Monte Carlo Simulations of D-Mesons with Extended Targets in the PANDA Detector

UPTEC F 16016 Examensarbete 30 hp April 2016

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

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

Teknisk- naturvetenskaplig fakultet UTH-enheten 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 Besöksadress: production and decay of charmed hadrons. The charm quark is three orders of Ångströmlaboratoriet Lägerhyddsvägen 1 magnitude heavier than the light up- and down-quarks which constitue the matter we Hus 4, Plan 0 consist of. The detection of charmed particles is a challenge since they are rare and often hidden in a large background. Postadress: Box 536 751 21 Uppsala 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 Telefon: requirements of high luminosity. However they have different properties, concerning 018 – 471 30 03 the effect on beam quality and the determination of the interaction point.

Telefax: 018 – 471 30 00 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 Hemsida: resolution and vertex resolution has been studied, as well as how the different targets http://www.teknat.uu.se/student 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.

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

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. 2006 så gjordes en likande studie av Örjan Nordhage, där han visade genom simuleringar hur stor andel av de simulerade D mesonerna som skulle sönderfalla utanför en given 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 %. Acknowledgements

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´enfor 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 Contents

Acknowledgementsi

Contents ii

List of Figuresv

List of Tables vii

Abbreviations ix

1 Aim of this thesis1

2 Introduction3 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 Contents iii

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 Contents iv

A.3 Two-body decay...... 53

B Plots from simulations 55

Bibliography 61 List of Figures

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) 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[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 reconstructed particles. (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 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 List of Figures vi

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 List of Tables

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 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]...... 5 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]...... 6 2.4 Properties of some baryons [5]...... 9 2.5 Diﬀerent types of mesons and their quantum numbers J PC [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 distances. 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. Rbeam is the radius of the antiproton beam and target width is the extension of target in antiproton beam direction...... 41

vii List of Tables viii

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 Abbreviations

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 Jülich 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 Abbreviations x

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 Chapter 1

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 experiment, 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 resolution 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 introduction 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 Chapter 1. Aim of this thesis 2

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 selection 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. Chapter 2

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 Chapter 2. Introduction 4

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

1 The standard model consist of twelve particles with half integer ( 2 ) 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 electromagnetic 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 ,νe), the second − generation the muonic leptons (µ ,νµ) and the third generation the tauonic ones − (τ ,ντ ). 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. Chapter 2. Introduction 5

Generation Name Symbol Charge Mass e [MeV/c2] Electron e−1 −1 0.511 1 Electron neutrino νe 0 Muon µ−1 −1 106 2 Muon neutrino νµ 0 Tau τ −1 −1 1777 3 Tau neutrino ντ 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 fundamental 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 10−18 m. 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. Chapter 2. Introduction 6

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 Hyper charge W boson W ± ±1 80.385 ± 0.015 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 Chapter 2. Introduction 7

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,

L P = PaPb(−1) . (2.3)

where the Pa and Pb 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 = CaCb (2.4)

where Ca and Cb 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 Chapter 2. Introduction 8

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 momentum 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

S + B Q = I + (2.7) 3 2

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 Chapter 2. Introduction 9 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 PC 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 PC quantum numbers, where J is the total angular momentum, P is parity and C is charge conjugation.

Type Quantum number J PC Scalar 0++ Pseudoscalar 0−+ Vector 1−− Axial vector 1+±

Table 2.5: Diﬀerent types of mesons and their quantum numbers J PC [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. Chapter 2. Introduction 10

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

Figure 2.1: Meson nonets

Name Symbol Quark Mass J PC Lifetime structure [Mev/c2] [s] 0 uu¯−dd¯ −+ −17 π √2 135.0 0 8.4 · 10 P ion 2 π+ ud 139.6 0− 2.6 · 10−8 K+ us¯ 493.7 0−+ 1.2 · 10−8 Kaon K0 ds¯ 497.7 0−+ ρ+ ud¯ 775.1 1− 4.4 · 10−24 Rho ¯ ρ0 uu¯√−dd 775.3 1−+ 4.5 · 10−24 2 ¯ Omega ω uu¯√+dd 782.7 1−− 7.8 · 10−23 2 Phi Φ ss¯ 1019.5 1−− ¯ Eta η uu¯+√dd−2ss¯ 547.9 0−+ 6 0 ¯ Eta prime η uu¯+√dd+ss¯ 957.8 0−+ 3

Table 2.6: Properties of some mesons [5].

2.4 Charmonium

Charmonium is a meson containing a charm-anticharm pair (cc¯), 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

2 (mc ∼ 1.3 GeV/c ), 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 Chapter 2. Introduction 11 that it ﬁts the asymptotic properties of the strong interaction. The known lowest

0 lying states today are the ηC , J/Ψ, χC , hC ,Ψ 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 PC = 1−− dominate completely, since this is the quantum number of the photon. States with other J PC have to be produced in decays from 1−− states. In a pp¯ experiment, like PANDA, any non-exotic J PC 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 Table 2.7. 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 Chapter 2. Introduction 12

Name Quark Mass Lifetime Decay structure [Mev/c2] cτ [µm] channels D0 cu¯ 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+ cd¯ 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 perform the planned research programme. Researchers from all over the world work together and contribute with their expertise in order to take the technology several steps further. Who can tell what inventions this will lead to, and what their applications will be? Chapter 3

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 experiment 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 Chapter 3. The PANDA Experiment 14

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 −5 −5 RMS momentum spread σp/p ≤ 4 × 10 , σp/p ∼ 4 × 10 , 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 cc¯ 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]. Chapter 3. The PANDA Experiment 15

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 (qq¯) and baryon (qqq). Hence there is a possibility that other colourless combinations of quarks and gluons might exist. Such as hybrids (qqg¯ ), glueballs (gg, ggg) and multiquarks (qqq¯ q¯, qqqqqq, qqqqq¯, ...). 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 Zc(3900) , support the theory of multiquarks. The ± particle Zc(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 Zc(3900) has led to a huge activity in the ﬁeld and has been enthusiastically received by the scientiﬁc community. The indication that

± ± the Zc(3900) is a multiquark state, is because it decays into J/Ψ π . The large

mass of the Zc and that it decays into J/Ψ, implies that it must consist of a ± cc¯-pair. From the net charge of the ﬁnal state particles, the Zc(3900) must be charged. However the cc¯-pair is electrically neutral and therefore there must be other particles, together with the charm-anticahrm pair, that gives the appropriate

charge to the Zc.

3.2.2 Electromagnetic structure of baryons

Within the PANDA experiment, it is also possible to investigate the electromagnetic structure of the proton. This using three diﬀerent methods: studying Form Chapter 3. The PANDA Experiment 16

Factors in the Time-like region (T LF F 0s)[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]. Chapter 3. The PANDA Experiment 17

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]. Chapter 3. The PANDA Experiment 18

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 Chapter 3. The PANDA Experiment 19

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 vp through a medium with refraction index n, it is possible that it moves faster than

c light in this medium, i.e. n ≤ vp ≤ c. Then they emit electromagnetic shock 1 waves, so-called Cherenkov radiation, in a cone with an angle θc = arccos( /nβc). The information of the momentum, given by the tracking detectors, in combination

with the velocity information given by the angle, θc, 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 Chapter 3. The PANDA Experiment 20

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 σE/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. Chapter 3. The PANDA Experiment 21

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 Chapter 3. The PANDA Experiment 22

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 electrons 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 design 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 2·1032 cm−2s−1, which requires a target thickness around 4 · 1015 atoms per cm2, assuming 1011 antiprotons 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. Chapter 3. The PANDA Experiment 23

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 Table 3.2, 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. Chapter 3. The PANDA Experiment 24

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 Münsterand at Forschungszentrum Jülich (FZJ) are developing the pellet target design. The Pellet target has been operating in the experiment at WASA at COSY-Jülich 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 Figure 3.3b. The aim is to Chapter 3. The PANDA Experiment 25

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 Chapter 3. The PANDA Experiment 26

(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]. Chapter 4

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 cc¯ resonance and has a mass of 3.77 GeV/c2, which is just above the DD¯-threshold. This means that it can decay strongly into DD¯. 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 Chapter 4. Motivation for this work 28

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 experiment.

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 thepp ¯ → Ψ(3770) → DD¯ 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 AppendixA and calculations of decay length are outlined in 4.2.1.

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

2 Vint = πRxyZint, (4.1)

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

p 2 2 Rxy = x + y . (4.2) Chapter 4. Motivation for this work 29

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). Table 4.1 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 Rxy or Zint, results are shown in Table 4.2.

Target Cluster-jet Untracked pellet Tracked pellet

σx[mm] 0.1 1 1

σy[mm] 0.1 1 1

Zw[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 distribution.

The ﬁrst criterion for every target is applied at a Zint 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 Chapter 4. Motivation for this work 30

(a) Distribution of primary vertex[3][4] (b) 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 Table 4.1 for the diﬀerent target and antiproton widths[3][4]. Chapter 4. Motivation for this work 31

Vint Results from Ref.[4]

Target Zint[mm] Rxy[mm] Cut 1[mm] η[%] Cut 2[mm] η[%] Cut 3[mm] η[%]

Cluster ± 7.5 0.2 |z| > 7.5 4 Rxy > 0.2 16 Untracked ± 2 1 |z| > 1 23 |z| > 2.5 9 Tracked ± 0.1 1 |z| > 50 µm 91 |z| > 200µm 69 |z| > 1 16

Table 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.

given by m P (x) = e−mxγ/|~p| (4.3) |~p| τ Then the expectation value of the travel distance is given by

Z ∞ Z ∞ m |~p| τ xˆ = xP (x)dx = x e−mxγ/|~p|dx = = γβτ (4.4) 0 0 |~p| τ m

Thus, x can be generated from an exponential distribution exp(− |~p| τ)/m).

4.3 This work

Since the PANDA experiment will use both a cluster-jet and a pellet target, it is important to investigate how the choice of target aﬀects the data quality and the possibility to reduce background. Therefore I have studied the reaction,pp ¯ → Ψ(3770) → D+D−, D± → K∓π±π±. In this study, the PandaRoot simulation package is used to achieve a realistic description of the detector. This means that the detector resolution and eﬃciency are taken into account, in contrast to Nordhage´s work. Chapter 5

Software tools

In this thesis, we want to learn how to reconstruct D mesons produced in pp¯- collisions and how the data quality depends on the target dimensions. Therefore we perform Monte Carlo simulations of thepp ¯ → → DD¯ reaction with the subsequent propagation of the particles and their decay produced through the detector. The simulation framework is called PandaRoot which will be introduced in the following:

5.1 PandaRoot

PandaRoot[34] is an offline software that is used to simulate experiments with the PANDA detector. It is based on the ROOT and Virtual MonteCarlo packages, where transport codes such as GEANT3[35] and GEANT4[36] are used. PandaRoot is also part of the FairRoot[37] framework, in order have a common structure of code for the different experiments at the future facility FAIR. The detector set up and the reconstruction code is implemented into PandaRoot. PandaRoot simulations comprise five different steps: simulation, digitization, reconstruction, particle identification (PID) and analysis.

32 Chapter 5. Software tools 33

5.1.1 Simulation

In the first step of the simulation, the reaction of interest is generated using an event generator. PandaRoot handles event generators such as EvtGen [38], DPM1, PYTHIA and UrQMD2. The event generator generates the physical reaction where the initial particles are produced. In this work, EvtGen was used to generatethe reactionpp ¯ → Ψ(3770) → DD¯ with the subsequent decay of the D-mesons. The geometry of the detector and the different sub-detectors are defined at this stage. After the particles have been generated and decayed according to some user-defined model, the decay products are transported through the detector material. As the particles are propagated, interactions with the detector material, i.e. ionization and multiple scattering, are taken into account. Information about energy loss, position, direction, hits in the detector material and velocity comprise the output and is given as so-called MC points.

5.1.2 Digitization

In this step the stored information, the MC points, from the diﬀerent sub-detectors will be converted to so called MC hits. The MC hits are the response in the sensors of the diﬀerent detectors, which is converted into signals in the electronics of the individual detectors. This will produce a digitized detector output, that mimics the output of the real experiment.

5.1.3 Reconstruction

To be able to reconstruct the path of charged particles, the MC hit information from diﬀerent detectors are used and combined into tracks using pattern recog- nition algorithms. The hits in the MVD, the GEM and the STT will give the necessary information, such as momentum and spatial coordinates, to reconstruct tracks. The EMC will provide information, such as direction and energy, which is necessary to reconstruct tracks for the photons.

1Dual Parton Model 2Ultra relativistic Quantum Molecular Dynamics Chapter 5. Software tools 34

5.1.4 Particle Identiﬁcation

In order to identify different particles, PandaRoot uses information from almost every sub-detector. Variables from tracks that are useful for a good PID is for example energy loss, dE/dx, and the angle of the Cherenkov light emitted in e.g. the DIRC detector. From the MVD and STT the dE/dx is used for particle identification whereas the DIRC detector us the Cherenkov angle. As a first step of the PID software, each subsystem will provide particle hypothesis for all five particles (e, µ, π, K and p). The second step is that the given probabilities from each subsystem are combined into a global probability by applying a standard likelihood method. The particle identification (PID) from the detectors have not been used in this work. Instead, information of the true particles, before interacting with the material, have been used for simplicity. This is because we are interested in other aspect of the data than PID and want to make sure our major source of uncertainty are from tracking and vertexing. With real data this will, of course, not be possible. Chapter 6

Analysis

6.1 Physics Reaction

The simulations are performed at a beam momentum of 6.57 GeV/c, which gives an energy in the CM system equal to the Ψ(3770) mass. 10000 events have been simulated using the EvtGenDirect generator. Pandaroot revision 24978 along with external packages dec13 has been used for the simulations. We are interested in the Ψ(3770) → DD¯ decay, and since we want precise tracking of the final state particles, we choose a D and D¯ decay channel where all decay products are charged: D+ → K−π+π+ and D− → K+π−π−. In Fig 6.1 the momentum and polar angle distributions are shown, using an ideal (point-like) target. In Appendix B, the distributions for the other three targets can be found. The decays are defined in a decay file, which is used as input for the EvtGenDi- rect generator. The branching ratio of D± → K∓π±π±, as given by the PDG1[5], is 25.7 ± 1.4 %, but in this analysis we let both the D+ decay into K−π+π+ and the D− decay into K+π−π− in 100 % of the events to increase the statistics.

1Particle Data Group

35 Chapter 6. Analysis 36

(a) D+ (b) D−

(e) π+ (f) π−

Figure 6.1: Momentum and polar angle distribution for all particles using an ideal target.

6.2 Input to simulations: Extended targets in Pandaroot

In PandaRoot it is possible for the user to define a three-dimensional vertex distribution with different size and properties. This is done in the initial step Simulation, described in 5.1.1. Pandaroot uses the function FairPrimaryGenerator, which is part of FAIRroot framework. The vertex distribution is defined as the overlap region between the antiproton beam and the target extension, i.e. the interaction volume. In the standard PandaRoot two interaction volumes are pre-defined: a box distribution and a gaussian distribution [39]. The first part of this work was to verify O.¨ Norhages study with the same vertex Chapter 6. Analysis 37

distributions that was used in his study, see Table 4.1. In Ref [4], a gaussian distribution in the xy-plane was used. This is motivated by the expected beam proﬁle when using a stocastically cooled beam.

6.3 Event selection

The analysis of this thesis is reconstruction of D-mesons from simulatedpp ¯ -collision data. Each event must be analysed to find out what kind of reaction the particle comes from. As mentioned in previous sections, we wish to reconstruct D-mesons which decays into K∓π±π±. In this work, PID from the detectors have not been used. Instead information of the true particles, before interacting with the material, have here been used for simplicity. With real data this will, of course, not be possible but it serves a purpose since it enables us to isolate the systematics from tracking and vertex reconstruction. To select events of interest, the origin of the corresponding MC truth track of each reconstructed track has been checked. Since the analysis concerns particles that can be used for a proper reconstruction of the whole decay chain, different particle lists are matched with the Monte Carlo truth information. Monte Carlo truth information handles the information about the whole decay tree, i.e. it checks for example i) if the kaons and the pions have the same mother, ii) the mother is a D-meson(this is only available for MC truth) and iii) if the D-meson is the daughter of a Ψ(3770). PandaRoot stores information about the mother of each track, and this information have been used to reduce the combinatorics in this work. The PDGs Monte Carlo particle numbering scheme [40] have also been used to be able to identify and confirm the different particles. With PandaRoot, candidate lists of reconstructed particles can be created. These are typically organised with respect to the charge of particles. First, we create a list of all positively charged tracks which we assume to be π+. This is also done for π−,K+andK−. Once the particle lists are filled with possible candidates there is a MC truth check to sort out bad candidates. If a candidate fulfil the criteria (i-iii), the different data such as position, mass and momentum of the Chapter 6. Analysis 38

candidate is extracted into histograms. The approved candidate is then stored into another list. To analyse the D mesons, the lists of the approved kaon and pion candidates are combined to a new candidate list. Each combination comprises two different pions, with same charge, and one kaon, of opposite charge with respect to the pions. When combining particle lists, double counting and overlaps are automatically prevented. Overlap is when the reconstructed object is used twice in the same decay tree and double counting is when the same particle combination is used twice. The list now only containing particles with a D meson as a mother. Once the list with the D candidate combinations is obtained, the analysis for the vertex positions of the D mesons can be made. This is done with the so-called vertex fit. The fit will set constraints on the trajectories of the charged particles to come from a common point, i.e. the trajectories are modified within errors such that the tracks come as close as possible to a hypothetical vertex.

6.4 Validation of the method

Using the dimensions given in Table 4.1, a small-scale simulation of 1000 events have been made in order to compare the results with the results given by O.Nordhage¨ [4]. The results contains both the Monte-Carlo truth result along with the results from the reconstructed vertices. The results from Monte-Carlo truth, see Table 6.1, is in good agreement with the results from Ref [4]. The cluster-jet as well as the tracked pellet shows the same amount of D-mesons that will decay outside the volume. For the untracked pellet there is a small difference when applying the |z| > 1 mm criterion, reconstruction efficiency η = 23% in O.Nordhages¨ study and the reconstruction efficiency η = 27% with this simulation, however this is within the statistical error of 3.8%. The results obtained including detector response, have a larger difference in the amount of D-mesons that will decay outside the interaction volume, see Table 6.2. The result for every target is different with respect to the results in Table 4.1. This is expected, since the full detector response is taken into account. Chapter 6. Analysis 39

(a) Distribution of the secondary vertex (b) Distribution of the secondary vertex from Monte-Carlo truth from reconstructed particles

(c) Distribution of the secondary vertex (d) Distribution of the secondary vertex from Monte-Carlo truth from reconstructed particles

(e) Distribution of the secondary vertex (f) Distribution of the secondary vertex from Monte-Carlo truth from reconstructed particles

Figure 6.2: Distributions of secondary vertex from Monte-Carlo truth and reconstructed particles. (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 table 4.1 for the diﬀerent target and antiproton widths. Chapter 6. Analysis 40

Vint Monte-Carlo Truth Vertex Results

Target Zint[mm] Rxy[mm] Cut 1[mm] η[%] Cut 2[mm] η[%] Cut 3[mm] η[%]

Cluster ± 7.5 0.2 |z| > 7.5 3.5±0.6 Rxy > 0.2 14.7±1.2 Untracked ± 2 1 |z| > 1 26.7±3.8 |z| > 1.5 10.5±1.0 Tracked ± 0.1 1 |z| > 50 µm 90.9±3.1 |z| > 200 µm 68.9±2.6 |z| > 1 15.8±1.3

Vint Results from Ref.[4]

Target Zint[mm] Rxy[mm] Cut 1[mm] η[%] Cut 2[mm] η[%] Cut 3[mm] η[%]

Cluster ± 7.5 0.2 |z| > 7.5 4 Rxy > 0.2 16 Untracked ± 2 1 |z| > 1 23 |z| > 1.5 9 Tracked ± 0.1 1 |z| > 50 µm 91 |z| ¿ 200µm 69 |z| > 1 16

Table 6.1: Results from Monte-Carlo truth 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. The grey part of the table shows the results from [4], as shown in 4.2.

Vint Reconstructed vertex Results

Target Zint[mm] Rxy[mm] Cut 1[mm] η[%] Cut 2[mm] η[%] Cut 3[mm] η[%]

Cluster ± 7.5 0.2 |z| > 7.5 3.9±1.6 Rxy > 0.2 21.3±3.7 Untracked ± 2 1 |z| > 1 29.4±1.6 |z| > 1.5 11.9±2.9 Tracked ± 0.1 1 |z| > 50 µm 91.3±7.5 |z| > 200 µm 70.4±6.6 |z| > 1 17.9±3.3

Table 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.

6.5 Realistic target dimensions

Using cyclotron accelerators, the beam profile of the beam is either elliptical or almost circular [41]. Since no studies have ben performed so far with a circular beam profile within the PANDA collaboration, this study included a first test with this shape of the antiproton beam. A circular beam profile gives a cylindrical beam-target overlap region, i.e. a cylindrical interaction volume. Hence, the implementation a homogeneous cylindrical interaction volume were made. This was done in discussion with target experts [41]. The cylindrical interaction volume is obtained by letting the user define a radius of the anti-proton beam, Rbeam. When defining a vertex distribution volume, one needs to define the vertex in cylindrical coordinates (R,Φ,z) which are related to cartesian coordinates x, y, z in the following way Chapter 6. Analysis 41

x = R × cos(φ) (6.1)

y = R × sin(φ) (6.2)

z = z (6.3)

where R is uniformly distributed in the interval 0 ≤ R ≤ Rbeam, φ is the angle uniformly distributed in the interval 0 ≤ φ ≤ 2π and z is deﬁned by the extension of the target in the beam direction. Also in z, the distribution is uniform. The diﬀerent properties of the target width and antiproton beam is presented in Table 6.3. The values have been taken from Ref [6] and along with discussion with target experts. When using a tracked pellet, the pellet rate, and thus the distance between pellets, will be larger than for untracked pellets. The distance will be of the order of the vertical antiproton beam diameter. With a larger distance between pellets it will be easier to detect pellet in the interaction. Hence the value of the Rbeam is larger for the tracked pellet than for the untracked pellet, see Table 6.3.

Target Rbeam [mm] Target width [mm] Cluster-jet 0.4 13.1 Untracked 1.5 2.5 Tracked 2.5 3.0

Table 6.3: Parameters for the diﬀerent targets. Rbeam is the radius of the antiproton beam and target width is the extension of target in antiproton beam direction. Chapter 7

Results

In this section the results in this study will be presented. The work has focused on two questions:

How is the data quality, i.e. efficiency, momentum resolution and vertex resolution, affected by different target dimensions?

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

7.1 Data quality

The momentum resolution is defined as, (prec − pMC )/pMC , i.e. the difference between the reconstructed momentum and the Monte Carlo truth momenta, divided by the Monte Carlo truth momentum. The vertex resolution is defined as the difference between the reconstructed coordinate and the Monte Carlo truth

coordinate, i.e. xrec − xMC . The results of the momentum resolution for the final state particles for the different targets are presented in Table 7.1 and the plot of the momentum resolution for a untracked pellet target are shown in Fig. 7.1, see Figure B.1 and B.2 inB for the plots of the momentum resolution of Cluster-jet target and Tracked pellet target respectively. Table 7.1 also show that both K+, η ∼60% and π−, η ∼68% has larger efficiency than K−, η ∼54% and π+, η ∼65%. Hence the final state particles of D− has larger reconstruction efficiency than for the final state particles of D+ for all three 42 Chapter 7. Results 43 targets. This is an interesting observation, since this should not be the case. The kinematic properties does not depend on the charge of mesons and neither should the detector response, i.e. the reconstruction efficiency should be the same for both the negative and positive kaons and pions. These results shows that the efficiency depend on the origin of the particle. This has also been observed in a simulation study of hyperons [17] and in the Ph.D thesis of Laura Zotti [42], where the Ψ(4040) decay was studied. The reason for this is not yet understood. Table 7.1 shows that the data quality, i.e. the momentum resolution and efficiency, does not depend on the choice of target. The results of the vertex resolution for the D mesons are presented in Table 7.2, see Figure B.1, 7.1 and B.2 in AppendixB for the plots of the vertex resolution of Cluster-jet target, Untracked pellet target and Tracked pellet target respectively. The results of the vertex resolution for the D mesons are presented in Table 7.2, Figure 7.1 shows the vertex resolution for a untracked pellet target, see Figure B.1 and B.2 in AppendixB for the plots of the vertex resolution of Cluster-jet target and Tracked pellet target. From Table 7.2, the values of the reconstruction efficiency of D-mesons in different targets shows that η is larger for D− than for D+ also when using the different targets. Table 7.2 show also that there is a slightly better vertex resolution when using pellet targets than for the cluster jet target, in both x- and z-direction.

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

In order to evaluate how many D mesons will decay outside a given target, the similar approach as in Ref [4] has been used, i.e. applying cuts at different distances to see how many of the D-mesons that will survive outside the interaction volume. The results are presented in Table 7.3 and they show that the efficiency for the cluster jet target is worse than for the different pellet targets, by a factor of 2-3. Since a cluster jet target has a larger distribution in the z-direction, a cut in |z| cannot be as tight as in the case of a pellet target and the background Chapter 7. Results 44

Cluster-jet target Final state particle η[%] δp/p [%] K+ 60.6 ± 0.8 2.03 ± 0.03 K− 55.4 ± 0.7 2.03 ± 0.03 π+ 66.6 ± 0.8 1.79 ± 0.02 π− 68.4 ± 0.8 1.75 ± 0.02 Untracked pellet target Final state particle η[%] δp/p [%] K+ 62.0 ± 0.8 2.03 ± 0.03 K− 56.4 ± 0.7 2.07 ± 0.03 π+ 67.9 ± 0.8 1.75 ± 0.02 π− 69.6 ± 0.8 1.73 ± 0.02 Tracked pellet target Final state particle η[%] δp/p [%] K+ 61.6 ± 0.8 2.01 ± 0.03 K− 56.8 ± 0.7 2.17 ± 0.04 π+ 67.9 ± 0.8 1.78 ± 0.02 π− 69.7 ± 0.8 1.69 ± 0.02

Table 7.1: Result of momentum resolution, δp/p, and reconstruction efficiency, η, of the final state particles with different targets.

Cluster-jet target

Particle η[%] σx [µm] σz [µm] D+ 13.3 ± 0.4 76.08 ± 2.30 135.6 ± 4.0 D− 15.5 ± 0.4 76.13 ± 2.21 131.5 ± 4.0 Untracked pellet target

Particle η[%] σx [µm] σz [µm] D+ 12.9 ± 0.8 71.37 ± 2.22 126.4 ± 3.9 D− 15.9 ± 0.7 73.09 ± 1.85 122.1 ± 3.1 Tracked pellet target

Particle η[%] σx [µm] σz [µm] D+ 13.9 ± 0.8 71.14 ± 1.82 123.7 ± 3.5 D− 16.0 ± 0.7 70.66 ± 1.87 131.9 ± 3.5

Table 7.2: Result of vertex resolution, after the use of vertex ﬁt, for the D-mesons at diﬀerent targets. Chapter 7. Results 45

(a) Momentum resolution for K+ (b) Momentum resolution for K−

(e) Vertex resolution for D+ in x. (f) Vertex resolution for D+ in z.

(g) Vertex resolution for D− in x. (h) Vertex resolution for D− in z.

Figure 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. Chapter 7. Results 46 reduction potential is thereby smaller. The pellet target setups should be more effective to reduce the background events, since all three cuts can be narrow in the z-direction.

Vint Results from reconstruction of D-meson vertex using a cylindrical distribution

Target Zint[mm] Rxy[mm] Cut 1[mm] η[%] Cut 2[mm] η[%] Cut 3[mm] η[%]

Cluster ± 6.55 0.8 |z| > 6.55 7.4±0.7 Rxy > 0.8 8.2±0.7 |z| > 6.7 6.3±0.6

Untracked ± 1.25 1.5 |z| > 1.25 22.7±1.2 Rxy > 1.5 24.9±1.3 |z| > 1.5 14.6±1.1

Tracked ± 1.5 2.5 |z| > 1.5 20.1±1.1 Rxy > 2.5 21.1±1.1 |z| > 1.75 13.0±0.9

Table 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.

From the different cuts with cluster jet target, there is only maximum 9 % of the D-mesons that will decay outside the cut at maximum beam radius. For the pellet targets, there is no big difference between the untracked and tracked pellets: η ∼25% for untracked pellet and η ∼21% for the tracked pellet. The largest difference is the radius of the anti-proton beam that will be used with the different pellet types. This is because when running experiment, the plan is to run with a beam with larger emittance with the tracked pellets. This study shows that this would reduce the precision and some of the advantages with tracked pellets are lost. Chapter 8

Summary and Conclusions

The results of the data quality of the final state particles for each target, simulations show no significant difference between the different targets. The reconstruction efficiency, for a particle, depends on from which particle it originates. The difference between positive and negative kaons and pions is an interesting observation. The kinematic properties does not depend on the charge of the meson, instead from where the particle originates and neither should the detector response. Both K+ and π−, which are the decay products from D−, have a larger efficiency than for K− and π+. This is an unexpected feature of the reconstruction that needs to be understood. The momentum resolution, δp/p, for the final state particles with different targets shows no significant difference, it is ∼2.0% for the K± and 1.7 − 1.8% for the π±. So the conclusions is that momentum resolution and efficiency does not depend on which target that is used. The results of the vertex resolution shows that the reconstruction efficiency of the D± does not depend on the target choice. The resolution in x and z- direction is better for the pellet targets than for the cluster jet target. However, one expects ”better” results for the tracked pellet, with respect to data quality and the reconstruction efficiency. The second question in this work was, for a given target how many D-mesons will decay outside the interaction volume. The results of a small-scale simulation study, with the aim of validating the

47 Chapter 8. Summary and Conclusions 48

method, both MC truth data and the reconstructed events reproduce the results from O.Nordhage’s¨ thesis [5] from 2006. For both the cluster-jet target and pellet target, the new results are compatible with the old ones. From the simulation with a more realistic interaction volume, the shape of a homogeneous cylinder, the first cut was made at the maximum width, in z- direction, for each target. This shows that ∼20 % of the D mesons will decay outside the tracked pellet target, ∼23% for the untracked pellet and ∼7 % for the Cluster-jet target. The second cut was made at the maximum beam radius. The results show a similar pattern, we see that for a untracked pellet target(η ∼25 %) there is a larger amount of D-mesons that will decay outside the interaction volume, than for a tracked pellet target(η ∼21 %). For the cluster jet target we see that η is higher than for the first cut. The third cut was done to see how the result changes with a larger value of the distribution in z-direction, as expected the values are worse because of the D-meson lifetime. The cluster jet target can use a smaller radius of the antiproton beam, but instead need a larger distribution in z-direction. This will make it difficult to reduce background events. The tracked and the untracked pellet targets have a more confined distribution in the z-direction and should therefore be more effective in reducing background events. From the results of how many D-mesons that will decay outside the given target, one expects a better result for the tracked pellet target than in this study. One reason for this is that in this study, the transverse size of the interaction volume for the tracked pellet was overestimated. Increasing the beam emittance in order to achieve higher luminosity may, from the point this point of view, mean that some of the positive aspects of tracked pellets are lost. Since this is just a short study on the topic of how different targets will affect the results on reconstructing events, more information must be gathered in order to validate the results further. This is also the first study made with an extended target distribution with the shape of a cylinder. Further tests, of how effective and realistic the interaction volume is, would be valuable. One important remark to this work, is that the full resolution of the tracked Chapter 8. Summary and Conclusions 49 pellet has not been used. The tracked pellet design uses the fact that when a reaction occur, the knowledge of the interaction point is known. There is a possibility to trace the pellet from which the reaction occurred. This is essential for the design and will affect the outcome of the study, since the background can be reduced by knowing if there was a pellet in the reaction or not. Another point worth mentioning is that for collecting data from reactions the time scale is about 1 microsecond, where the pellet tracking need about 100 milliseconds to be able to process the data. Hence the different time scales needs to be included in the analysis of the results for pellet tracking. Chapter 9

Outlook

This is a first study with a extended target that uses a cylindrical interaction volume. More simulations are needed, using this method in order to validate the results, with different target volumes and more updated versions of PandaRoot. Even more important is to make a systematic background study for different target volumes. In the real experiment the background will be many orders of magnitude larger than the signal reaction. One useful background generator is the Dual Par- ton Model (DPM), which is a event generator that produce particle distributions for known cross-sections inpp ¯ -collisions. It handles scattering processes such as Coulomb scattering, inelastic hadronic scattering and elastic hadron scattering. In this way, simulated background events resembles the data of a real experiment.

50 Appendix A

Relativistic kinematics in particle collisions

In particle physics the use of 4-vectors is a tool which simplify calculations. The 4-vector is a generalisation of the classical 3-vector and also includes time as a pa- rameter. The 4-vector is denoted uµ, where µ = 0,1,2,3 and the ﬁrst component,µ0 corresponds to the time component and the three indices 1,2,3 corresponds to the classical vector spatial part. The most common 4-vector treated in particle physics is the momentum vector, denoted pµ = (E, −p), where E is the total energy and p is the three momentum vector. The total energy of a relativistic particle is given by p|~p2| + m2 (A.1) where m is the rest mass of the particle.

A.1 Reference Frames

The two most used reference frames, in relativistic particle scattering, is the laboratory frame (LAB) and the center-of-mass frame (CM). The laboratory frame treats the reaction from a spectator’s point of view, where the spectator is stand- ing still on the ﬂoor of the laboratory. It is also the frame of the particle detectors. As a consequence the measured quantities made from the experiment are made in the laboratory frame. For the same reason, the quantities obtained by simulations

51 Appendix A. Relativistic kinematics 52 are by default in the lab frame. The generation of the physical reaction e.g. pp¯ → DD¯ , is in the CM frame since this is the reference frame where the particles are generated. The CM frame is also the frame used by theoreticians, since it is independant of experimental circumstances. Experimentalist often present their result in the CM frame since it is more straight forward to compare with theories or other experiments that way. In the CM frame the total momentum is zero, which simpliﬁes calculations.

A.2 Lorentz transformation

To be able to go from one frame into another, a Lorentz transformation is applied to the four vector in the original frame. After the Lorentz transformation, the four vector in the desired frame is obtained. Consider a particle p in a rest frame S, with an observer O, and another frame S0 , which is moving with a velocity v relative to the reference frame S. If an observer O0 , which is at rest in S0 , measure the momentum of the particle p in the the frame S0 , the momentum is given by

0ν ν µ p = Λµp (A.2) where the Λ is the transformation matrix. If the axis of the moving frame, S0 , coincide with the axis of the frame S, lets assume the z-direction, the transformation matrix is given by

  γ 0 0 −γβ     ν  0 1 0 0  Λ =   (A.3) µ    0 0 1 0    −γβ 0 0 γ Appendix A. Relativistic kinematics 53

Evaluating equation A.2 the new values of the four momentum in the moving reference frame S0 is:

0 E = γ (E − βpz)

0 px = px

0 py = py

0 pz = γ (pz − βE)

with β = v and γ = √ 1 c 1−β2

A.3 Two-body decay

The reaction of a two-body decay can be described as

a → b + c (A.5) i.e. particle a decays into two particles, b and c. By performing the calculations in the CM frame of the particle a, where it is at rest, we get the following 4- momentum for the diﬀerent particles

pa = ma,~0 (A.6a)

pb = (Eb, ~pb) (A.6b)

pc = (Ec, ~pc) (A.6c)

In the reaction both momentum and energy must be conserved. Which leads to

pa = pb + pc (A.7)

Since we are in the reference frame of the particle a, the equation A.7 becomes

~pb = −~pc. Then we can omit the subscript of the particle momenta and then the Appendix A. Relativistic kinematics 54

energy conservation takes the form

q 2 2 p 2 2 Eb + Ec = p + mb + p + mc = ma (A.8)

Solving for p we get

q 1 2 2 2 2 p = ma − (mb − mc) ma − (mb + mc) (A.9) 2ma

Now we want to calculate the energy of the particle a and c. Using the equation

p 2 2 2 A.8 and express Ec in terms of Eb to get Ec = Eb − mb + mc and solve for Eb

1 2 2 2 Eb = ma + mb − mc (A.10) 2ma

and similar is found for Ec

1 2 2 2 Ec = ma + mc − mb (A.11) 2ma

To go to the LAB frame on just have to use the Lorentz transformation on the 4 momentum of the daughter particles

0 Eb = γ (Eb + vpbz) (A.12a)

0 pbz = γ (pbz + vEb) (A.12b)

~0 pb⊥ = ~pb⊥ (A.12c)

where γ = Ea/ma and v = pa/Ea. Appendix B

Plots from simulations

In this section the plots of momentum resolution and vertex resolution are presented. For every target there is a plot of the momentum resolution, (prec − ± ± pMC )/pMC , for the ﬁnal state particles, K and π . There is also the vertex resolution, xrec − xMC , for both the D-mesons in both x and z-direction.

Momentum - and polar angle distribution, θ(deg) vs. prec for all decay particles using a cluster jet target, untracked pellet target and tracked pellet target are also presented.

55 Appendix B. Plots from simulations 56

(a) Momentum resolution for K+ (b) Momentum resolution for K−

(e) Vertex resolution for D+ in x. (f) Vertex resolution for D+ in z.

(g) Vertex resolution for D− in x. (h) Vertex resolution for D− in z.

Figure 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. Appendix B. Plots from simulations 57

(a) Momentum resolution for K+ (b) Momentum resolution for K−

(e) Vertex resolution for D+ in x. (f) Vertex resolution for D+ in z.

(g) Vertex resolution for D− in x. (h) Vertex resolution for D− in z.

Figure 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. Appendix B. Plots from simulations 58

(a) D+ (b) D−

(e) π+ (f) π−

Figure B.3: Momentum - and polar angle distributions for all particles using a cluster jet target Appendix B. Plots from simulations 59

(a) D+ (b) D−

(e) π+ (f) π−

Figure B.4: Momentum - and polar angle distributions for all particles using a untracked pellet target Appendix B. Plots from simulations 60

(a) D+ (b) D−

(e) π+ (f) π−

Figure B.5: Momentum - and polar angle distributions for all particles using a tracked pellet target Bibliography

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