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Author: Halimeh Vaheid Supervisor: Karin Schönning Subject Reader + ¯ 0 ¯ 0 0 Monte Carlo Simulation of e e− Σ Λ=Σ Σ Reaction ! Uppsla University Department Of Physics and Astronomy Master Thesis Author: Halimeh Vaheid Supervisor: Karin Sch¨onning Subject reader: Magnus Wolke i Contents 1 Introduction 2 1.1 Aim .............................................2 1.2 The Standard Model . .3 1.3 The Strong Interaction . .3 1.4 Hadrons . .4 1.4.1 Quantum Numbers . .4 1.4.2 Mesons . .7 1.5 Baryons . .8 1.5.1 Hyperon . .9 2 Formalism 10 2.1 Cross section . 10 2.2 Relativistic Kinematics . 11 2.2.1 Electromagnetic Form Factor . 13 3 Hyperon Production in e+e− Annihilation 16 3.1 The e+e− ΛΣ¯ 0 reaction . 16 ! 3.2 The e+e− Σ0Σ¯ 0 reaction . 18 ! 3.3 Previous studies . 19 4 The BESIII Experiment 20 4.1 BEPC-II . 20 4.1.1 The BES III Detector . 21 5 Software Tools 26 5.1 Jupyter . 26 5.2 BOSS . 27 ii 5.2.1 Event generation . 27 5.2.2 Particle transport and detector response . 28 5.2.3 Digitalization . 28 5.2.4 Reconstruction . 28 5.2.5 Analysis . 28 6 Parameter Estimation Using Monte Carlo method 29 6.1 The Method of Moments . 29 6.1.1 Extracting the ratio R from an angular distribution by applying MM . 30 6.2 The Least Squares Fit . 32 6.3 Hit-or-Miss Generator . 32 6.4 Simulating angular distributions . 33 6.4.1 The Results . 33 6.5 Results and Discussion . 35 7 Full Simulation Study with BES III 36 7.1 The pre-selection criteria . 38 7.2 The e+e− ΛΣ¯ 0 Reaction . 38 ! 7.2.1 Photon Selection . 40 7.2.2 The reconstruction of Σ¯ 0 ............................. 45 7.2.3 Selection of e+e− ΛΣ¯ 0 .............................. 48 ! 7.2.4 Predicted precision of R . 52 7.2.5 Angular Distribution of Σ¯ 0 ............................. 53 7.3 The e+e− Σ0Σ¯ 0 Reaction . 57 ! 7.3.1 Photon selection . 59 7.3.2 The Σ¯ 0 reconstruction . 60 7.3.3 Selection of e+e− Σ0Σ¯ 0 ............................. 61 ! 7.3.4 Predicted precision of R for the Σ0 in e+e− Σ0Σ¯ 0 reaction . 64 ! Summary 65 Appendices 67 A Noether Current 68 A.1 Isospin Operator . 68 iii Acknowledgement First of all, I would like to thank my thesis advisor Karin Sch¨onningof the Hadron Physics Group at Uppsala University for her support of my study and providing the opportunity for this project for me. I must express my profound gratitude to her, not only because of her academic support but also for her concern about other issues. I would also like to acknowledge Michael Papenbrock of the Hadron Physics Group at Uppsala University, for his technical help and support. Without his help, this project could last a long time. I would like to sincerely thank Magnus Wolke of the Nuclear Physics division at the Uppsala University as the subject reader of this thesis. I do appreciate his valuable comments on this thesis. iv Sammanfattning En av de st¨orstautmaningarna inom modern fysik ¨aratt f¨orst˚ade grundl¨aggandeegenskaperna hos hadroner och k¨arnori termer av QCD. Under det senaste decennierna har ett flertal experimentella och teoretiska metoder utvecklats f¨oratt studera hur kvarkar och gluoner innesluts i hadroner. Ett s¨attatt studera detta ¨aratt m¨atahadroners elektromagnetiska struktur. Denna kan kvantiseras i ter- mer av s˚akallade formfaktorer. Hyperoner ¨arett slags hadroner som liknar v˚arabyggstenar protonen och neutronen. Skillnaden ¨arat en eller flera l¨attakvarkar bytts mmot en tyngre s¨ar-,charm- eller bottenkvark. BESIII-experimentet i Peking, Kina, ¨aren av f˚afaciliteter d¨ar hyperonstruktur kan de- taljstuderas. Uppsalas hadronfysikgrupp ¨aren del av den internationella BESIII-kollaborationen och h˚allerf¨orn¨arvarande p˚aatt f¨orbereda en str˚altidsans¨okan f¨orprecisionsm¨atningarav den s˚akallade Sigma-hyperonens struktur. F¨orh˚allandenaf¨oren s˚adanm¨atning¨ar optimala vid en CMS-energi p˚a 2.5 GeV. Detta project syftar till att bidra till denna ans¨okan genom Monte Carlo-simuleringar av reaktionerna e+e− ΛΣ¯ 0 och e+e− Σ0Σ¯ 0. S¨arskiltfokus ligger p˚afotonerna fr˚anSigmabar0- s¨onderfallet.Uppl¨osningenoch! rekonstruktionseffektiviteten! har ber¨aknatsutifr˚ansimulerade data. v Abstract A central objective of the field of nuclear physics is understanding the fundamental properties of hadrons and nuclei in terms of QCD. In the last decade, a large range of experimental and theoretical methods have been developed to study the nature of quark confinement and the structure of hadrons which are composites of quarks and gluons. One important way to address some questions of hadron physics is studying the electromagnetic form factors of hadrons. The electric and magnetic form factors are related to the distribution of charge and magnetization in hadrons. The internal structure of hyperons, which are a subgroup of hadrons, is a topic of interest of particle physicists. The BES III experiment is one of the few current facilities for studying hadron structure. The Uppsala Hadron Physics group, which is a part of the BES III collaboration, is preparing a proposal for data taking for ΛΣ¯ 0 transition form factors and Σ0 direct form factors at 2:5 GeV. Aiming the electromagnetic form factors of Σ hyperons, this work contributes to this proposal by a simulation study of the e+e− ΛΣ¯ 0 and e+e− Σ0Σ¯ 0 reactions. The efficiency and resolution of the electromagnetic calorimeter! sub-detector of BES! III and kinematic properties of the detected particles are studied in this work. Our final goal is to provide input for the beam time proposal and optimize the future measurement. In the first chapter the theoretical background including the Standard Model, strong interaction, QCD and hadrons are studied. In the second chapter, some concepts like the formalism of cross section, relativistic kinematics and electromagnetic form factors are briefly presented. The third chapter is dedicated to introducing the e+e− ΛΣ¯ 0 and e+e− Σ0Σ¯ 0 reactions. The BES III experiment at BEPC-II is introduced in chapter! 4. In chapter 5, the! software tools which have been used for this work are introduced. In the sixth chapter, the result of a toy-Monte Carlo study for parameter estimation is presented. The last chapter is dedicated to the results of a full BES III software simulation. 1 Chapter 1 Introduction 1.1 Aim Understanding the four fundamental interactions - gravitational, electromagnetic, weak and strong interactions - has been the main purpose of contemporary physics. In spite of a fact that the Standard Model (SM) has been successful in describing the particles interactions up to energies around 100GeV and it is accepted as the more fundamental theory of particle physics, it leaves many questions unanswered. These questions are usually categorized into two groups: one is related to possible new particles at unexplored energy scales and the other to non-perturbative phenomena of the strong interaction. It is suggested that new particles and new interactions appear at higher energies, can say 1 TeV, solve some inconsistencies within the SM. Such physics subjects belong to the first category of questions and are addressed at the Large Hadron Collider (LHC) [1]. The non-perturbative effects of the strong interaction are very basic to the field of particle physics and include e.g. the structure of hadrons (for instance, hyperon form factors) and the spectrum of hadronic states. To address these questions we need lower energy facilities with high luminosity. Getting information about the structure of hadrons help us to find the answer for some fundamental questions like: How are quarks confined into hadrons? How does the strong interaction generate the rest 99%? Only 1% of nucleon mass is generated by quarks mass. How is the total spin of nucleons generated? only 1/3 of total spin of nucleons is from sum of the spin of the valance quarks. The Beijing Spectrometer (BES III) experiment is a facility for studying hadron physics. In BES III the electron and positron beams collide and annihilate with the subsequent production of hadrons. The BES III has collected an unprecedented amount of data dedicated to hadron structure studies. Electromagnetic form factors quantify the inner structure of hadrons. Besides the theory and experiment, Monte Carlo simulations are helpful in understanding, preparing and calibrating real experiment and interpret the result from it. 2 1.2 The Standard Model The Standard Model (SM) is a theory of particle physics which describes the strong, electromagnetic and weak interactions of elementary particles in a quantum field theory framework. The strengths and ranges of fundamental forces are listed in table 1.1. The SM explains the quarks and leptons which are fermions, and the interactions between them which are mediated by gauge bosons. The types of quarks are referred to as flavor of quarks like up and down (u and d) flavors. The SM contains three generations of fermions (Fig. 1.1). The first generation, which consists of u and d quarks (the lightest quarks), electron and electron neutrino , constitutes most visible matter in the universe. The second and third generations are only observed in very high-energy environments like particle accelerators and cosmic rays. The members of the first generation have lighter mass than corresponding particles from higher generations [2]. The SM also contains the gauge bosons photons (γ), gluons (g), Z0 boson and W ± bosons. The elementary fermions interact by exchanging these gauge bosons. The electromagnetic force is carried by photons while Z and W bosons mediate weak interactions [3, 4]. The gluons are the force carriers of the strong interaction [5]. The SM has been successful in describing and predicting a wide range of experimental observations.
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