Monte Carlo simulations of D-mesons with extended targets in the PANDA detector

April 2016

Monte Carlo simulations of D-mesons with extended targets in the PANDA detector

Mattias Gustafsson

Teknisk- naturvetenskaplig fakultet UTH-enheten

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Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

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Monte Carlo simulations of D-mesons with extended targets in the PANDA detector

Mattias Gustafsson

Within the PANDA experiment, proton anti-proton collisions will be studied in order to gain knowledge about the strong interaction. One interesting aspect is the

production and decay of charmed hadrons. The charm quark is three orders of magnitude heavier than the light up- and down-quarks which constitue the matter we consist of. The detection of charmed particles is a challenge since they are rare and often hidden in a large background.

There will be three different targets used at the experiment; the cluster-jet, the untracked pellet and the tracked pellet. All three targets meet the experimental requirements of high luminosity. However they have different properties, concerning the effect on beam quality and the determination of the interaction point.

In this thesis, simulations and reconstruction of the charmed D-mesons using the three different targets have been made. The data quality, such as momentum

resolution and vertex resolution has been studied, as well as how the different targets effect the reconstruction efficiency of D-meson have been analysed. The results are consistent with the results from a similar study in 2006, but provide additional information since it takes the detector response into account. Furthermore, a new target distribution have been implemented in the software package. This is the first results obtained from a cylindrical target distribution. The results are very important for PANDA since they show the limitations of different target types regarding the possibilities to reduce background. Simulations with the new target distribution have been made for all three targets and the results are presented.

ISSN: 1401-5757, UPTEC F 16016 Examinator: Tomas Nyberg Ämnesgranskare: Tord Johansson Handledare: Karin Schönning

Den starka kraften är den kraft som binder ihop kvarkar till partiklar, s.k. hadroner. Hadroner delas in i två grupper; Baryoner, som består av tre kvarkar, och mesoner, som består av två kvarkar. Hadronfysik studerar således hur den starka kraften växelverkar mellan olika kvarkar. Teorin bakom den starka kraften kallas QCD (Quantum ChromoDynamics) och den beskriver hur kvarkar och gluoner växelverkar. Teorin beskriver växelverkan mellan kvarkar och gluoner väl vid höga energier, då kopplingskonstanten är låg och man kan använda sig utav störningsteorier för att beskriva kvark- gluon växelverkan. Vid lägre energier så blir kopplingskonstanten större, man kan inte längre använda sig utav störningsteorier för att beskriva vad som händer. Detta är ett mindre känt område inom fysiken, man hoppas att forskningsprojektet PANDA kommer lösa några av de frågeställningar man har om den staka kraften och samtidigt öka förståelsen om den.

I Darmstadt, Tyskland ligger forskningscentrumet för Heavy Ion Research (GSI). Man håller nu på att utöka GSI med Facility for Antiproton and Ion Research (FAIR), där PANDA detektorn kommer att vara ett av de viktigaste projekten för att utföra

hadronfysikexperiment. Projektet är en kollaboration mellan ca 20 länder och mer än 500 forskare världen över. PANDA, antiProton Annhilation at Darmstadt, kommer att studera kollisioner mellan protoner och antiprotoner. Strålmålsmaterialet som kommer att användas i de flesta experimenten kommer att vara väte, d.v.s. protoner, men även tyngre gaser kan komma att användas. De strålmål som kommer att användas i PANDA-experimenten är:

kluster jet och pelletar. Kluster jet skapas då man använder nedkyld vätgas som leds genom vakuum via ett munstycke, när gasen passerar munstycket så kyls den ner adiabatiskt och kommer att skapa atomer/molekyler som formar en jet av klusters. Pelletar skapas då man använder flytande väte som passerar ett vibrerande munstycke som skapar droppar av det flytande vätet. Dropparna fryser till fast form genom att passera vakuum och pelletar har bildats.

I detta arbete har simuleringar med antiproton – proton kollisioner utförts, fokus har legat på reaktionen . sönderfaller inom 10^-23s, vilket kan ses som direkt, till D mesoner. D mesoner har en livslängd på ca 1040

*10^-15s, vilket motsvarar att de färdas ca 0.3 mm innan de sönderfaller. Alltså kan man skilja på när sönderfaller och när D mesonerna sönderfaller. Eftersom överlappet mellan antiprotonstrålen och strålmålet utgör en volym, en så kallad interaktions volym där kollisionen äger rum, så är det intressant att studera om D mesonerna sönderfaller innanför volymen eller utanför. Då detta har stor inverkan på hur väl man kan rekonstruera

sönderfallskedjan.

interaktions volym. Detta gjordes med beräkningar för rörelsemängd för de olika partiklarna och med beräkningar av sönderfallslängd. I detta arbete så har samma simulationer

genomförts, men här har även detektorns upplösning tagits med. Det har även gjorts jämförelser, med sluttillståndspartiklarna, hur datakvalitén påverkas av valt strålmål.

Det har även gjorts en första studie med en cylindrisk interaktions volym, då man tidigare använde sig utav en gaussisk distribution av antiprotonstrålen. Här har en cirkulär

distribution av antiproton strålen använts för att se hur detta påverkar hur många D mesoner som kommer att sönderfalla utanför den givna interaktionsvolymen.

Resultaten från 2006 överensstämmer väl med de resultat som gjorts i denna studie, när man även tar med detektorns upplösning i simuleringarna.

Det är ingen signifikant skillnad i datakvalitén mellan de olika strålmålen. Varken mellan upplösningen i rörelsemängd eller i rekonstruktions effektivitet.

Resultaten från simuleringar med en cylindrisk interaktions volym visar att man kan välja en volym där 20 % av D mesonerna sönderfaller utanför volymen. Medans för en klusterjet så ligger värdet endast på 8 %.

First I would like to pay most gratitudes to Tord Johansson and Karin Sch¨onning, for letting me do this project at the Hadron division at Uppsala University. Many thanks to my supervisor Karin, for always have time to answer questions when I ran into trouble spots. With all the help with the report, regarding structure and for through reading. Also for letting me go to the FAIR facility in Darmstadt, I have learned so much during the work of this thesis. I would also like to thank Hans Carl´en for your discussions regarding targets and for showing me the pellet at TSL.

Finally, I want to express my most profound gratitude to Louise for always supporting me. I will always be grateful for having you in my life.

i

Acknowledgements i

Contents ii

List of Figures v

List of Tables vii

Abbreviations ix

1 Aim of this thesis 1

2 Introduction 3

2.1 Subatomic physics and the Standard Model . . . 3

2.1.1 Quarks and Leptons . . . 4

2.1.2 Fundamental forces . . . 5

2.2 Spin, Parity and Charge conjugation . . . 6

2.3 Hadrons . . . 8

2.4 Charmonium . . . 10

2.5 D-meson/ Open Charm. . . 11

2.6 Aim of this thesis . . . 11

2.7 Curiosity driven research . . . 11

3 The PANDA Experiment 13 3.1 Introduction . . . 13

3.2 The PANDA Physics Program . . . 14

3.2.1 Charmonium spectroscopy . . . 14

3.2.2 Electromagnetic structure of baryons . . . 15

3.2.3 Baryon spectroscopy and hyperon physics . . . 16

3.2.4 Electroweak physics. . . 16

3.2.5 Hypernuclear studies . . . 16

3.3 The Target Spectrometer . . . 17

3.3.1 MVD. . . 17

3.3.2 STT . . . 18

3.3.3 GEM . . . 18 ii

3.3.4 Particle identification detectors . . . 19

3.3.5 The Electromagnetic Calorimeter . . . 20

3.4 Muon detector. . . 21

3.5 Forward Spectrometer . . . 21

3.5.1 Forward Trackers . . . 21

3.5.2 Forward Particle ID. . . 21

3.5.3 Forward Electromagnetic Calorimeter . . . 22

3.5.4 Forward muon detector . . . 22

3.6 Targets. . . 22

3.6.1 The Pellet Target . . . 24

3.6.1.1 The Pellet TRacking system . . . 24

3.6.2 The Cluster-jet target . . . 25

4 Motivation for this work 27 4.1 Motivation . . . 27

4.2 Previous study . . . 28

4.2.1 Particle decay length . . . 29

4.3 This work . . . 31

5 Software tools 32 5.1 PandaRoot . . . 32

5.1.1 Simulation . . . 33

5.1.2 Digitization . . . 33

5.1.3 Reconstruction . . . 33

5.1.4 Particle Identification. . . 34

6 Analysis 35 6.1 Physics Reaction . . . 35

6.2 Input to simulations: Extended targets in Pandaroot . . . 36

6.3 Event selection . . . 37

6.4 Validation of the method . . . 38

6.5 Realistic target dimensions . . . 40

7 Results 42 7.1 Data quality . . . 42

7.2 For a given target, how many D-mesons will decay outside it ? . . . 43

8 Summary and Conclusions 47 9 Outlook 50 A Relativistic kinematics in particle collisions 51 A.1 Reference Frames . . . 51

A.2 Lorentz transformation . . . 52

A.3 Two-body decay. . . 53

B Plots from simulations 55

Bibliography 61

2.1 Meson nonets . . . 10 3.1 Side view of the PANDA detector . . . 14 3.2 Pictures of the different targets. . . 23 3.3 Figure (A) shows the model for the lasers and cameras that will be

used when tracking pellets. Figure (B) shows the different stations of cameras and lasers when tracking pellets [1][2]. . . 26 4.1 Decay chain investigated . . . 28 4.2 Distributions of primary and secondary vertex for different targets.

(A) and (B) corresponds to a cluster-jet target,(C) and (D) corre- sponds to a untracked pellet target and (E) and (F) corresponds to a pellet target with tracking. See Table 4.1 for the different target and antiproton widths[3][4]. . . 30 6.1 Momentum and polar angle distribution for all particles using an

ideal target. . . 36 6.2 Distributions of secondary vertex from Monte-Carlo truth and re-

constructed particles. (A) and (B) corresponds to a cluster-jet tar- get,(C) and (D) corresponds to a untracked pellet target and (E) and (F) corresponds to a pellet target with tracking. See table 4.1 for the different target and antiproton widths. . . 39 7.1 Plots of momentum resolution and vertex resolution for untracked

pellet target. Figures (A)-(D) shows the momentum resolution for the final state particles K^±,π^±. Figures (E)-(H) shows the vertex resolution for D-mesons after use of vertex fit. . . 45 B.1 Plots of momentum resolution and vertex resolution for cluster-

jet target. Figures (A)-(D) shows the momentum resolution for the final state particles K^±,π^±. Figures (E)-(H) shows the vertex resolution for D-mesons after use of vertex fit. . . 56 B.2 Plots of momentum resolution and vertex resolution for tracked

pellet target. Figures (A)-(D) shows the momentum resolution for the final state particles K^±,π^±. Figures (E)-(H) shows the vertex resolution for D-mesons after use of vertex fit. . . 57 B.3 Momentum - and polar angle distributions for all particles using a

cluster jet target . . . 58 v

B.4 Momentum - and polar angle distributions for all particles using a untracked pellet target . . . 59 B.5 Momentum - and polar angle distributions for all particles using a

tracked pellet target . . . 60

2.1 Overview of all quarks in the Standard Model. Given are the symbol of each quark, the electric charge and mass. To all quarks there exists an antiquark with the same mass but with opposite charges [5]. 4 2.2 Overview of all leptons in the Standard Model. Given are the sym-

bol of each lepton, electric charge and mass. For each lepton there exist an anti-lepton with the same mass but with opposite charges.

[5]. . . 5 2.3 All the fundamental forces in nature, with its respective force car-

rier. Given are the symbol of the boson, electric charge and mass [5]. . . 6 2.4 Properties of some baryons [5] . . . 9 2.5 Different types of mesons and their quantum numbers J^{P C} [5]. . . . 9 2.6 Properties of some mesons [5]. . . 10 2.7 Table of the lightest D-mesons and their properties [5]. . . 12 3.1 Parameters of the two different operation modes for HESR at FAIR. 14 3.2 Properties on internal targets an PANDA[6]. . . 23 3.3 Parameters of the two different pellet operation modes [6]. . . 25 3.4 Parameters of different cluster-jet targets [7]. . . 26 4.1 Dimensions of analysed targets. σx and σy are the width of the

antiproton beam in the horizontal and vertical direction, using a Gaussian distribution. . . 29 4.2 Results from cuts at different distances. η is the result of how many

of the D-mesons, in percent, that will decay outside each cut.. . . . 31 6.1 Results from Monte-Carlo truth vertex with cuts at different dis-

tances. η is the result of how many of the D-mesons, in percent, that will decay outside each cut. The grey part of the table shows the results from [4], as shown in 4.2. . . 40 6.2 Results of reconstructed vertex with cuts at different distances. η is

the result of how many of the D-mesons, in percent, that will decay outside each cut. . . 40 6.3 Parameters for the different targets. R_beam is the radius of the

antiproton beam and target width is the extension of target in an- tiproton beam direction. . . 41

vii

7.1 Result of momentum resolution, δp/p, and reconstruction efficiency, η, of the final state particles with different targets.. . . 44 7.2 Result of vertex resolution, after the use of vertex fit, for the D-

mesons at different targets.. . . 44 7.3 Results from cuts at different distances. η is the result of how many

of the D-mesons, in percent, that will decay outside each cut.. . . . 46

ANKE Apparatus for studies of Nucleon and KaonEjectiles Brokhaven Nuclear and high-energy physics facility, New York USA

CM Center-of-mass frame

COSY Cooler Synchrotron

DIRC Detection of Internally Reflected Cherenkov light EMC ElectroMagnetic Calorimeter

FAIR Facility for Antiproton and Ion Research

FAIRRoot Data analysis framework at FAIR, based on CERN’s ROOT FERMILAB Fermi National Accelerator Laboratory facility, Illinois USA

FS Forward Spectrometer

FZJ Forschungzentrum J¨ulich

GEANT3 A Monte Carlo event generator and propagator GEANT4 A Monte Carlo event generator and propagator GEM Gas Electron Multiplier

HESR High-Energy Storage Ring

IP Interaction point

LAB Laboratory frame

MC Monte Carlo

MPEI Moscow Power Engineering Institute MVD Micro Vertex Detector

PANDA antiProton ANnhiliation at DArmstadt

PandaRoot Data analysis framework for the PANDA experiment PID Particle Identification

PHL Pellet High Luminosity ix

PTR Pellet TRacking

QCD Quantum ChromoDynamics

QED Quantum ElctroDynamics

ROOT Data analysis framework from CERN

SLAC Stanford Linear Accelerator Center facility, California USA

SM Standard Model

STT Straw Tube Tracker

TOF Time Of Flight

TPC Triple point chamber

TS Target Spectrometer

WASA Wide Angle Shower Apparatus

Aim of this thesis

The aim of this thesis is to reconstruct D mesons from simulations of proton anti-proton collisions, using different extended targets. Within the PANDA ex- periment, there are three different targets that will be used: Cluster jet and two different pellet targets, untracked pellet and tracked pellet. In this project we want to see how the data quality, i.e reconstruction efficiency, momentum reso- lution and vertex resolution, is affected between the different targets. The aim is also to find out how many D mesons, for a given target, will decay outside the interaction volume, i.e the overlap between anti-proton beam and target. This information can help reduce background, which is a large problem for charmed meson particles.

The thesis is structured as follows:

In Chapter 2, a brief introduction to particle physics is given, describing all known elementary particles today and their interaction. Followed by a description of different hadrons, mesons and baryons, where focus lies on mesons that contains a charm quark.

The PANDA experiment is described in Chapter 3. The chapter gives an in- troduction to the physics program that will be addressed at the experiment. The different detector parts of the PANDA detector are also described, along with the different targets that have been used in the work.

Chapter 4 gives a motivation for this work, along with an explanation of an similar study by ¨O.Nordhage.

1

In Chapter 5 the software tools used in this work is outlined. Describing the different steps of the simulation chain in PandaRoot.

The analysis in this work is outlined in Chapter 6. Information of event se- lection and the results from validating the method used by ¨O.Nordhage. Also an explanation of a new homogeneous cylindrical interaction volume is given.

The results from simulations are outlined in Chapter 7, how data quality is affected by different target dimensions and how many D mesons that will decay outside a given target.

Chapter 8 concludes this thesis and summarizes the results.

Introduction

2.1 Subatomic physics and the Standard Model

All matter in the universe is built up by elementary particles. A tree is built up by cells, the smallest living organism. Cells consist of smaller components: molecules, which in turn are made of atoms. The atom has a nucleus of protons and neutrons, surrounded by electrons. For a long time the proton and neutron were believed to be elementary particles just like the electron, but this was proven wrong with the discovery of quarks.

There are four fundamental forces in nature: gravity, the electromagnetic force, the weak force and the strong force. Gravitation affects massive objects, like planets and galaxies, and is present in our daily life. However, on a particle level it has no significant effect. The electromagnetic force act on electrically charged particles and is the force that keeps the electrons and nucleons together in the atom. The weak interaction is responsible for radioactive decays e.g. the β-decay.

The strong force confines quarks to hadrons, like the protons and neutrons, and protons and neutrons into nuclei.

During the 20th century, many particles were found by experiments. The Stan- dard Model(SM) is a unified field theory which describes the known elementary particles and their interactions. Throughout the years the theory has been very successfully predicting new particles that were later confirmed by experiment. The recent discovery of the Higgs boson was predicted by the Standard Model [8][9]

3

and demonstrates its success. The discovery of the Higgs boson is an important step in explaining the Higgs field, which give mass to elementary particles, such as quark and leptons [10][11].

2.1.1 Quarks and Leptons

The standard model consist of twelve particles with half integer (¹₂) spin, called fermions, and five particles with integer spin, called bosons. The fermions are six quarks and six leptons, where both quarks and leptons are divided into three generations. Just after the Big Bang, all generations were abundant, but the world as we know it today consist of quarks and leptons from the first generation. This is because particles from the second and third generations are short-lived and will eventually decay into the first generation particles. However, the former can be produced in high energy cosmic interactions or in laboratories.

Generation Name Symbol Charge Mass e [MeV/c²]

up u +2/3 1.5 − 3.0

1 down d −1/3 4.5 − 5.2

strange s −1/3 95 ± 5

2 charm c +2/3 1275 ± 25

bottom b −1/3 4180 ± 30

3 top t +2/3 17320 ± 900

Table 2.1: Overview of all quarks in the Standard Model. Given are the symbol of each quark, the electric charge and mass. To all quarks there exists

an antiquark with the same mass but with opposite charges [5].

Leptons are interacting via the weak interaction, gravitation, and the electro- magnetic interaction (except the electrically neutral neutrinos). However, unlike quarks, they do not interact via the strong interaction. The first generation of lep- tons, as shown in Table 2.2, comprises the electronic leptons (e⁻,ν_e), the second generation the muonic leptons (µ⁻,ν_µ) and the third generation the tauonic ones (τ⁻,ν_τ). The e, µ and τ leptons carry electric charge, whereas neutrinos do not.

All leptons carry lepton number, mass and spin. For every lepton, there exist an antilepton with the same mass and spin but with the opposite lepton number.

Generation Name Symbol Charge Mass e [MeV/c²]

Electron e⁻¹ −1 0.511

1 Electron neutrino ν_e 0

Muon µ⁻¹ −1 106

2 Muon neutrino ν_µ 0

Tau τ⁻¹ −1 1777

3 Tau neutrino ν_τ 0

Table 2.2: Overview of all leptons in the Standard Model. Given are the symbol of each lepton, electric charge and mass. For each lepton there exist an

anti-lepton with the same mass but with opposite charges. [5].

There are six types, or flavours of quarks: up(u), down(d), strange(s), charm(c), bottom(b) and top(t) , see Table 2.1. Quarks are interacting via all four funda- mental forces, Table 2.3. Quarks carry electric charge, mass, spin and a charge called colour. There are three different colours: red, green and blue. For every quark, there exist an antiquark with same mass and spin but with opposite electric charge and colour.

2.1.2 Fundamental forces

The electromagnetic interaction has infinite range and effects all particles that carry charge. It is mediated by the electrically neutral and massless photon. The theory of the electromagnetic interaction is described by the Quantum Electrody- namics (QED).

The weak interaction has a range of about 10⁻¹⁸m. All quarks and leptons are interacting via the weak interaction. The mediators are the massive Z⁰, W⁺ and W⁻ bosons. The theory of weak interaction has successfully been unified with QED into the so-called electroweak theory. The weak interaction can also change the flavour of quarks.

All quarks interact via the strong interaction, which is mediated by massless particles called gluons. Gluons couple to the colour charge of particles and it carries one colour and anti-colour itself. This means that the gluon self-couples.

The range of the strong interaction is about 10⁻¹⁵ m. The theory of the strong interaction is described by the Quantum ChromoDynamics (QCD) [12] [13].

Quarks cannot be observed as single particles, but only bound into colourless states, hadrons see section 2.3. This phenomenon is called ”colour confinement”

and is a consequence of the strong interaction. Unlike the other forces, the strong interaction increase in strength as the distance increase. When trying to separate a quark-antiquark pair by increasing the distance between them, the potential energy increases with distance and eventually becomes so large that it becomes more energetically favourable to create a new quark-antiquark pair than to separate them further [14].

Force Name Symbol Charge Mass Couples to

e [GeV/c²]

Electromagnetic Photon γ 0 0 Electric charge

Z boson Z⁰ 0 91.188 ± 0.002 W eak

W boson W^± ±1 80.385 ± 0.015 Hyper charge

Strong Gluon g 0 0 Colour charge

Gravitation Graviton G Energy

Table 2.3: All the fundamental forces in nature, with its respective force carrier. Given are the symbol of the boson, electric charge and mass [5].

2.2 Spin, Parity and Charge conjugation

Spin

Every particle or composite system of particles carries spin, which is often viewed as an intrinsic angular momentum. The spin projection of a spin 1/2 fermion can take two values, either up or down which is generally denoted with (+) or (↑) for up, and (-) or (↓) for down.

In particle physics the intrinsic spin is denoted with S. A composite particle, i.e. a hadron, can also have orbital angular momentum denoted L and the total

spin is denoted with J . The total spin J is defined as

J = ~~ L + ~S (2.1)

and can take the values

|L − S| ≤ J ≤ |L + S| (2.2)

Parity

Changing a particle’s parity can be seen as taking the mirror image of the particle, i.e. changing the sign of the spatial coordinates. In particle physics, parity is denoted by P , and is built up by the internal parity of the constituents of the system. For example the parity of a system of two particles a and b is denoted,

P = P_aP_b(−1)^L. (2.3)

where the P_a and P_b is the internal parity of each particle and L is the relative orbital angular momentum between particle a and b.

Charge conjugation

The operation of charge conjugation changes a particle into its antiparticle. Hence it changes the sign of quantum numbers like electrical charge, lepton number and flavour charge, whereas quantum numbers like spin, momentum and mass remain the same. It can be seen as turning a particle in the matter world into its image in the antimatter world, where it is believed that the same physical laws are applicable. The eigenstate of the charge conjugation operator is called C-parity, and they can only be constructed from particle-antiparticle pairs. The eigenvalues for a composite system of particles, particle a and particle b, is denoted,

C = C_aC_b (2.4)

where C_a and C_b is the internal charge conjugation for each particle. However, the C-parity is different for bosons and fermions. For bosons the C- parity is defined

as

C = (−1)^L (2.5)

where L is the orbital angular momentum of the system. For fermions the C- parity is defined as

C = (−1)^L+S (2.6)

where L is the angular momentum of the system and S is the spin angular mo- mentum of the system.

Isospin

Isospin is a quantum number, related to the strong force, that is used to describe groups of particles or quarks with nearly the same mass, e.g. proton and neutron or the up and down quarks. Isospin is not a spin, although it contains the name, but it follows the same rules as the intrinsic angular momentum (or spin) and it is dimensionless. It is denoted with the letter I and the projection of isospin, I₃, is the quantum number which distinguish different particles, e.g. the three pions (π⁻, π⁰, π⁺) form a triplet isospin state. All three pions have isospin, I = 1, but the projection is different, I₃ = −1, I₃ = 0, I₃ = +1 respectively.

Isospin is related to other quantum numbers by

Q = I₃+S + B

2 (2.7)

where Q is charge, S is strangeness, B is baryon number and I₃ is the projection of isospin.

2.3 Hadrons

Hadrons are bound colourless states of quarks and can be divided into two groups;

baryons and mesons. Baryons consist of three quarks (qqq), have half-integer spin and are thus fermions. The most well-known baryons are the proton (uud) and neutron (udd). Baryons carry a quantum number called baryon number, B. The

baryon number of a quark is B = +1/3 and B = −1/3 of an antiquark . Hence B = +1 for three quarks and B = −1 for three anti-quarks.

Name Symbol Quark Mass J^{P C} Lifetime

structure [Mev/c²] [s]

Proton p uud 938.27 1/2⁺ stable

Neutron n udd 939.57 1/2⁺ 880.3 ± 1.1

Lambda Λ uds 1115.68 1/2⁺ 2.6 · 10⁻¹⁰ Sigma Σ uus 1189.37 1/2⁺ 8.0 · 10⁻¹¹

Delta ∆ udd 1232 3/2⁺ 5.6 · 10⁻²⁴

Xi Ξ uss 1314.86 1/2⁺ 1.6 · 10⁻¹⁰

Table 2.4: Properties of some baryons [5]

Mesons consist of a quark-antiquark pair (q¯q) and they have integer spin, and are thus bosons. Unlike for baryons, there is no such thing as a meson number.

Since all mesons are unstable they will eventually decay and end up as electrons, neutrinos or photons. Both baryons and mesons are classified by their J^{P C} quan- tum numbers, where J is the total angular momentum, P is parity and C is charge conjugation.

Type Quantum number J^{P C}

Scalar 0⁺⁺

Pseudoscalar 0⁻⁺

Vector 1⁻⁻

Axial vector 1^+±

Table 2.5: Different types of mesons and their quantum numbers J^{P C} [5].

Hadrons are ordered into multiplets, i.e. representation of particles grouped by their properties. In 1961, before quarks were known and when the multitude of newly discovered particles were believed to be elementary, Murray Gell-Mann introduced the eightfold way. This model arrange mesons according to their spin, strangeness and isospin. Strangeness is associated to the net content of strange quarks in hadrons. The representations are two nonets: one with the pseudoscalar mesons and one with the vector mesons, see Figure 2.1.

(a) Nonet of pseudoscalar mesons with spin

0. (b) Nonet of vector mesons with spin 1.

Figure 2.1: Meson nonets

Name Symbol Quark Mass J^{P C} Lifetime structure [Mev/c²] [s]

π^{0 u¯u−d ¯}√2 ^d

2 135.0 0⁻⁺ 8.4 · 10⁻¹⁷ P ion

π⁺ ud 139.6 0⁻ 2.6 · 10⁻⁸

K⁺ u¯s 493.7 0⁻⁺ 1.2 · 10⁻⁸

Kaon K⁰ d¯s 497.7 0⁻⁺

ρ⁺ u ¯d 775.1 1⁻ 4.4 · 10⁻²⁴ Rho ρ^{0 u¯u−d ¯√ d}

2 775.3 1⁻⁺ 4.5 · 10⁻²⁴ Omega ω ^{u¯u+d ¯√}₂^d 782.7 1⁻⁻ 7.8 · 10⁻²³

Phi Φ s¯s 1019.5 1⁻⁻

Eta η ^{u¯u+d ¯√d−2s¯s}

6 547.9 0⁻⁺

Eta prime η^{0 u¯u+d ¯√d+s¯}₃ ^s 957.8 0⁻⁺

Table 2.6: Properties of some mesons [5].

2.4 Charmonium

Charmonium is a meson containing a charm-anticharm pair (c¯c), hence the total charm is zero. This is sometimes referred to as hidden charm. The first discovery of a charmonium state were made in 1974 by two groups at Brokhaven and SLAC [15][16]. They discovered, almost simultaneously, the narrow resonance J/Ψ, which also implied the discovery of the charm quark. The high mass of the charm quark (m_c∼ 1.3 GeV/c²), makes it possible to describe the dynamical properties in terms of a non-relativistic potential model, in analogy with positronium, i.e. a bound state of a positron and an electron. The non-relativistic model is then adapted so

that it fits the asymptotic properties of the strong interaction. The known lowest lying states today are the η_C, J/Ψ, χ_C, h_C, Ψ⁰ and Ψ(3770).

Most of the experiments where charmonium spectroscopy is studied today, are e⁺e⁻ colliders, where a virtual photon is produced in the e⁺e⁻ annihilation. The virtual photon then decays into other particles. In these machines, states with quantum number J^{P C} = 1⁻⁻ dominate completely, since this is the quantum number of the photon. States with other J^{P C} have to be produced in decays from 1⁻⁻states. In a p¯p experiment, like PANDA, any non-exotic J^{P C} is allowed.

PANDA therefore has prospects of revealing new particle states [17].

2.5 D-meson/ Open Charm

The D-meson contains a single charm quark (c) and a light antiquark (¯u or ¯d), it is the lightest particle which contains a charm quark. The charm number is different from zero, in contrast to charmonium. That is why it is referred to as open charm.

Open charm spectroscopy will study the interaction of heavy-light quark system, in analogy with the hydrogen atom in QED, to gain more information of the strong force.

The D-meson decay via the flavour changing weak interaction. The most estab- lished D-mesons are presented in Table2.7. The charm quark decays into a strange quark and a W boson which subsequently decays into hadrons or leptons. From Table 2.7 many decays of the D-mesons include kaons and pions, which means that studies of D-mesons suffer from a large background. Since the D-meson is the lightest particle that contains a charm quark, it can only decay weakly. It is therefore favourable to study its properties to understand the weak interaction.

2.6 Aim of this thesis

2.7 Curiosity driven research

To understand how the world around us work and why, has been an essential part of the human culture. Whether it is science, politics, economics or just to

Name Quark Mass Lifetime Decay structure [Mev/c²] cτ [µm] channels

D⁰ c¯u 1864.84±0.17 122.9 K⁻anything 54.7 ± 2.8 % K⁻π⁺ 3.8 ± 0.05 % D¯⁰ ¯cu 1864.84±0.17 122.9

D⁺ c ¯d 1869.61±0.09 311.8 K⁻anything 25.7 ± 1.4 % K⁻π⁺π⁺ 9.13 ± 0.19 % D⁻ ¯cd 1869.61±0.09 311.8

Table 2.7: Table of the lightest D-mesons and their properties [5].

understand more basic things like fixing a bicycle. It is in our nature to strive for gaining more knowledge and insight about our surrounding. From early age, we gather information about how things work. Experiences and knowledge are past through generations in order to develop new theories and inventions. An example is the development of the internet and the WorldWideWeb. The Internet have opened up a new world to explore. Nowadays everybody has their own library in their computer. Hence the availability for all kind of information is easy to access.

With internet there is also the possibility to discuss problems with people from all over the world in order to gain new insights or just to gain more knowledge.

The PANDA experiment needs state-of-the art technology to be able to per- form the planned research programme. Researchers from all over the world work together and contribute with their expertise in order to take the technology sev- eral steps further. Who can tell what inventions this will lead to, and what their applications will be?

The PANDA Experiment

3.1 Introduction

The future Facility for Antiproton and Ion Reasearch (FAIR) [18], will be fea- tured in the present GSI facility at Darmstadt. The PANDA¹ [19] detector will be an integrated part of the High Energy Storage Ring (HESR) at FAIR. The ex- periment will use cooled antiproton beams, accelerated and stored in the HESR, with a momentum range between 1.5 GeV/c and 15 GeV/c. The beam interacts with internal targets of protons, deuterions or heavier nuclei. There will be two operational modes for PANDA, see table 3.1, the high resolution mode and the high luminosity mode. The high resolution mode will be used for high precision physics studies with a very well-defined momentum of the antiproton beam, while the high luminosity mode will be used for experiments that require high statistics.

The PANDA detector will be an almost 4π solid angle detector, which will be able to detect charged and neutral particles with high precision. It will be divided into two parts, the Target Spectrometer(TS) and the Forward Spectrometer(FS) which will be explained in 3.3 and 3.5, respectively.

1AntiProton Annihilation at Darmstadt

13

Mode High resolution High luminosity Peak Luminosity 2 × 10³¹ cm⁻²s⁻¹ 2 × 10³² cm⁻²s⁻¹ Number of stored antiprotons 1 × 10¹⁰ 1 × 10¹¹

Target beam density 4 × 10¹⁵ atoms/cm² 4 × 10¹⁵ atoms/cm² RMS momentum spread σ_p/p ≤ 4 × 10⁻⁵, σ_p/p ∼ 4 × 10⁻⁵,

1.5 to 8.9 GeV/c 1.5 to 15 GeV/c Table 3.1: Parameters of the two different operation modes for HESR at FAIR.

Figure 3.1: Side view of the PANDA detector.

3.2 The PANDA Physics Program

3.2.1 Charmonium spectroscopy

Charmonium spectroscopy will be one of the main activities at PANDA. The spectrum of charmonium can be derived in a similar way as that of positronium.

Due to the relatively massive charm quarks, their motion is almost non-relativistic and one can use potential models to describe the energy levels between the charm anticharm quark. With PANDA one will be able to collect several thousands of c¯c states per day. Together with higher luminosity, better beam momentum resolution and a better detector than previous experiments, one hopes to not only find new states, predicted by theoretical models, but also to gain more information about already existing states [14] [20].

Search for Glueballs, hybrids and multiquarks

As mentioned before, quarks form colourless objects, hadrons. Until recently no unambiguous experimental evidence have been found of more complex systems.

However, QCD allows other states than the ordinary meson (q ¯q) and baryon (qqq).

Hence there is a possibility that other colourless combinations of quarks and gluons might exist. Such as hybrids (q ¯qg), glueballs (gg, ggg) and multiquarks (q ¯qq ¯q, qqqqqq, qqqq ¯q, . . .).

Hybrids are mesonic states where excited gluons contribute to the quantum numbers, whereas glueballs are pure gluonic states. Both hybrids and glueballs can be created in so-called gluon-rich environments. Gluons can be created when a quark and an antiquark annihilate, hence antiproton-proton collisions provide a gluon-rich environments. Investigations of the possibility to find states containing excited gluons, such as glubealls and hybrids, are performed at running facilities today and will be preformed, with higher precision and larger statistics, at PANDA [21].

The resent finding of the Z_c(3900)^±, support the theory of multiquarks. The particle Z_c(3900)^±is a charged particle discovered by the the BESIII Collaboration at the Beijing Electron Positron Collider, China, [22] and the Belle Collaboration at the High Energy Accelerator Research Organization in Tsukuba, Japan [23].

The discovery of the Z_c(3900)^± has led to a huge activity in the field and has been enthusiastically received by the scientific community. The indication that the Z_c(3900)^± is a multiquark state, is because it decays into J/Ψ π^±. The large mass of the Z_c and that it decays into J/Ψ, implies that it must consist of a c¯c-pair. From the net charge of the final state particles, the Z_c(3900)^± must be charged. However the c¯c-pair is electrically neutral and therefore there must be other particles, together with the charm-anticahrm pair, that gives the appropriate charge to the Z_c.

3.2.2 Electromagnetic structure of baryons

Within the PANDA experiment, it is also possible to investigate the electromag- netic structure of the proton. This using three different methods: studying Form

Factors in the Time-like region (T LF F⁰s) [24], structure functions probed by the Drell-Yan process [25] and measurement of Generalized Parton Distributions (GPDs) [26] [27].

3.2.3 Baryon spectroscopy and hyperon physics

The high energy of the anti-proton beam will make the cross section for baryon – antibaryon production high. This means that it is favourable to study baryon spectroscopy. In particular, the spectrum of baryons containing strange and single- charmed quarks, so called hyperons, is poorly known experimentally and PANDA will therefore fill a gap. In PANDA, reactions involving different hyperons will also be studied in order to achieve a better understanding of the production mech- anism of quark-antiquark pair and their arrangement into hadrons[14]. By inves- tigating all hyperons and single-charmed hyperons, one hopes to find information of strangeness production and their spin variables which often can be related to the individual quarks.

3.2.4 Electroweak physics

As discussed in previous sections PANDA will be able to produce a large amount of D-mesons. This will be used to search for rare decays and study processes beyond the standard model (see [28] and references therein). Such processes may be lepton flavour number violating or CP-violating. Since these processes are very rare, one can expect to see results after a few years of runtime and analysing data.

The ability to reduce background will be crucial for this.

3.2.5 Hypernuclear studies

The PANDA experiment will also cover hypernuclei physics. A hypernuclei is a nucleus where one or more nucleon is replaced by a hyperon. Studies of hypernuclei and hyperon-hyperon interaction will give better understanding of the nuclear structure and the features of the hyperon-nucleon interaction [21] [29].

3.3 The Target Spectrometer

The Target Spectrometer has a cylindrical shape and will detect charged and neutral particles. It surrounds the interaction point (IP) and will detect particles with polar angels larger than 5^◦ in the vertical plane and 10^◦ in the horizontal plane.

The detectors will be surrounded by a superconducting magnet with a solenoid magnetic field of 1-2 T, which will help determining the momentum of charged particles by bending their trajectories [21]. The Target Spectrometer consist of the MVD, the GEM, the STT, the barrel and endcap EMC, the barrel and endcap DIRC and the TOF.

3.3.1 MVD

The Micro Vertex Detector (MVD) will surround the IP and it will be used for tracking charged particles, in particular charged D mesons, hyperons and their decay products. The aim of the MVD is to give information of charged particles close to the interaction point. The MVD will provide precise information of the origin, a three dimensional hit point, of a track and the signal will give a time reference to be used for other detectors. The MVD will provide vertex resolutions

< 100 µm.

The MVD comprises four barrel layers and six forward parts. The two innermost barrel layers will consist of silicon hybrid pixel sensors and the other two layers of double-sided silicon micro-strip sensors. Both sensors will use n-doped silicon as a bulk material, i.e. have a higher concentration of electrons. When charged particles pass through the sensor, they will ionize the silicon and create electron- hole pairs. Due to the electric field, the electrons and holes will be separated and travel to either side of the sensor. The current of charge carriers are then measured with the read-out electronics. The innermost and outermost layer will have a radii of 2.5 cm and 13.5 cm, respectively. With this detector layout, one will achieve detector coverage with a minimum of four track points within the polar angle interval 9^◦ and 145^◦. The forward part will detect particles in the forward direction and consists of eight detector discs perpendicular to the beam[30].

3.3.2 STT

The Straw Tube Tracker (STT) consists of thin straws that are made of aluminised mylar tubes filled with an Argon based gas with CO₂ as a quencher. Through the straws a coaxial cathode and anode wires runs. Between the cylindrical wall and the wire an electric field is then applied. When a charged particle enter the STT, it will ionize the gas and produce ions and free electrons. The electrons drift towards the wire and the ions towards the wall of the tube. When the electron approaches the wire, it will knock out other electrons from the atoms/molecules in the gas.

This will create more free electrons and ions are produced in an avalanche-like manner. This will amplify the primary charge and when all free electrons are collected on the anode, it will be possible to read out an electric signal. The STT will enable hit point measurements with resolutions better than 150 µm in the x-y plane and 3mm in the z direction. The tubes will be arranged in planar layers which will have a hexagonal shape surrounding the MVD. In total there will be 27 layers and 4636 straws that will be placed at a radial distance between 15 cm and 42 cm from the beampipe[31]. The straws have an overall length of 150 cm and a diameter of 10 mm. The wire will be made of 20 µm thick gold plated tungsten, and the gas will be a mixture of Argon and CO₂.

3.3.3 GEM

The STT will not cover particles which are emitted at angles below 22^◦. These particles will instead be detected by 4 gaseous micro-pattern detectors based on the Gas Electron Multiplier (GEM) technique. The micro-pattern detectors are circular plates made of GEM-foils, which is a metal-coated polymer perforated with holes. The GEM detector will detect hit points with resolutions < 100 µm.

The idea with the GEM-foils is to capture the electrons released when charged particles interact with the gas in the detector. If a high voltage is applied over the foils, the electrical field in the holes can become strong enough for the primary electrons to be guided through the holes. This will cause an avalanche where secondary electrons are created. The electrons will create a signal or a current for the read-out electronics. The GEM detectors will be placed at 81, 117, 153 and

189 cm from the target and will be placed in the forward region along the beam direction [21].

3.3.4 Particle identification detectors

In order to be able to identify different charged particles, which are emitted within a large range of momenta and angles, the PANDA detector will use two kinds of Cherenkov detectors (Barrel DIRC² and Forward Endcap DIRC) for the fast particles and a Time-Of-Flight (TOF) detector for the slow.

DIRC

The Barrel Detection of Internally Reflected Cherenkov Light (DIRC) will cover angles between 22^◦ up to 140^◦ and will use the detection of reflected Cherenkov light for particle identification. When a particle travels with a velocity of v_p through a medium with refraction index n, it is possible that it moves faster than light in this medium, i.e. _n^c ≤ v_p ≤ c. Then they emit electromagnetic shock waves, so-called Cherenkov radiation, in a cone with an angle θ_c = arccos(¹/nβc).

The information of the momentum, given by the tracking detectors, in combination with the velocity information given by the angle, θ_c, provides the information about the mass of the particle. The separation of pions and kaons will have a resolution of ≤ 3σ level for a momentum range up to 4 GeV/c. The Barrel DIRC consists of 1.7 cm thick artificial quartz, refraction index n = 1.47, encapsulating the beam line at a radial distance of 45-54 cm [21].

TOF

The barrel TOF will be used to detect and identify slow particles, i.e. particles with low momenta, at large polar angles. The principle is to measure the time it takes for a particle to travel a given distance in order to calculate the velocity. By combining the calculated velocity with the momentum from the tracking detectors, the mass can be extracted. In the TS the flight path is of order 50-100 cm, which set the requirement on the detector to have a time resolution of order 50-100 ps.

2Detection of Internally Reflected Cherenkov Light

The detector will be placed 42-45 cm from the target and cover angles between 22^◦ up to 140^◦[21].

3.3.5 The Electromagnetic Calorimeter

Many of the reactions that will be studied within the PANDA experiment involves photons or particles like π⁰, which instantly will decay into photons. Therefore a detector is needed that will measure their energy. Since photons do not carry any electrical charge, they will give no signal in the MVD nor the STT. Instead they are detected in the Electromagnetic Calorimeter (EMC). Due to the limited space in the TS and high count rates, a fast scintillator material with short radiation length is required. A material which fulfils these criteria is lead-tungsten (PbWO₄), which is a high-density inorganic scintillator. A scintillator is a material that emits light when traversed by a charged particle. The photons are neutral but will interact with the scintillating material via e⁺e⁻ pair production and compton scattering, which give rise to fast electrons and positrons. These in turn will produce new photons and give rise to a shower of photons, electrons and positrons. At the end of the shower, the charged shower products will be detected and give rise to a signal which is amplified and then read out by the electronics. Lead-tungsten is a dense and radiation hard material, which is a requirement due to the high count rates. It also has the capacity to meet the PANDA detector requirements for detecting photons, electrons and hadrons from a few MeV up to several GeV, with energy resolution σ_E/E =≤ 1 % [32].

The EMC is divided into three parts: the barrel part surrounding the beam pipe, a forward encap and a backward endcap. The barrel part will be 2.5 m long, have an inner radius of 57 cm and consist of 11360 crystals. The forward endcap will be located 2.1 m from the target in the forward direction with a radius of 2 m and the backward endcap will be located 1 m in the backward direction from the target with a radius of 50 cm.

3.4 Muon detector

Muon detectors will surround the solenoid magnet in the TS and there will be a detector placed in between the TS and FS. The detector planes will be alternated with layers of lead. This is because the lead will absorb all other particles except the muons. In the detector placed in between the TS and FS, the lead layers need to be thicker due to the higher momenta of the particles.

3.5 Forward Spectrometer

Particles that are emitted at polar angles lower than 10^◦in the horizontal direction and 5^◦ in the vertical direction will not be detected in the TS. Instead they will enter the Forward Spectrometer, which comprises a dipole magnet with a bending power of 2 Tm, tracking detectors and PID detectors to measure forward going particles [21].

3.5.1 Forward Trackers

There will be three pairs of forward trackers in the FS. One pair will be located in front of the dipole magnet, one pair inside the magnet and one pair behind the magnet. The main purpose of the forward trackers is to measure the trajectories of charged particles, which are bent by the dipole magnet. The detection principle is the same as for the STT. Each of the six forward trackers will be made of four double layers of straw tubes. Two of the layers will have wires vertical to the beam direction and two will have the wires at an angle of 10^◦. This construction will make it possible to reconstruct tracks in each pair of the tracker separately, with spatial resolution ≤ 100 µm [21].

3.5.2 Forward Particle ID

RICH

An Aerogel Ring Imaging Cherenkov Counter (RICH) detector is proposed to detect the separation of pions, kaons, protons and antiprotons. The RICH detector

uses two radiators, silica aerogel and C₄F₁₀, which makes it possible to detect separation of π/K within a broad momentum range of 2−15 GeV/c. The principle is similar to the DIRC.

Forward TOF

Another device to identify particles in the FS will be the Forward Time-Of-Flight.

It consist of a wall of slabs made of plastic scintillators. It will be suited at about 7 m downstream from the target along with similar setup at the dipole magnet opening [21]. The principle is the same as for the TS Time of Flight.

3.5.3 Forward Electromagnetic Calorimeter

The forward electromagnetic calorimeter will be used to detect photons and elec- trons with high resolution and high efficiency. The calorimeter will be placed 7-8 m from the target and will use a lead-scintillator sandwich, which is a de- sign that uses lead and scintillator in alternate layers, based read-out coupled to photo-multipliers [21].

3.5.4 Forward muon detector

The last detector along the beam line will be a muon detector. It will use similar design as for the muon detector in the TS and will be placed 9 m downstream the beam line. However, due to the higher momenta of the particles in the forward direction, the lead layers will be thicker to absorbing particles and thereby be able to distinguish muons.

3.6 Targets

The PANDA experiment has a design luminosity of 2·10³²cm⁻²s⁻¹, which requires a target thickness around 4 · 10¹⁵atoms per cm², assuming 10¹¹antiprotons stored in the HESR ring[6]. The luminosity is proportional to the number of collisions between the beam particles and target particles per unit area and per unit time.

Since the geometry of the TS is compact, along with the request of having the vertex tracker at a minimal distance to the IP, the restrictions of the internal targets is high. At the moment, two different designs of internal targets are under construction: the cluster-jet target and the pellet target. Both designs are capable to meet the PANDA requirement of luminosity but they have different properties, see Table3.2, concerning the effect on beam quality and the determination of the IP.

Target Cluster-jet Pellet

Effective target thickness 1 × 10¹⁵ atoms/cm² 5 × 10¹⁵ atoms/cm² Target thickness adjustable yes(0-max) yes(by reduction of pellet rate)

Volume density distribution homogeneous granular

Size transversal to ¯p 2-3 mm ≤ 3 mm

Size longitudinal to ¯p 15 mm ≤ 3 mm

Target particle size nm scale µm

Mean vertical particle distance ≤ 10 µm 2-20 mm

Target material H₂, D₂ H₂, D₂, N₂, Ar heavier gases optional heavier gases optional Table 3.2: Properties on internal targets an PANDA[6].

(a) Picture of the cluster-jet beam[21].

(b) Picture of the pellet stream[21].

Figure 3.2: Pictures of the different targets.

3.6.1 The Pellet Target

The pellets are frozen hydrogen micro-spheres, which are produced using a triple- point chamber (TPC). Liquid hydrogen is passed through a vibrating nozzle, after which the liquid breaks up into droplets. The droplets pass through hydrogen gas, close to triple-point conditions, where they freeze to form solid pellets. Below the intersection between the beams, there will be a pellet dump that will prevent pellets to bounce back into the interaction region. The Pellet target was first developed at the The Svedberg Laboratory (TSL) at Uppsala University [33].

Today institutes as TSL, Moscow Power Engineering Institute (MPEI), University of M¨unster and at Forschungszentrum J¨ulich (FZJ) are developing the pellet target design. The Pellet target has been operating in the experiment at WASA at COSY-J¨ulich and at the CELSIUS storage ring at TSL [6]. The operation has been successful over the years and the WASA pellet design fullfill many of the PANDA requirements; such as target density, homogeneous volume target density and point-like target. However some modifications of the structure of the design must be done to agree fully with the PANDA experimental requirements.

The Pellet design have two operation modes: the pellet tracking mode (PTR) and the pellet high luminosity mode (PHL). The differences are given in table 3.3. The PHL mode will create a high target thickness, using smaller pellets to allow more pellets at the IP, to obtain a high luminosity. The pellet tracking will use lasers and fast line-scan cameras to get position and velocity information of individual pellets, more information in sec.3.6.1.1.

3.6.1.1 The Pellet TRacking system

The theory and design of the Pellet TRacking mode have been developed in Upp- sala, where also a prototype is placed. The idea with the PTR is that it is possible to detect the individual pellet that will interact with the beam in a given event.

Keeping track of the pellet will make the reconstruction of the primary vertex more efficient. The design uses fast Line Scan (i.e one-dimensional) CCD cameras together with lasers to detect and trace individual pellets, see Figure 3.3a. The cameras and lasers will be placed at different levels, see Figure3.3b. The aim is to

Pellet mode PTR PHL

Pellet diameter ≥20µm ≤15µm

Pellet frequency ≈15k plt/s ≈150k plt/s

Average pellet velocity ≈60m/s ≈60m/s

Total spread in pellet rel. velocity σ ≥2% as small as possible

Average distance between pellet ≥4 mm 4 mm

Effective target thickness ≤ 2 × 10¹⁵at./cm² ≥ 4 × 10¹⁵at./cm²

Pellet stream diameter ≈3 mm ≤3 mm

Accelerator beam vertical diameter ≥3.5 mm ≤3.5 mm(σ ≥1 mm)

Average no. of pellets in acc. beam ≈1 ≈10

Table 3.3: Parameters of the two different pellet operation modes [6].

measure the pellet position and time when the pellet passes cameras, both before and after the interaction region. The read-out system for the cameras, which must be synchronized, is under development. The complete system will handle up to 16 cameras and will be able to compress data flows from a few Megabytes/second up to 2 Gigabytes/second [1][2].

3.6.2 The Cluster-jet target

For the cluster-jet target a pre-cooled gas is injected through a laval-nozzle, with a diameter of 10µm - 100µm, into vacuum. When the gas passes through the nozzle, it will expand adiabatically and cooled bellow the vapour-pressure curve, where the formation of micro droplets, the so called clusters, occur. The cluster-jet target is operating under low temperature, around 10-30K, and high pressure, up to 20 bar [7].

The cluster-jet design has been implemented in other experiments, such as WASA at CELSIUS, E835 at FERMILAB and ANKE and COSY-11 at COSY [6], and is present under construction/testing at the University of M¨unster, see table 3.4.

Results show that using a temperature of 19K and a pressure of 18.5 bar, it is possible to produce a target thickness of more than 10¹⁵ atoms/cm² [7]. This is the minimum requirement to fully exploit the antiproton production rate. From

(a) CAD design of the cameras and lasers that will be used for tracking of pellets [1][2].

(b) Schematic view of the camera and laser position for tracking pellets [1][2].

Figure 3.3: Figure (A) shows the model for the lasers and cameras that will be used when tracking pellets. Figure (B) shows the different stations of cameras

and lasers when tracking pellets [1][2].

table 3.4 we see that a target thickness of more than 10¹⁵ cm⁻² was achieved at a distance of 2.1 m from the nozzle, comparable with the ANKE experiment where the distance was 0.65 m.

The disadvantage with this design is the large interaction zone of beam and target due to the large lateral spread of the cluster-jet. The reconstruction of the IP will then be dependent of the precision of the tracking system.

WASA E835 ANKE, COSY-11 PANDA

(CELSIUS) (FERMILAB) (COSY) (M¨unster)

nozzle diameter < 100 µm 37 µm 11 − 16 µm 28 µm

gas temperature 20 − 35 K 15 − 40 K 22 − 35 K 19 − 35 K

gas pressure 1.4 bar < 8 bar 8 bar > 18 bar

distance from nozzle 0.325 m 0.26 m 0.65 m 2.1 m

target thickness 1.3 × 10¹⁴ cm⁻² 2 × 10¹⁴ cm⁻²  10¹⁴ cm⁻² ≥ 10¹⁵ cm⁻² Table 3.4: Parameters of different cluster-jet targets [7].

Motivation for this work

4.1 Motivation

As discussed in section 3.2, charmonium spectroscopy and open charm studies constitute an important part of the PANDA physics programme. For example a large data sample is foreseen to be collected at the Ψ(3770). The Ψ(3770) is a c¯c resonance and has a mass of 3.77 GeV/c², which is just above the D ¯D-threshold.

This means that it can decay strongly into D ¯D. Therefore it has a short life-time, τ = 10⁻²³ s, which is smaller than the experimental resolution and the decay of the Ψ(3770) can be seen as instant. The D mesons, on the other hand, have a mean life time τ = 1040 × 10⁻¹⁵ s, which means they travel a distance of the order of 0.3 mm (on the average) before they decay. Provided the track reconstruction is precise enough, it is possible to distinguish the production vertex of the D meson (i.e. the decay of the Ψ(3770)) and the decay vertex of the D meson. One common problem when studying D-meson is the large background. In order to reduce the background already when the data is being collected, a trigger could be constructed. A trigger selects events that fulfils certain requirement. In this case, we would like to select events with particles that decays outside the interaction volume, i.e. the volume defined by the overlapping beam and target.

The pellet target and the cluster-jet target have different spatial distributions and they will be operated in combination with different antiproton beam radii.

This means that the beam-target cross section area will be different in the two

27

Figure 4.1: Ψ(3770) decay channel with final state particles.

cases.

Since these properties are different, it is important to investigate the different targets with simulations using conditions that will occur during the real experi- ment.

4.2 Previous study

In 2006 ¨Orjan Nordhage presented his study on properties and implementation of pellets into the PANDA experiment. In his Ph.D-thesis [4], he also investigated how each of the three targets would affect the possibility to detect the D-meson vertex outside a given target. He used the ¯pp → Ψ(3770) → D ¯D as a benchmark channel for his simulations study of different targets, see Fig 4.1. Calculations of the kinematics of a two-body decay are outlined in Appendix A and calculations of decay length are outlined in4.2.1.

For each target a ”possible volume of interaction”, Vint was defined:

Vint= πR²_xyZint, (4.1)

where Zint is the extension of the target in the beam direction and R_xy² is the square of the transverse distance, defined as

Rxy =p

x²+ y². (4.2)

Here, x refers to the extension in the horizontal direction and y to the vertical direction. Three different cases, corresponding to different targets, were tested:

cluster-jet, untracked pellet (PHL) and tracked pellet (PTR). Table4.1 shows the different sizes that were used for simulations of the different targets and in Fig.

4.2 the results are shown. In order to estimate how many D-mesons decay outside a given interaction volume, selection criteria were applied. Events were selected if they contained D mesons decaying outside a given R_xy or Z_int, results are shown in Table 4.2.

Target Cluster-jet Untracked pellet Tracked pellet

σ_x[mm] 0.1 1 1

σ_y[mm] 0.1 1 1

Z_w[mm] 15 2 0.1

Table 4.1: Dimensions of analysed targets. σx and σy are the width of the antiproton beam in the horizontal and vertical direction, using a Gaussian dis-

tribution.

The first criterion for every target is applied at a Z_int distance which is equal to the total width of the given target. The second criterion sets a minimum |z|

of the D meson decay. For the cluster-jet target only 4% will decay outside the interaction volume, while the rest of the D-mesons will decay inside the target. It will therefore not be possible to separate the primary vertex from the secondary vertex. For the tracked pellet target, 91% of the D-mesons will decay outside the interaction volume. This means that in this case, a volume can be chosen so that most of the D-mesons will decay outside it.

One drawback of Nordhage´s study was that the detector resolution and effi- ciency was not taken into account. The results are therefore only valid for an ideal detector, which is unrealistic.

4.2.1 Particle decay length

The total travel distance of an unstable particle before decaying follows a statistical distribution. A particle with mass m, 3-momentum ~p and a proper lifetime τ = 1/Γ has the probability to travel a distance x or greater from the probability function

(a) Distribution of primary vertex[3][4] (b) Distribution of secondary vertex[3][4]

(c) Distribution of primary vertex[3][4] (d) Distribution of secondary vertex[3][4]

(e) Distribution of primary vertex[3][4] (f) Distribution of secondary vertex[3][4]

Figure 4.2: Distributions of primary and secondary vertex for different targets.

(A) and (B) corresponds to a cluster-jet target,(C) and (D) corresponds to a untracked pellet target and (E) and (F) corresponds to a pellet target with

tracking. See Table4.1 for the different target and antiproton widths[3][4].