · ~Sc̄ δ(~x) +1m2c

[(2αsr3

− b2r

)~L · ~S + 4αs

r3T

]

The experimental and theoritical masses are shown in Fig. 3.1. One can see that thereis a reasonably good agreement between the experimental spectrum and the potential modelpredictions. Notice that the predictions are really good for the lowest energy states butdepreciates for higher masses.

3.2 J/ψ and ψ′ resonances

3.2.1 Basic facts

The J/ψ resonance was independently discovered in 1974 by two different research groups,one led by Burton Richter [10] at SLAC and another one led by Samuel Ting [11] at theBrookhaven National Laboratory. They respectively gave the name J and ψ to their discoveryand since then all scientific papers refer to it as J/ψ. Richter and Ting both received theNobel Prize of Physics in 1976 for their work.


Figure 3.1: Predicted and observed spectrum of charmonium states. The solid lines representthe experimentally established states and the labels give their masses. The left doted linesrepresent the predicted states by a fully non-relativistic model.


J/ψ ψ(2S)m (MeV) 3096.916 ± 11 3686.0.93 ± 0.034Γ(keV ) 93.4 ± 2.1 337 ± 13IG(JPC) 0−(1−−) 0−(1−−)

Table 3.1: J/ψ and ψ′ main parameters

Later, the ψ′ and other excited charmonium states were discovered experimentally. Thebasic parameters of J/ψ and ψ′ are presented on Table 3.1. J/ψ and ψ′ decays to lighthadrons proceed via the annihilation of the c and c̄. This annihilation decay dominates theJ/ψ decay rate but accounts for only 15% of the ψ′ decay rate, where hadronic transitionto other charmonium states dominate. The inclusive decay rates to light hadrons can becalculated in the frame of NRQCD.

3.2.2 Physics at BES-III

The upgraded BEPCII/BES-III is definitly designed to be a “J/ψ-factory” as it’s a uniqueand powerful facility for studying physics up to 4 GeV. With a peak luminosity of 1033cm−2s−1

BEPC should produce 1010J/ψ events per year which will provide the world largest J/ψsample and a significant amout of other interesting data as can be seen on Table 3.2.

ECMS Lum. σ EventsJ/ψ 3.097 0.6 3400 10×109ψ(2S) 3.686 1.0 640 3.2×109τ+τ− 3.670 1.0 2.4 12×106D0D̄0 3.770 1.0 3.6 18×106D+D− 3.770 1.0 2.8 14×106DsDs 4.030 0.6 0.32 1.0×106DsDs 4.170 0.6 1.0 2.0×106

Table 3.2: Expected BEPCII production for a one year run

This unique set of datas will enable to pursue research in the following high-energy physicstopics :

• light hadrons spectroscopy and search for new hadronic states : using the large J/ψsample and its rich gluon environment to seek for glueballs, study the properties of lighthadrons as f0(1500) and f0(1700), and probe the existence of exotics hadrons ;

• D-physics : production of D+, D0 and Ds mesons to measure decay constants with abetter accuracy, extract some of the CKM matrix elements and study of the possiblyCP-violating D-D̄ mixing ;

• τ -physics : further study of leptonic decays and universality of electroweak interaction,better measurement of the τ mass (compared to BES-I) ;

• and charmonium physics :


BES-III should be able to measure the J/ψ and ψ′ decay widths with a precision betterthan 1%. J/ψ has many different decay modes : in two-body decays, final-state particlescan be a pseudoscalar, a scalar, a vector, an axial vector or a tensor meson, which can allbe studied more precisely than before. BES-III should also provide a guidance to a solutionof well known problems such as the ρ π puzzle (12%-rule violation) and the non D-D̄ decayof the ψ(3770) (or ψ′′) and offer better precision on transition between charmonium statesmeasurements.

It will also be possible to detect some Cabibbo-suppressed J/ψ decay channels, in whichthe charmed quark decays via the weak interaction, while the anticharm quark combines withanother quark to form a D-meson. This will open the door to the study of new physics beyondthe Standard Model at BES-III.

3.3 The “ρ π puzzle”

So called “experimental puzzles” have frequently played a leading role in new discoveriesin high energy physics and therefore often attract attention of theorists. The perturbativeQCD (pQCD) predicts for J/ψ and ψ′ the following relation (Ref. [14, 15]) :

Qh =Bψ′→hBJ/ψ→h

=Bψ′→e+e−BJ/ψ→e+e−

≈ 12.7%

This relation is known as the “12% rule” and is expected to be valid at a reasonable degree(from a QCD point of view). The “ρπ puzzle” is the observation that this prediction is clearlyviolated for the ρπ and several other channels, which has been reported since 1983 (Ref. [16]).A full range of theoritical explanations tries to explain this result, they are classified in threemain categories providing the following hypothesis :

• existence of an enhanced braching fraction for J/ψ decays ;

• suppression of branching fractions for ψ′ decays ;

• many others (final state interaction, large phase, mass reduction, vector-meson-mixing).

All these models are reviewed in Ref. [17].

Chapter 4

Reconstruction checks

The aim of this preliminary work was to get familiar with the BOSS environment whilechecking the efficiency of some recontruction processes mainly by comparing direct infor-mations from the event generator (MC truth) with the reconstructed datas. All this wasperformed using J/ψ → ρ π (see Section 5.1.1) simulated events.

4.1 Charged tracks

4.1.1 Kalman filter

Generally speaking, the Kalman filter is a set of mathematical equations that providesan efficient recursive computational mean to estimate the state of a process in a way thatminimizes the mean square error. This formalism can be used in kinematic fitting with variouskind of constraints to refit tracks momentum for example.

(GeV/c)true

−prec

p−0.02 −0.01 0 0.01 0.02 0.03 0.04 0.05 0.06

even

ts

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

MdcKal

Mdc

Figure 4.1: Pions reconstructed and true momentum difference with and without Kalmanfilter.

14

CHAPTER 4. RECONSTRUCTION CHECKS 15

In the BOSS software two kind of MDC data are available, without (“Mdc”) and withKalman filter (“MdcKal”) applied. The Figure 4.1 shows the difference between reconstructedand true momentum with and without Kalman filter (that is (| ~prec,Kalman | − | ~ptrue |) and(| ~prec,noKalman | − | ~ptrue |)). One can see from the sharp symmetric peak centered aroundzero of the MdcKal data that the Kalman filtered reconstructed momentum matches muchbetter the true momentum (for most of them δp < 10 Mev/c), whereas the non-filteredmomentum tends to be larger than the true one.

This doesn’t mean the non-filtered data are useless, actually it can be used for the rawselection of charged tracks, but later only the Kalman-filtered ones should be employed.

4.1.2 Pions true and reconstructed momentum

Once the better quality of Kalman-filtered momentum is established, one should checkfurther the Kalman-filtered reconstructed and true momentum match. Figure 4.2 shows thedifference of reconstructed and true momentum separately for the transverse and longitudinalmomentum. Peaks are quite sharp (and quasi-gaussian for pz) with RMSpt< 5 MeV/c andRMSpz< 4 MeV/c which is very good.

(GeV/c)T

pδ−0.015 −0.01 −0.005 0 0.005 0.01 0.015

even

ts

0

1000

2000

3000

4000

5000

6000

7000

Entries 137334

Mean 0.0004421

RMS 0.004874

Entries 137334

Mean −5.909e−05

RMS 0.003986

(GeV/c)z

pδ−0.015 −0.01 −0.005 0 0.005 0.01 0.015

even

ts

0

1000

2000

3000

4000

5000

6000

7000

Entries 137334

Mean −5.909e−05

RMS 0.003986

Figure 4.2: Pions reconstructed and true energy momentum difference for pt and pz.

Also, the reconstructed momentum almost exactly the true spectrum as shown on Figure4.3 . The peak at ∼1.5 GeV (half mass of J/ψ) is not shifted but just slightly attenuated.Globally, the reconstruction of simulated charged tracks (pions) is really satisfying.

4.2 Photons

4.2.1 Energy distribution

Similar considerations can be made for the photons, involving the simulated EMC perfor-mances this time. Figure 4.4 shows the difference between reconstructed and true energy. Ithas a peak centered around zero but is definitly not symmetric as it has a long tail on the


(GeV/c)π

p0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

even

ts

0

2000

4000

6000

8000

10000

Figure 4.3: Pions reconstructed (crosses) and true (line) momentum spectrum.

left proving that the recontructed energy tends to be smaller than the true one. This can beexplained by energy leaks due to crytals limited size and other holes in the detector design.

(GeV)true−ErecE−0.06 −0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 0.02

even

ts

1000

2000

3000

4000

5000

Figure 4.4: Photons reconstructed and true energy difference.

This is confirmed by Figure 4.5, that shows the compared true and reconstructed energyspectrum of photons. For single photons it is not obvious as the match is quite good but forthe total energy of photon pairs the peak at about 1.5 GeV of the reconstructed distribution


is clearly attenuated by a factor 2 and slightly shifted to the left, that is to lower energy.

E (GeV)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

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Figure 4.5: True (lines) and reconstructed (crosses) energy spectrum for : single photons(left), photon pairs (right).

4.2.2 π0 resolution

The above mentionned losses must have an impact on the mass plot of π0 (Fig. 4.6). Themass of π0 is 135 MeV but the distribution is not centered aroud this value but shifted tothe left, and is not symmetric but much larger on the left also. As the π0 appears in bothstudied ψ′ decay channels, its resolution is crucial and will later affect the resolutions of J/ψand ψ′. In fact, some packages of the BOSS software already apply corrections to the photonenergy but this is not enough. This kind of problem is usually fixed using kinematic fits byimposing the mass of π0 as a constraint and then refit the momentum (see Section 5.2.3).

4.3 Dalitz plot for J/ψ → ρ πThe Dalitz plot is a very useful tool in this kind of decay. If it’s a true three-body decay,

with the particle decaying directly into the 3 decay products, then the distribution on theDalitz plot can be uniform. However, three-body decays are often imply resonant processes,in which the particle decays into two decay products, with one of those decay productsimmediately decaying into two additional decay products. In this case, the Dalitz plot willshow a non-uniform distribution, with a peak around the mass of the resonant decay.

The Dalitz plot shown on Figure 4.7 is typical for decays that are strongly dominated byresonances. Ithas three clearly visible bands which correspond to J/ψ → ρ+π−, J/ψ → ρ−π+and J/ψ → ρ0 π0. The Figure 4.8 shows the invariant masses m(π+π0), m(π−π0) andm(π+π−) which figure the masses of ρ+, ρ− and ρ0 respectively.


)2) (GeV/cγγm(0.1 0.11 0.12 0.13 0.14 0.15 0.16

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Figure 4.8: Invariant mass for pairs of pions.

Chapter 5

Event selection and backgroundstudy

This section focuses on the compared analysis of Monte-Carlo and real datas. Once thefinal states of studied decay channels are clearly identified it is necessary to perform MCsimulation to tune the event selection parameters (that is the cuts) and later also computethe detection efficiency, by simulating both wanted channels and expected noise so as to findthe best way to reject it. Remaining background should appear while processing the real dataand be further explored.

5.1 Decay channels

5.1.1 J/ψ → ρ π

With a branching ration B(J/ψ → ρ π) = (1.69± 0.15)%, J/ψ → ρ π is the main hadronicdecay channel of J/ψ and thus the easiest to study. A big sample of this decay has alreadybeen analyzed in the BES-II experiment [12]. The ρ(770) resonance quickly decays in almost100% of the cases in two pions as follows :

ρ→ ππ =

ρ+ → π+π0 BR = 1/3ρ− → π−π0 BR = 1/3ρ0 → π+π− BR = 1/3

So the final state is J/ψ → π+π−π0 and this is what should be sought in the selection :two charged tracks and the π0 shall appear as two photon hits in the EMC as it also quiclydecays as π0 → γγ with B(π0 → γγ) = (98.798± 0.032)%.

5.1.2 ψ′ → J/ψ π+π−

Charmonium transitions are also a wide field to explore and one excited state of J/ψ whichis ψ′ (or ψ′) decays at about 56% into ψ′ → J/ψ +anything and ψ′ → J/ψ π+π− is the mainof those with a branching fraction B(ψ′ → J/ψ π+π−) = (31.8± 0.6)%.

20

CHAPTER 5. EVENT SELECTION AND BACKGROUND STUDY 21

Here only the case with J/ψ → ρ π (as described above) will be considered. It naturallyleads to a final state ψ′ → π+π−π+π−π0 , that is four charged tracks and two matchingphotons should be detected. Notice that there is an unegligible probabilty for ψ′ to decay into2(π+π−)π0 without transitional J/ψ state that should be rejected during the event selection(see Section 5.3.2).

5.1.3 ψ′ → ρ π

The last decay channel that matters for this work is ψ′ → ρ(770) π. Selection process isquite the same as for J/ψ → ρπ but its branching fraction is much smaller B(ψ′ → ρ(770)π) =(3.2± 1.2)× 10−5 which makes the background rejection more critical

Comparison of branching fractions can already be done and the the expected value is :

B(ψ′ → ρ π)B(ψ′ → J/ψ π+π−)

∼ 10−4

5.2 Selection of events

5.2.1 Charged tracks selection

Each charged track reconstructed using hits in the MDC is assumed to be a pion and must:

1. have a valid reconstructed helix according to the reconstruction algorithm ;

2. originate from the interaction region, that is have its origin contained in the cylinderr0< 1 cm and | z0 | < 5 cm centered around the primary vertex to reject unwantedtracks like possible cosmic ray events ;

3. have a transverse momentum greater than 50 MeV/c to ensure the particle didn’t loopin the detector ;

4. belong to the range of polar angle | cos θ | < 0.9 to be in the range of detection whichis constrained by the MDC geometry.

These criteria allow to select most of the reasonably good π (and K) tracks.

5.2.2 Photons selection

Photon candidates must satisfy the following requirements :

1. the deposite energy is greater than 40 MeV to be in the EMC energy detection rangeand reject low-energy noise ;

2. the angle between the photon and the nearest charged track is greater than 15◦ so asto reject the radiation photons emitted by the pions as they pass through the MDC ;

3. for ψ′ → ρ π, energy of the higher momentum photon candidate selected by 4C-fit isrequired to be less than 1.5 GeV to remove part of ISR background.

After this first raw selection still more than two photons might be selected. A 4C-fitshould at least be performed to choose the two best photons and maybe a 5C-fit to ensurethey fit the π0 mass.


5.2.3 Additional criteria and kinematic fits

The following criteria must also be respected during the selection :

1. two or four good charged tracks must be selected with a total charge of zero accordingto the wanted decay final state ;

2. at least two good photon candidates must be selected as they’re required to recover theπ0 ;

3. only events with χ2< 40 can successfully pass the 4C and 5C-fit which shall reject mostof the known background ;

4. for ψ′ → ρ π, events for which | M(π+π−)−mJ/ψ | < 0.1 GeV are rejected during the4C-fit to suppress ψ′ → J/ψ π0 contamination.

Kinematic fitting is a Lagrange multiplier method based procedure in which one uses thephysical laws governing a particle interaction or decay to improve the measurements describingthe process. The constraints are usually related to invariant masses of known particle andenergy-momentum conservation. The tracks are refitted using these constraints which reducesthe noise and thus considerably increases the quality of selection and improves the resolution.

4C- fit is applied in both cases to find out the two best photons that match the ψ′ masstogether with the selected charged tracks. 5C-fit is used differently :

• in the ψ′ → J/ψ π+π− selection, the two photons chosen from 4C-fit are assumed tocome from the π0 and are refitted with the charged tracks to find out the charged pionsthat fit the J/ψ mass (the constraint) so as to perform a Dalitz plot and check thepresence of ρ resonances ;

• in the ψ′ → ρ π selection, 5C-fit is performed independently and only uses the π0 massconstraint to reselect the two photons.

5.2.4 Selection process

Summary of the whole selection process can be seen on Table 5.1.

5.3 Sources of noise and background rejection

5.3.1 KK? channel

Decays involving KK? are the first known sources of background, especially by their decayKK? → K+K−π0 as it can be taken for a π+π−π0 final state. Two cases are interesting,each one concerning one of the studied ψ′ decays :

• for ψ′ → J/ψ π+π−, selection can be contaminated by ψ′ → K+K−π+π−π0 events(with B(ψ′ → K+K−π+π−π0) = (1.24 ± 0.10)× 10−3) ;

• for ψ′ → ρ π, selection can be contaminated by ψ′ → K+K−π0 events (with B(ψ′ →K+K−π0)< 2.96× 10−5).


Step ψ′ → J/ψ π+π− ψ′ → ρ π

1. chargedtracks selec-tion

4 charged tracks with totalcharge 0

2 charged tracks with totalcharge 0

2. photonsselection

at least 2 good photons at least 2 good photons

3. chargedtracks andphotonsmomentum

2 good positive and 2 goodnegative charged tracks, getvalid enegy for photons

1 good positive and 1 goodnegative charged tracks, getvalid enegy for photons

4. 4C-fit select the 2 photons that fitthe best the ψ′ mass with the4 pions

select the 2 photons that fitthe best the ψ′ mass with the2 pions and remove events forwhich | M(π+π−)−mJ/ψ | <0.1 GeV

5. 1.5 GeVphotons

- remove events with photonhigher momentum greaterthan 1.5 GeV

6. 5C-fit knowing the 2 photons from4C-fit, find out the 2 chargedpions coming from the J/ψresonance decay ; the 4 pionsand 2 photons must fit the ψ′

mass under the constraint ofthe J/ψ resonance

select the 2 photons that fitthe best the ψ′ mass with the2 pions under the constraintof the π0 mass

Table 5.1: Event selection process.


Selection step Events Relative efficiency Absolute efficiency0. no cut 100000 100% 100%1. charged tracks 52337 52.34% 52.34%2. photons 38796 74.13% 38.80%3. momentum 38729 99.83% 38.72%4. 4C-fit 9 0.02% 0.01%5. 5C-fit 1 11.11% 0.001%

Table 5.2: Detection efficiency of ψ′ → K+K−π+π−π0 from MC simulation.

Selection step Events Relative efficiency Absolute efficiency0. no cut 100000 100% 100%1. charged tracks 76231 76.23% 76.23%2. photons 57188 75.01% 57.19%3. momentum 57136 99.91% 57.14%4. 4C-fit 41 0.07% 0.04%5. 1.5 GeV ph. 41 100% 0.04%6. 5C-fit 22 53.66% 0.02%

Table 5.3: Detection efficiency of ψ′ → K+K−π0 from MC simulation.

100 000 events of each channel have been simulated to check how they would pass throughthe selection. Detailed process is presented on Tables 5.2 and 5.3. The rejection is really goodas only ∼ 0.001% of ψ′ → K+K−π+π−π0 and ∼ 0.02% of ψ′ → K+K−π0 can go through thewhole selection. The necessity of a 4C-fit is definitly proven as its rejects most of the events: only ∼ 0.02% and ∼ 0.07% respectively pass the 4C-fit. Figure 5.1 is even more interestingas it shows the compared good channel and noise χ2 distribution and justifies the choice ofselecting only the events for which χ2 < 40.

5.3.2 Non-resonant decays to pions

The other major source of background comes from the non-resonant decays of ψ′ to finalstates with several π. Again two cases at least have to be considered :

• for ψ′ → J/ψ π+π−, selection can be contaminated by ψ′ → π+π−π+π−π0 events (withB(ψ′ → π+π−π+π−π0) = (2.66 ± 0.29)× 10−3) ;

• for ψ′ → ρ π, selection can be contaminated by ψ′ → π+π−π0 events (with B(ψ′ →π+π−π0) = (1.68 ± 0.26)× 10−4).

100 000 ψ′ → π+π−π+π−π0 events have been simulated and tested by the selection (Tab.5.4) and brought out that such a background is mainly rejected by the performed 5C-fit (only∼ 0.34% of events pass through) so that only ∼ 0.085% of events can go through the wholeselection. Figure 5.2 shows the χ2 distribution for both good and noise channels : the χ2< 40cut still remains a good choice but the rejection is not as efficient as for the KK? background.The situation is completly different for ψ′ → π+π−π0 as ∼ 38.5% of the events pass trough


2χ0 20 40 60 80 100 120 140 160 180 200

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Figure 5.1: KK? noise χ2 distribution of 4C-fit from MC simulation. Top : ψ′ → J/ψ π+π−(red) and ψ′ → K+K−π+π−π0 (black). Bottom : ψ′ → ρπ (red) and ψ′ → K+K−π0 (black).Only events with χ2 < 40 are selected.



Table 5.4: Detection efficiency of ψ′ → π+π−π+π−π0 from MC simulation.

Selection step Events Relative efficiency Absolute efficiency0. no cut 1000 100% 100%1. charged tracks 773 77.3% 77.3%2. photons 637 82.4062% 63.7%3. momentum 637 100% 63.7%4. 4C-fit 423 66.405% 42.3%5. 1.5 GeV ph. 398 94.0898% 39.8%6. 5C-fit 385 96.7337% 38.5%

Table 5.5: Detection efficiency of ψ′ → π+π−π0 from MC simulation.

the selection which is about the same efficiency as for ψ′ → ρ π detection (see Section 6.1.1).This background channel is not rejected at all and thus will affect the final measurements.Possible rejection strategies are discussed in Section 6.3 .

2χ0 20 40 60 80 100 120 140 160 180 200

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Figure 5.2: χ2 distribution of 4C-fit from MC simulation for ψ′ → J/ψ π+π− (red) andψ′ → π+π−π+π−π0 (black). Only events with χ2 < 40 are selected.


5.3.3 Other backgrounds

There exists many other possible origins for background that should be analyzed to achievea better event selection. Here are the other backgrounds :

• ψ′ → J/ψ π0 channel (with J/ψ → π+π−) : with a branching ratio B(ψ′ → J/ψ π0) =(1.26 ± 0.13) × 10−3 it cannot be neglicted and affects the ψ′ → ρ π events selection,but it’s almost fully rejected by the condition that |M(π+π−)−mJ/ψ | < 0.1 GeV ;

• other non-resonant decays : besides ψ′ → 2(π+π−)π0 and ψ′ → π+π−π0, other channelslike ψ′ → 3(π+π−)π0 , ψ′ → 2(π+π−π0) , ψ′ → 2(π+π−) or ψ′ → 3(π+π−) should beconsidered ;

• Initial State Radiation (ISR) : photons can also be emitted by initial e+ and e− givinge+e− → γ ψ′ called radiative events, a good rejection of this kind of events is necessary.

But the above list is not exhaustive and one should expect to encounter other sources of noice.

Chapter 6

Results

6.1 Detection performance

6.1.1 Efficiency

100 000 MC events have been simulated for both channels and their detection efficiencycomputed. It is as follows :

• 23.47% of ψ′ → J/ψ π+π− are detected (see Tab. 6.1) ;

• 37.91% of ψ′ → ρ π are detected (see Tab. 6.2).

These values are reasonable enough to perform an analysis on real data.


Table 6.1: Detection efficiency of ψ′ → J/ψ π+π− from MC simulation.

Selection step Events Relative efficiency Absolute efficiency0. no cut 100000 100% 100%1. charged tracks 76362 76.36% 76.36%2. photons 63674 83.38% 63.67%3. momentum 63647 99.96% 63.65%4. 4C-fit 43212 67.89% 43.21%5. 1.5 GeV ph. 39041 90.35% 39.04%6. 5C-fit 37906 97.09% 37.91%

Table 6.2: Detection efficiency of ψ′ → ρ π from MC simulation.

28

CHAPTER 6. RESULTS 29

6.1.2 Mass resolution

The Figure 6.1 shows the compared simulated and real data for invariant mass of π0, J/ψand ψ′ from the ψ′ → J/ψ π+π− analysis. One can see that even if the mass plots fromreal data tend to be slightly wider than in the simulated case, they prove to match quitewell. Then, the quality of reconstruction and data sample are reliable enough to perform aconsistent data analysis.

6.2 Branching ratio comparison

A sample of 108 ψ′ events taken in March-April 2009 has been analyzed. The selectionprocess can been seen step by step on Tables 6.3 and 6.4 and its result is :

• 8564 ψ′ → J/ψ π+π− candidates have been selected ;

• 812 ψ′ → ρ π candidates have been selected.

This a is quite few amount of selected events considering the large sample and the com-puted detection efficiency. Tables show that the raw charged tracks selection has a very lowefficiency (1.32% and 4.64% respectively) which might indicate that wether the reconstructionefficiency of real charged tracks need to be improved or that the quality of the sample is justnot so good. Nevertheless, one can still estimate the ratio of branching fractions.


Table 6.3: Selected ψ′ → J/ψ π+π− candidates from data sample.

Selection step Events Relative efficiency Absolute efficiency0. no cut 100000000 100% 100%1. charged tracks 4637852 4.64% 4.63%2. photons 1120436 24.16% 1.12%3. momentum 1118864 99.86% 1.12%4. 4C-fit 6831 0.61% 0.0068%5. 1.5 GeV ph. 4980 72.90% 0.0050%6. 5C-fit 812 16.31% 0.00081%

Table 6.4: Selected ψ′ → ρ π candidates from data sample.

The branching ratio is defined has follows :


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B(ψ′ → X) =NobsX

Nψ′ · �ψ′→X

where Nψ′ is the total number of ψ′ events, NobsX the observed number of final state X and�ψ′→X the detection efficiency for X obtained from MC simulation. So the ratio of the wantedbranching fractions is :

B(ψ′ → ρ π)B(ψ′ → J/ψ π+π−)

=Nobsρ π

NobsJ/ψ π+π−

·�ψ′→J/ψ π+π−

�ψ′→ρ π

wich with the above values gives :

B(ψ′ → ρ π)B(ψ′ → J/ψ π+π−)

∼ 5.9%

This is clearly bigger than the expected value (∼ 10−4) by two orders. There is not muchdifficulty to select ψ′ → J/ψ π+π− events : the 5C-fit performed makes sure J/ψ resonanceappears and its Dalitz plot (Fig. 6.2) shows clearly that its decay is dominated by ρ π.

2)2) (GeV/c+π0π(2m0 1 2 3 4 5 6 7 8 9

2 )2)

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Figure 6.2: Dalitz plot for J/ψ → ρ π issued from ψ′ → J/ψ π+π− candidates.

So the main problem obviously comes from the numberNobsρ π of selected ψ′ → ρπ candidates.

The Dalitz plot is not very useful as it has too few points but some remarks can be made bylooking at the invariant masses of pion pairs on Figure 6.3 where the ρ resonance is supposedto be clearly visible :


1. the invariant mass M(π+π−) (in the bottom) shows a peak in the 3.5-3.6 GeV/c2 region,close to the ψ′ mass, which can be due to radiative events such as e+e− → γψ′ (withψ′ → π+π−) ; whatever it is, such a suspicious peak could easily be rejected by removingthe events for which |M(π+π−)−mψ′ | < 0.1 GeV ;

2. in the selection process of ψ′ → ρπ there is no guarantee of the presence of a ρ(770) res-onance, thus this sample is necessarly contaminated by the non-resonant ψ′ → π+π−π0decay at least ; this background can be removed by some appropriate kinematic fitor by cutting the events for which the condition “| M(π+π0) − mρ | < 0.2 GeV or| M(π−π0) − mρ | < 0.2 GeV or | M(π+π−) − mρ | < 0.2 GeV” is not respected ;but still a slight peak can be guessed in the ρ mass area, from which one can roughlyestimate that probably less than 10% of the selected events are real ψ′ → ρ π, whichcould make the branching fractions ratio definitly closer to its expected value ;

3. it seems that there is peak around 2.2 GeV on the M(π+π0) and M(π−π0) plots, butmore data are required for a better investigation...

6.3 Improvements and future perspectives

Once applied the above suggested cuts, the selection of ψ′ → ρ π should be considerablyimproved and the computed branching fraction ratio more accurate to its known approxi-mate value. But sure that when a backgroud is clearly identified and rejected some othersources of noise appear that should be analysed and a new strategy should be found to rejectthem. Some non-resonant decay channels might still interfere and ISR background effect isnot clearly identified. Basically, experimental high-energy physicists are mostly busy withrejecting background(s).

To be more rigourous and provide the most trustable physical values, a detailed systematicerror analysis should be performed in order to provide correction factors and systematic errorvalues. The main sources of uncertainties can be studied separately, they are the following :

• MDC tracking efficiency : comparison of MC and real data ;

• photon detection efficiency : can be studied using the π0 ;

• kinematic fit error : comparison of clean sample selection with and without the fit ;

• uncertainty on the hadronic model : depends on the model used by the MC eventgenerator ;

• uncertainty of background : due to uncertainties on known background branching ratioand unknown background.

These sources all play a role in the simulation, reconstruction or analysis process and have tobe taken into account.

Finally, BES-III experiment has been launched less than one year ago and many things stillhave to be improved. This work has been performed on one of the very first sets of ψ′ eventsthat might not be kept later as they will be replaced by much better datas which will enableto produce innovating results on charmonium physics.


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Figure 6.3: Invariant mass of pion pairs for selected ψ′ → ρ π candidates.

Chapter 7

Conclusion

Using the first data produced by the BES-III experiment, the ratio of ψ′ → ρ π andψ′ → J/ψ π+π− branching fractions has been estimated and its value is :

B(ψ′ → ρ π)B(ψ′ → J/ψ π+π−)

∼ 5.9%

We know that this value is too big because of the presence of important background in theselection of ψ′ → ρ π especially. But some additional cuts in the selection process could in asimple way evidently reduce this ratio to the order of 0.1% approximatively or maybe better.Still the main conclusion is that the “12%-rule” violation could be observed.

This thesis also proved that the detection and reconstruction of charged tracks and photonsin the present state of the detector calibration and BOSS software development work at areasonably good level to perform basic charmonium physics analysis. The coming improve-ments of detector, software and in the end of J/ψ and ψ′ data production let expect veryinteresting perspectives for the BES-III collaboration.

34

Acknowledgments

I sincerely thank Prof. Gao Yuanning for his warm welcome and his constant guidancethroughout my work as well as Prof. Aurelio Bay for having allowed this exchange to be donein the best conditions.

I also wish to thank Doc. Fu Chengdong from IHEP for his precious help with the BOSSsoftware and all the members of TUHEP for their kindness and support.

Thank you to all the people who somehow contributed to the success of this year in China.

35

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laboratoire de physique des hautes énergies ‐ epfl · figure 2.4: time-of-flight system location...

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