Coherent Double Neutral Pion Photoproduction

Transcription

1 UNIVERSITY OF BASEL MASTER THESIS Coherent Double Neutral Pion Photoproduction Author: Michael GÜNTHER Schwarzwaldstr. 9a DE-7965 Schopfheim Supervisors: Prof.Dr. Bernd KRUSCHE Dr. Natalie WALFORD October 1, 215

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3 A search for a coherent double neutral pion signal from photoproduction of a deuterium target was performed. Data taken during December 27, February 29, and May 29 at the A2-Experiment at MAMI in Mainz, Germany has been analyzed. With Monte Carlo simulations of the detector setup, the detector efficiency was calculated. Thus, the total cross section from the deuteron was extracted.

4 Acknowledgements This work would not have been possible without the help and support of many people. I would like to mention a few of them. First, I want to thank Prof. Dr. Bernd Krusche for the opportunity to work in his research group and to write this work. He was always helpful and did not reject any of my questions during the work in his group. Also I want to thank Manuel Dieterle, not only for the often funny moments in the office, and the paid coffee, which was the fuel of this work, but especially for the introduction into the A2 simulation program and many other great tips during the analysis progress. Furthermore I also want to thank my fellow students Fabian Mueller and Samuel Abt, for a lot of help with the programming aspects of this work and many hours of discussions of our results and problems. Also I want to mention Natalie Walford for helping me regarding writing in the English language. Additionally I want to thank Alexander Käser for setting up the whole programming environment, and many many hours of bug fixing (and at least many hours of common curse). A special thanks to my whole family. Without the help of my parents and my sister, It would never have been possible for me to study physics and to get this far. Michael Günther IV

5 Contents List of Figures List of Tables IX XI 1. Introduction and Motivation Particles The Standard Model of Particle Physics Hadronic Particles - Mesons and Baryons Quantum Chromodynamics - Possible Particles The ABC-Effect Photoproduction of Mesons Coherent Double Neutral Pion Photoproduction Theoretical Background and Reconstruction Methods Special Relativity for Particle Production Basic Ideas of Special Relativity Kinematics Cross Section Differential Cross Section Experimental Setup The MAMI Electron Accelerator Detector System Crystal Ball PID TAPS VETO Glasgow Photon Tagger V Contents

6 Contents 3.3. Liquid Deuterium Target Data Acquisition Beam Time Overview Analysis Software ROOT PreAnalysis with AcquRoot OSCAR Analysis Geant4 and MonteCarlo Simulations Data Analysis Tagger Photon identification Energy and time calibration Presort with AcquRoot Event Selection Stucked Deuterons Pion identification and reconstruction Analysis level after the Presort algorithm OSCAR detail analysis Stucked Deuteron Coplanarity BacktoBack Invariant Mass of Pions Missing Mass of Deuteron Graphical Time of Flight Cut Data Corrections Crystal Ball Energy Sum Corrections Background Correction Detection Efficiency Data Merging Results Total Cross Section Conclusion 69 Michael Günther VI

7 Contents 8. Declaration on Scientic Integrity 71 Bibliography 73 A. Appendix 75 A.1. Kinematic Cuts A.1.1. Coplanarity A.1.2. Back to Back A.1.3. Invariant Mass of Pions A.1.4. Missing Mass of Deuteron VII Contents

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9 List of Figures 1.1. The ABC Effect The main setup of the A2-Experiment. Figure taken from [17] Floorplan of MAMI facility. Figure taken from [9] Sketch of a Race Track Microtron. [3] CB and TAPS setup Scheme of Crystal Ball Crystals TAPS Configurations Target Cell Random Background subtraction. Photon Tagger Back to back of stucked deuterons Coplanarity Cut Coplanarity of stucked deuterons Back to Back Back to back Cut Invariant mass Cut Missing Mass Cut Time of flight Simulation and Data Time of flight cut position CB Energy sum correction Detection Efficiency Cross Sections E() Cross Section Merged E() Cross Sections W Cross Section Merged W A.1. Coplanarity Dec IX List of Figures

10 List of Figures A.2. Coplanarity Feb A.3. Coplanarity May A.4. Back to back Dec A.5. Back to back Feb A.6. Back to back May A.7. Invariant Mass Dec A.8. Invariant Mass Feb A.9. Invariant Mass May A.1.Missing Mass Dec A.11.Missing Mass Feb A.12.Missing Mass May Michael Günther X

11 List of Tables 3.1. Summary of MAMI electron accelerators [17] Beam Time overview Different energy calibration methods XI List of Tables

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13 1. Introduction and Motivation For centuries, two of the most fundamental questions are regarding elementary particles and the fundamental forces. How many particles and fundamental forces do exist? How can the elementary particles and the fundamental forces be described? Up to now, there are still many open questions. Many different theories and concepts try to help understand the complexity of our universe. In the field of particle physics, the strong nuclear force, or strong interaction, is one of the most interesting things to study. Responsible for the building of nuclei or hadrons, the strong interaction is of great interest. This work aims to contribute a small portion to solve the secrets of the strong interactions Particles Physicists divide particles into two major groups: the group of elementary particles and compound particles. Elementary particles are indivisible whereas compound particles, such as the proton, consist of a mixture of other particles and can be divided. In the beginning of the 2th century, the list of elementary particles was small. Only protons, neutrons and electrons were known. Today, within the theory of the Standard Model of particle physics, 17 different elementary particles are identified. With particle experiments, mostly at particle accelerators six quarks were discovered. Quarks are considered to be elementary as, up to now, no excited quark states have been found. The six known quarks are referred to as up, down, strange, charm, bottom, and top quark. It was discovered that proton and neutron are part of a particle family referred to as hadrons. Hadrons are a composite made up of two or three quarks. Besides the electron and the electron-neutrino, four similar particles were found. These six particles are referred to as leptons and are the electron, electron-neutrino, muon, muonneutrino, tau, and tau-neutrino. As the quarks, the leptons are considered to be elementary. 1 CHAPTER 1. INTRODUCTION AND MOTIVATION

14 1.1. PARTICLES Additionally, for each lepton and quark, an antiparticle exists. Antiparticles do have the same mass and spin as their particle counterpart, but the electric charge, and other chargelike quantities are inverted. Besides the newly discovered particles and antiparticles, also the understanding of the fundamental forces has changed dramatically. Today, four fundamental forces are known: the gravitational force, electromagnetism, weak interaction, and the strong interaction. Beside gravity, all other three fundamental forces are described by the Standard-Model of particle physics The Standard Model of Particle Physics The Standard-Model of particle physics is a gauge quantum field theory based on the internal symmetries of the unitary product group SU(3) C SU(2) L U(1) Y. The Standard- Model explains the existence of nearly every particle known up to now and also the interactions between them. In this modern concept, interactions between the particles are mediated by gauge bosons. Each of the three forces, described in the Standard Model, is mediated by its own gauge boson. The electromagnetic force is mediated by photons, the weak interactions by Z and W ±, and the strong interaction is mediated by gluons. Within quantum field theory of the Standard Model, spontaneous symmetry breaking, and there the masses of the particles are explained. Within the explanation of spontaneous symmetry breaking a combination of the weak and electromagnetic interactions to the electroweak theory is performed. Also a new particle, the Higgs-boson was postulated. In 212, scientists from the LHC-experiments at CERN were able to confirm the existence of of a new boson. It seems likely that this new boson is in fact the famous Higgs-boson [6]. Today, it is well known that the Standard-Model is not a complete theory of fundamental interactions. Limitations of the standard model are, for example, the missing neutrino masses, missing dark matter, the lack of dark energy, and it does not include the gravitational force and therefore the concept of general relativity. Nevertheless, the Standard-Model has demonstrated a huge success by providing many experimental results. The best known predictions are the top quark (discovered in 1995), the tau neutrino (2), and the Higgsboson (likely to be discovered in 213). Michael Günther 2

15 1.1. PARTICLES Hadronic Particles - Mesons and Baryons As already mentioned, the proton is a composite of quarks. The proton is formed by two up-quarks in combination with a down-quark, notated as (uud). Particles, consisting of quarks, such as the proton, are called hadrons. Beside the baryons, which consist of three quarks, also the existence of mesons is known. Mesons consist of a quark anti-quark pair. The positive charged pion, for example, is built by an up-quark and an anti-down-quark, notated as (u d). All hadrons are effected by the strong interaction, and are therefore described by Quantum Chromodynamics (QCD) Quantum Chromodynamics - Possible Particles The non-abelian gauge theory which explains the strong interaction, is QCD. QCD describes the interactions between quarks and gluons, which then form hadrons, such as protons, neutrons, or pions. The fundamental symmetry group of QCD is the SU(3) C. Quarks and anti-quarks are represented by the fundamental representation (3), which means they form a triplet within QCD. Gluons, which are the exchange particles of the strong interaction, contain an octet of fields and belong to the adjoint representation (8) of the SU(3) C. All other known particles belong to the trivial representation (1). As a consequence, gluons and quarks carry a QCD charge and all other elementary particles do not. Therefore, the other elementary particles are not effected by the strong interaction at all. The charge of QCD, somehow equivalent to the electronic charge of quantum electrodynamics (QED), is color charge. Between the charges of QED and QCD there is a huge difference. The photon as the exchange particle of QED is not carrying electronic charge itself, but the gluon is carrying color charge. For QED, this means that the electric force has an infinite range. For two electric charged particles, the electric field between them is losing its power with growing of the distance between them. For QCD on the other hand, the charged exchange particle leads to a phenomena called confinement. For two color charged particles, the force between the particles is constant, regardless of the distance between the particles. This leads to a certain point where it is more favorable to form a new quark-antiquark pair. In consequence, it is not possible to create an isolated color charged particle. Every "free" particle has to be of neutral color charge. 3 CHAPTER 1. INTRODUCTION AND MOTIVATION

16 1.2. THE ABC-EFFECT Up to now, the only known bound particles of quarks are baryons and mesons. However, there are many theories which predict bound states of quarks with more than three quarks, such as tetraquarks or pentaquarks. One way of forming these so called exotic hadrons would be a dibaryon. A dibaryon is hypothetical particle formed by six quarks of any flavour. One goal of this work is to search for the evidence of the existence of a dibaryon within the total cross section of the photon induced reaction + d d + π + π The ABC-Eect In 196s, the scientists Abashian, Booth, and Crowe found an enhancement in the ππinvariant mass spectrum of the double pion fusion reaction pd 3 Heππ [11]. They measured the spectra of the 3 He in pd 3 He + X and discovered an enhancement at M x 3 MeV. In Figure 1.1, the enhancement is visible at the black arrow [1]. The enhancement got named after the initials of the authors of the first publication, ABC-Effect. Over time, many different theories tried to explain this enhancement, however many of them were proven wrong. One of the still possible explanations of this enhancement uses a bound six-quark particle called the d (238) resonance. Recently published results of the WASA-at-COSY Collaboration did provide the idea of an exotic quark system being responsible for the enhancement [8] Photoproduction of Mesons Photoproduction of mesons has become the most important tool for physicists studying the strong interaction in nuclei, especially in the energy regime in which the strong interaction can no longer be consistently calculated by using perturbation theory. In fact, in these regimes, lattice gauge theories are used to describe the interaction inside a nuclei. The usage of photon induced mesonproductions is only possible due to modern high accuracy detector system and electron accelerators. As the cross sections of photoproduction of mesons are up to three magnitudes smaller than hadron induced reactions, the ability to produce photon beams with high enough flux was necessary to start studying meson Michael Günther 4

17 1.3. PHOTOPRODUCTION OF MESONS Figure 1.1.: Shown is the 3 He momentum spectra for a incoming proton energy of 743 MeV. The solid curves show the calculated phase space function for the 3 He momentum spectra. The dashed curves show the best fit version of this function. At the black arrow, the enhancement referred to as the ABC effect is visible. This picture was taken from [1]. 5 CHAPTER 1. INTRODUCTION AND MOTIVATION

18 1.3. PHOTOPRODUCTION OF MESONS production induced by photons. Two of the accelerator/detector combinations which are currently able to perform high accuracy measuring of meson photoproduction are located at ELSA in Bonn, Germany and MAMI in Mainz, Germany [2]. In fact, most of the nucleon resonances were found with hadron induced reactions. But many resonances couple only weakly to pions or kaons. This leads to the situation that some of the nucleon excited states could not be investigated at all. The need for an alternative was given. Photoproduction off nuclei was then, with better experiments, the most beneficial way of coupling to those resonances. Electromagnetic induced meson production off nuclei can be separated into three main reaction types. These are: coherent reactions: + A X A X + m incoherent reactions: + A X A X + m X + + m break up reactions: + A X A n X + n N + m Where X is an arbitrary target nuclei with atomic number A. N is the nuclei fragment knocked out of the nuclei X with atomic number n. m is the produced meson. For break-up reactions, at least one nucleon is removed from the target nuclei which leads to a radical change of the target nuclei. Break-up reactions include quasi-free meson production. In these special cases, the photon interacts with only one nucleon as the other nucleons are only acting as spectators. However, the validity on the act as spectator drops with higher nuclei mass, as final state interactions (FSI) and other interactions contribute. Break-up reactions are, for example, used to study in-medium properties of hadrons or FSI of the produced mesons. In incoherent reactions, the target nuclei is left in an excited state. Typically, the deexcitation comes with an emission of -radiation. Incoherent reactions provide the possibility of studying the -in-medium properties and could give access to nuclear transition form factors. However, due to very small reaction cross sections these reactions are mostly unexplored. In coherent reactions, the target nuclei remains unchanged. The typical cross sections are still small, but not as small as for incoherent reactions. Therefore, a few experiments have already been done, but not as much as for break-up reactions. The study of coherent meson photoproduction provides, for example, information about meson-nucleon bound states or the in-medium properties of the (1232) resonance [1]. Michael Günther 6

19 1.3. PHOTOPRODUCTION OF MESONS Coherent Double Neutral Pion Photoproduction Within the last decades many possible bound states for quarks within the QCD were excluded, with only a few possible candidates for exotic multi-quark systems remaining. In the meson sector, the x,y, and z states, found at e + e -Rings and at LHCb, are candidates for exotics. One of these candidates is the dibaryon. Prediction were made that within the rise of the total cross section of coherent double neutral pion photoproduction, a peak at E = 573 MeV should be found. With the existence of such a peak another evidence for the existence of the dibaryon could be found. 7 CHAPTER 1. INTRODUCTION AND MOTIVATION

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21 2. Theoretical Background and Reconstruction Methods In this chapter, the most important tools for the reconstruction of particles out of the experimental data and the final extraction of the cross section is explained. This will include concepts of special relativity, as well as some basic statistical problems, which appear in accelerator experiments Special Relativity for Particle Production Within the analysis of scattering experiments, the most important tool is special relativity. In the energy region in which the experiment at MAMI is performed, the conditions for a relativistic approach is easily fulfilled. Therefore, the most basic kinematics will be calculated using Einstein s concept of special relativity. In this section, the most needed calculations and results are shown, which will later be needed to analyze the experimental data and to decide if a certain cut is useful or not. As already mentioned earlier, in coherent reactions the target nucleus stays unchanged (except for momentum transfers). This however, leads to a few conditions which will make the calculation much easier. Due to the reaction taking place on the nucleus itself, the Fermi momentum does not affect the reaction at all, which means it can be ignored for the missing mass, angular distribution, and energy threshold calculations. 9 CHAPTER 2. THEORETICAL BACKGROUND AND RECONSTRUCTION METHODS

22 2.1. SPECIAL RELATIVITY FOR PARTICLE PRODUCTION Basic Ideas of Special Relativity Up to this date, the concept of special relativity is the best theory to describe the laws of motion, regardless of the speed of the particle. However, the older classical mechanics are still very useful since for slower velocities, it is very accurate and it is much easier to calculate within Newton s laws of motion than with Einstein s concept. Nevertheless, special relativity is an unavoidable theory, especially for particle physicists. It is based on two postulates: 1. The laws of physics are the same (invariant) in all inertial systems (IS). This is also called the principle of relativity. 2. The speed of light in vacuum is the same for all observers, regardless of their speed or the speed of the IS. Numerous consequences follow these two postulates. However, only a few can be mentioned within this work. In the beginning, one may first look at the first postulate, the theory of relativity. One consequence is that there is no such thing as an absolute reference frame and one may switch between different IS as often as desired. The only thing to notice is that by switching between the IS, a Lorentz transformation must be used to calculate the transformation correctly. A reference frame consists of one time-like dimension and three space-like dimensions. On the first look, one may say that this is the same as for classical mechanics as there is also a time dimension and three space dimensions. However, within special relativity, there is no such thing as an absolute time and additionally, space and time are firmly related to the so called space-time. In special relativity, particles are described by a four-vector. A four-vector is a vector with four coordinates. As a convention, the first entry of a four-vector represents the time dimension and the last three are the "normal" space dimensions. This leads the following convention for a four-vector of a particle (in Minkowski space): c t ( ) x = x y = c t x. z where c is the speed of light, t the time, and x, y, and z the space dimensions. Before writing the relativistic mechanics, one should define the metric tensor g µν in the Minkowski Michael Günther 1

23 2.1. SPECIAL RELATIVITY FOR PARTICLE PRODUCTION space: g µν = Law of Motion, Energy and Momentum Newton s first axiom, the law of inertia, can be written for the relativistic case as: p ν = const. or d dτ pν =. (2.1) Where p is the four-momentum vector, ν =, 1, 2, 3 is an index, and d dτ is the time derivative. Be aware that τ is not the absolute time, but the proper time. The proper time is different for different observers. The four-momentum can be written with the invariant mass of the particle m: p ν = mu ν = ( ) mc, m v 1 β 2 1 β 2 with β = v/c, and c being the speed of light. v is the three dimensional space vector. The conservation of the four-momentum of Equation 2.1 is a direct consequence of the claim for homogeneity of space-time. Newton s second axiom can be written as:, (2.2) d dτ pν = m duν dτ = Kν, (2.3) where K ν is a tensor and is related to Newton s second Axiom, the Minkowski force. Equation 2.3 is in fact the law of motion for a particle within relativistic mechanics. Now, one may look on a magnitude called dynamic mass. The dynamic mass, m τ, is related to the invariant mass m by: m τ = m, (2.4) 11 CHAPTER 2. THEORETICAL BACKGROUND AND RECONSTRUCTION METHODS

24 2.1. SPECIAL RELATIVITY FOR PARTICLE PRODUCTION where = 1. As one can see directly, this means that a particle will get heavier the 1 β 2 faster it travels. In fact, this also has the consequence that no particle wit rest mass m = can ever be accelerated to the speed of light. Another consequence of Equation 2.3 is the equivalence of energy and mass. It is known as E = mc 2. In fact, this is only the special case of a particle at rest, and should normally be written as: E = mc2 1 β 2. (2.5) As a consequence, massive particles can be created with the energy produced by particle collisions. In the following subsection "Kinematics", some special and important mechanical problems will be discussed which will be needed for the analysis of the experimental data and especially the reproduction of the produced mesons Kinematics Reaction Threshold The production threshold will be calculated in the labframe. The labframe is the reference frame where the experimental setup is at rest and usually all measurements are done. For the coherent reaction + d d + π + π, a photon in motion can be represented with the four-momentum vector p. The other participating particle will be the target deuteron, which is at rest. It is described by the fourmomentum vector p d. p = (E,,, E ) p d = (m d,,, ), where m d is the invariant mass of the deuteron and E is the photon energy. For the production of a new particle, the following inequation for the total invariant mass s has to be ful- Michael Günther 12

25 2.1. SPECIAL RELATIVITY FOR PARTICLE PRODUCTION filled: s > md + m m. (2.6) where m m is the invariant mass of the neutral pion pair. The square of the total invariant mass is: s = (p + p d ) 2 = 2E m d + m 2 d. (2.7) Now with Equations 2.6 and 2.7, it is possible to derive the needed threshold photon energy to be able to produce a pair of neutral pions: E threshold = m m + m2 m 2m d, (2.8) where the neutral pion mass m π = MeV [13] and the deuteron mass m d = MeV [13] this leads to a threshold photon energy of E = MeV. Reconstruction of Meson and Recoil Deuteron As a matter of fact, π cannot be detected directly, but the decay products can be detected. The π decays into two photons. Therefore, the information about the initial state photon and the target deuteron are known. The full four-vector of all four photons and the kinetic energy of the deuteron and its direction of flight, in the final state, are known. What is not known is the mass of the recoil particle as well as the four-vectors of both neutral pions. However, they can be calculated as best as possible. The meson reconstruction will be discussed next. The π meson will, because of its small lifetime, decay into two photons (branching ratio: [13] %) which can be seen with the detector system. Due to the fact that photons have an invariant mass equal to zero, their full four-momentum vector is known. Therefore, the 13 CHAPTER 2. THEORETICAL BACKGROUND AND RECONSTRUCTION METHODS

26 2.1. SPECIAL RELATIVITY FOR PARTICLE PRODUCTION four-momentum of the pion can be calculated using: ) ( E p π = p 1 + p f inal 2 = 1 + E 2 f inal p 1 + p 2, (2.9) where p π is the full four-vector of the pion, p 1 and p f inal 2 are the four-vectors of both f inal detected photons, E represents the energy of the particle, and p is the "normal" three dimensional momentum vector. The invariant mass of a particle can be written as: m 2 inv = p2 = E 2 p 2. (2.1) Be aware of the difference between p the four-momentum vector and p, which is the three dimensional momentum vector. Together with Equation 2.9 one can calculate the invariant mass of the reconstructed pion with: m π inv = (E 1 + E 2) 2 ( p 1 + p 2) 2. (2.11) For the reconstruction of the deuteron four-momentum vector, additional information is required. As already mentioned, the kinetic energy, as well as the direction of flight for the deuteron can be measured, but one can not get any information about the invariant mass of the deuteron candidate. Therefore, a missing mass analysis is required. As the relativistic four-momentum is a conserved quantity, one can use that the sum over all momenta is the same for the initial and for the final state: p initial + p dtarget = p d f inal + p 1 f inal + p 2 f inal + p 3 f inal + p 4 f inal (2.12) p initial + p dtarget = p d f inal + p π 1 + p π 2. (2.13) Solving for the deuteron final state four-momentum: ) p d f inal = p initial + p dtarget (p π + p 1 π 2. (2.14) So with Equation 2.14, one can calculate the four-momentum of the recoil deuteron. Additionally, the invariant mass of the recoil deuteron m miss, referred to as missing mass, can be calculated. Note that, p target = ( ). Then the missing mass can be calculated us- Michael Günther 14

27 2.2. CROSS SECTION ing: m miss = (E initial + m dtarget E 1 f inal E 2 f inal E 3 f inal E 4 f inal ) 2 ( p initial p 1 f inal p 2 f inal p 3 f inal p 4 f inal ) 2. (2.15) After the calculation, the missing mass is compared to the invariant mass of the deuteron. If the calculated missing mass does not lay within a certain range around the invariant mass of the deuteron, the event is rejected. Using Equation 2.11 and Equation 2.15 one is able to reconstruct all participating particles for the reaction channel Cross Section The main goal of this work was to extract the total cross section of the double neutral pion photoproduction on a deuteron target. The cross sections were calculated individually for each data set. Later on, they were merged using weighted average calculations. For the final cross section calculation, it is mandatory to know the detection efficiency of the detector setup. The detection efficiency is therefore calculated using the simulated data. For the detector efficiency ɛ(e ), one can simply count the positive events generated and the events detected. As the analysis cuts and filters could also reject some signal events, one should take into account how many events will go through the final analysis program. The equation used is then: ɛ(e ) = #Events going through analysis cuts + filters(e ) #Events generated(e ). (2.16) With the calculated efficiency, the cross section of the reaction can now be calculated. The cross section describes the likelihood of a reaction to occur within a scattering experiment. Historically it is measured in units of area and is denoted by σ. Generally, the cross section is described with: σ tot = #Reactions / time (#Projectiles / time) (#Targets / area). (2.17) For this experiment, Equation 2.17 is used in a slightly varied version: 15 CHAPTER 2. THEORETICAL BACKGROUND AND RECONSTRUCTION METHODS

28 2.2. CROSS SECTION σ tot (E ) = N good (E ) Φ(E )ɛ(e )Γ branch ρ Target, (2.18) where N good (E ) is the number of good events getting through the analysis filters dependent on the incident photon energy, Φ(E ) is the incoming flux of photons, Γ branch is the branching ratio of the π -decay into two photons (98.82%), and ρ Target is the target surface density. Tagging Eciency For the calculation of the flux of incoming photons, the tagging efficiency ɛ tagging of the Glasgow Photon Tagger is required. The Glasgow Photon Tagger is part of the experimental setup and is described in subsection "Glasgow Photon Tagger". Since it is not possible to measure the number of photons directly during the experiment, the tagging efficiency is measured and one can then calculate the number of incoming photons by measuring the number of incoming electrons. The tagging efficiency is: ɛ tagging = # #e ɛ PMT = N N e, (2.19) where ɛ PMT 1 is the detection efficiency of the photomultipliers used in the Glasgow Photon Tagger, N e the real number of electrons producing bremstrahlung photons, and N the number of photons produced. The tagging efficiency is measured prior to the actual data run. For this task, the electron beam coming from MAMI is set to a low intensity, such that every single photon flying into the experiment is measured by a special detector, which is moved directly into the beam. The incoming electrons are measured and then the percentage of the scattered electrons and the corresponding tagging efficiency can be calculated. Michael Günther 16

29 2.3. DIFFERENTIAL CROSS SECTION Target surface density The target surface density describes how many possible target particles are available for the photons to interact with. The surface density is defined as: ρ Target = ρ material l m d, (2.2) where ρ material is the material density measured in [g/cm 2 ], l is the target length, and m d is the nucleon mass of a deuteron. The target densitiy was b 1 for the December 27 and February 29 runs, and b 1 for the May 29 run Dierential Cross Section The total cross section is a global value that represents a reaction rate of a target, projectile, and reaction combination. In contrast, the differential cross section represents a function that measures the reactions rate depending on other quantities. Differential cross sections, for example, can be calculated depending on invariant mass distributions. The most common used differential cross section is depending on the angular distribution of the recoil particle. Therefore, Equation 2.18 changes to: dσ dω (E ) = N good (E, cos θ) Φ(E )ɛ(e, cos θ)γ branch ρ Target Ω. (2.21) Different to the previously described formula for the total cross section, are only the Θ dependency of N good and ɛ and Ω is the solid angular that is covered by each cos θ bin in the analysis. The usage of cos θ instead of the direct angle θ has the advantage that every bin covers the same solid angle range. As a consequence, Ω is defined as: Ω = 4π # cos θbins. (2.22) All other values are still the same as in Equation As you may notice, the total cross section can be calculated from the differential cross sec- 17 CHAPTER 2. THEORETICAL BACKGROUND AND RECONSTRUCTION METHODS

30 2.3. DIFFERENTIAL CROSS SECTION tion by integrating the differential cross section over the full solid angle: σ tot = 4π dσ dω. (2.23) dω Michael Günther 18

31 3. Experimental Setup Figure 3.1.: The main setup of the A2-Experiment. Figure taken from [17]. In this chapter, the experimental setup, which was used to obtain the data analyzed for this work, will be described. The data was taken by the A2-Real-Photon Collaboration in Mainz, Germany. Figure 3.1 shows the main setup used for the measurement. The 1.5 GeV electron beam from MAMI was used to produce a photon beam via bremsstrahlung. After passing the radiator, the electron beam was deflected by a dipole magnet and sent into the Glasgow photon tagger. Withing the tagger, the energy of the deflected electron was measured and therefore the energy of the corresponding photon is known. The photon beam then reaches the liquid deuterium target. Around the target, the PID (Particle Identification Detector) detector is built to obtain a identification of charged particles. 19 CHAPTER 3. EXPERIMENTAL SETUP

32 3.1. THE MAMI ELECTRON ACCELERATOR The main detector then is the Crystal Ball. The hole in forward direction of the nearly 2π detector is covered by the TAPS detector. Right in front of the TAPS, the thin VETO detector, which works as a charged particle identifier in the same way as the PID for the Crystal Ball, is mounted The MAMI Electron Accelerator Figure 3.2.: Floorplan of MAMI facility. Figure taken from [9] The MAinzer MIcrotron (MAMI) is a cascade electron accelerator. MAMI is able to provide Michael Günther 2

33 3.1. THE MAMI ELECTRON ACCELERATOR a polarized or unpolarized continuous electron beam. With the latest stage (HDSM), MAMI is able to provide beam energies up to 1.5 GeV. As the bunches of electrons at MAMI have very small spacing, which additionally is not resolvable by the detectors, a continuous beam state is reached. This suppresses the background from accidental coincidences inside the detector readout. In Figure 3.2, the floorplan of the MAMI accelerator is shown [9]. After leaving the sources, the electrons in MAMI have 611 kev and are then guided into the injector. The injector is a linear accelerator (linac) in which the electrons are brought to energies of 3.97 MeV. Afterwards, the electrons are guided into the first Race Track Microtron (RTM). In a cascade of three RTMs, the electrons are accelerated up to 855 MeV. In a race track microtron, the electrons are accelerated several times by the same linac. Therefore, the electrons are deflected by dipole magnets at each end of the linac. Each time the electrons pass the 2.45 GHz linac, they are accelerated by a constant fraction. Figure 3.3 shows a sketch of the RTM schematics. After several loops inside the microtron, the electrons reach a maximum energy the RTM is capable to give them. Such an energy cap is mostly set by the dipole magnets as the radii of the trajectories are increased with increased energy. Figure 3.3.: Sketch of a Race Track Microtron. [3] 21 CHAPTER 3. EXPERIMENTAL SETUP

34 3.2. DETECTOR SYSTEM The final stage of MAMI is the harmonic double sided microtron (HDSM or MAMI-C). This microtron is somewhat different to the other three used in Mainz. Due to higher energies, the radii of the electron trajectories will be increasing and therefore the magnetic field of the dipole magnets has to be increased as well. However, in Mainz a point was reached were another bigger RTM was not suitable or financeable. In the purpose of saving steel, the bending magnets of MAMI-C were split in half. Therefore, each magnet now deflects the electrons only by 9. This also gives the advantage that the electrons can be accelerated on both long sides of the microtron. With this last stage, MAMI is now able to produce a high quality and stable electron beam up to 1.5 GeV, with a possible current of maximum 1µA. In Table 3.1, key data of the MAMI electron accelerator is summarized. [16] [17] Injector RTM1 RTM2 RTM3 HDSM inject. energy 611 kev 3.97 MeV MeV 18 MeV 855 MeV extr. energy 3.97 MeV MeV 18 MeV 855 MeV 158 MeV σe 1.2 kev 1.2 kev 2.8 kev 13 kev 11 kev # of turns magn. field -.1 T.55 T 1.28 T T magn. weight t 91.2 t t 13 t linac lentgh 4.93 m.8 m 3.55 m 8.87 m 8.57 / 1.1 m Table 3.1.: Summary of MAMI electron accelerators [17] 3.2. Detector System The main detector system is the Crystal Ball/TAPS calorimeter. The combination with PID/VETO provides a high-precision measurement of mesons by detecting the decay photons with high efficiency. The individual parts are described in the corresponding section following here. The main setup is shown in Figure Crystal Ball The Crystal Ball (CB) is a nearly 2π particle detector. The CB is built as an icosahedron consisting of twenty identical triangular faces. Each major triangle consists of four minor triangles. Finally, each minor triangle consists of nine thallium doped sodium iodide Michael Günther 22

35 3.2. DETECTOR SYSTEM Figure 3.4.: The main detector scheme is shown. The hole of the Crystal Ball in forward direction is covered by the TAPS spectrometer. The figure is taken from [1] (NaI(Tl)) crystals, again shaped as a truncated triangular pyramid. The main scheme is shown in Figure 3.5. Although the geometry leads to 72 segments, the CB only consists of 672 NaI(Tl) crystals. This is due to the necessity of an entrance as well as an exit window for the photon beam. Therefore, 24 crystal positions are left open. Each crystal has a length of 4.6 cm, which corresponds to 15.7 radiation lengths. The Crystal Ball is divided into two hemispheres. This is mostly due to practical reasons, for example for maintenance work as the upper hemisphere can be lifted up. Each hemisphere is evacuated, on the one hand this leads to mechanical stability and on the other this is needed for the NaI(Tl) crystals, which are hygroscopic and therefore have to be protected from moisture. Outside of the hemisphere, photomultipliers (PMTs) are installed for each individual crystal. The optical coupling between the crystals and the PMTs are made with a glass window. Unfortunately, a part of the light is lost due to air gaps between the crystals, glass, and the PMTs. Photons lose typically 98% of their energy in 13 adjacent crystals. Therefore, the detector sees a "cluster hit". Other particles can not be stopped by the CB. Charged pions for example, can only be stopped if the pion energy is lower than 24 MeV, and for protons this energy cap is at a proton energy of 425 MeV. The polar angular acceptance of the CB is 23 CHAPTER 3. EXPERIMENTAL SETUP

36 3.2. DETECTOR SYSTEM Figure 3.5.: On the left-hand side, the main geometry of the CB detector with its 2 major and 8 minor triangles. On the right-hand side, the geometry of a single NaI(Tl) crystal is shown. Figure taken from [14]. between 2 and 16. The acceptance in the azimuthal angle is only slightly reduced by the gap between the hemispheres. [17] [12] PID Inside the Crystal Ball, surrounding the target, the Particle Identification Detector (PID) is mounted. The PID is a small detector built with 24 plastic scintillators, each with a length of 5 cm and 5 mm in thickness. They are mounted such that they will form a cylindrical tube around the target. Each of the 24 scintillators is readout by a corresponding PMT connected to a light guide. The PID covers the whole acceptance angular region of the CB. The PID was especially built and designed for the CB experiment in Mainz. The main task of the PID is to detect charged particles, or rather to mark them as being charged. The information about the deposited energy in the PID, together with the information deposited in the CB, can be used for particle identification. In a two dimensional E versus E plot, where the energy deposited in the PID ( E) is compared with the energy deposited in the CB (E), different particles have their "typical"-regions and can therefore be differentiated. [17] [12] Michael Günther 24

37 3.2. DETECTOR SYSTEM TAPS The Two Armed Photon Spectrometer (TAPS) forward wall was built in the 198s with the goal to perform high precision photon measurements. During this experiment, it was placed in the forward direction to cover the hole of the Crystal Ball. The TAPS wall consists of 384 barium fluoride (BaF 2 ) crystals. During February 29 and May 29 however, the two most inner rings were replaced by smaller lead tungstate (PbWO 4 ) crystals. This increases the handling at forward angles. For each BaF 2 crystal, four PbWO 4 crystals were mounted. Therefore, the new configurations was a total of 72 PbWO 4 plus 366 BaF 2 crystals. The configuration of February 29 and May 29 is shown in Figure 3.6. The BaF 2 crystals have a length of 22.5 cm, which corresponds to 12 radiation lengths. Again, nearly all photons, which reach TAPS, are stopped and detected. Charged pions are stopped up to a pion energy of 185 MeV and protons up to a proton energy of 38 MeV. A special property of the BaF 2 crystal is the ability to emit two components of scintillation light. The "fast" component provides a very good time resolution due to its fast decay time of only.9 ns and is therefore perfectly useful for the necessary time of flight (TOF) measurements. The "slow" component however, gives a good energy resolution because of a high light yield. The decay time of the slow component is about 65 ns. Furthermore, the two components alone can be used to differentiate between different particles. As the relative contributions of the slow and fast component are different for different particles, one can use this information for the Pulse Shape Analysis (PSA). Each crystal is read-out individually by a PMT. The PbWO 4 crystals have a smaller decay time of only about 1 ns. Therefore, they are better suited for the high rates at small forward angles. With the crystals having a higher density, smaller crystals could be used which leads to a even better position resolution. The length of the crystals is 2 cm, which corresponds to 22.5 radiation lengths. Unfortunately, due to the installation shortly before the beam times of February and May 29, the PbWO 4 crystals were not ready for use and therefore could not be used for this analysis. [17] [12] 25 CHAPTER 3. EXPERIMENTAL SETUP

38 3.2. DETECTOR SYSTEM Figure 3.6.: Geometry of the TAPS Configurations. This configuration was used in February and May 29 [17] Michael Günther 26

39 3.2. DETECTOR SYSTEM VETO The VETO particle identifier has the same use as the previously described PID. Installed in front of the TAPS spectrometer, it works as a charged particle identifier. In front of each TAPS crystal, a EJ-24 plastic scintillator is mounted. The VETO elements are read out by PMTs, which are connected with an optical fiber. Again, the information of the VETO can be used in the same way as the information from the PID. For this work, the VETO is sometimes used as a single detector. This is the case if a deuteron gets stuck in the VETO and doesn t reach the TAPS spectrometer. In chapter 4, more information about the analysis will be given. [17] [12] Glasgow Photon Tagger As described in section 3.1, MAMI is an electron accelerator and produces an electron beam which is guided into the A2-Experiment hall. However, within the A2 collaboration, a photon beam is used. This photon beam is produced in front of the Glasgow Photon Tagger. A radiator produces a photon beam via bremsstrahlung. The thin radiator was a 1µm copper foil or in the case of a Møller radiator, a combination of cobalt and iron called Vacoflux. Due to the heavy masses of the nuclei inside the radiator, only a few kev of the electron were transmitted towards the nuclei and can therefore be neglected. The energy of the produced photon, E, can then be calculated by: E() = E(e ind ) E(e scat ), (3.1) where E(e ind ) is the energy of the induced electron and E(e scat ) is the energy of the scattered electron. The energy of the induced electron comes directly from MAMI and only the information about the energy of the scattered electron is still required. This energy is provided by the Glasgow Photon Tagger (GPT). To avoid photon hits outside of the target, a collimator cuts of the photons which would not hit the target. All this leads to a spot size on the target of 1.3 cm in diameter. The GPT measures the energy of the scattered electrons by deflecting them with a large dipole magnet (weight 7 t). Using a maximum current of 44 A, the magnet produces a 27 CHAPTER 3. EXPERIMENTAL SETUP

40 3.3. LIQUID DEUTERIUM TARGET magnetic field of 1.9 Tesla. The main electron beam that did not interact with the radiator is led into a beam dump where a Faraday cup measures the electron beam current. The scattered electrons however, are deflected, according to their momentum, to different positions on a focal plane. On the focal plane, a ladder consisting of 353 EJ-2 scintillators is mounted. Each scintillator covers an equal energy range. From the position of the scintillator, the momentum/energy of the corresponding electron is deduced. As the single detectors are partly overlapping, 352 logical detectors lead to a resolution of 2-5 MeV for an incoming electron beam of 1.5 GeV. Each scintillator is read out by an individual PMT. Due to the 1/E() spectrum of bremsstrahlung production, the high electron energy region (low photon energy) can easily be saturated, which would cause radiation damage to the corresponding PMTs. To avoid this, the detectors for the highest electron energies were disabled. This leads to an energy range of the photons of 4-14 MeV. Finally, the photon flux, mentioned in section 2.2, is determined from the number of detected electrons and the tagging efficiency ɛ tagging = N /N e. [17] [12] 3.3. Liquid Deuterium Target For this experiment a deuterium was mounted inside the CB. To achieve a high density of scattering centers, the deuterium was used in a liquid state. Gaseous deuterium, which was kept in a storage tank, was cooled down to approximately 2 K. The liquid deuterium was led to a storage reservoir and later to the target cell. The target cell is a cylinder made of Kapton. For this work the length of the target cell was 4.72 ±.5 cm (beam times of December 27 and February 29) and 3.2 ±.3 (beam time of May 29). During the data run, the target cell was isolated by eight layers of a super-isolating foil (8 µm Mylar plus 2 µm aluminum). The target cell was then placed inside a carbon-fiber plastic tube. [17] [15] 3.4. Data Acquisition In this section, a short overview of the data acquisition will be provided. However, some details will be spared or just shortly mentioned. For more detailed information, it is Michael Günther 28

41 3.4. DATA ACQUISITION Figure 3.7.: Photo of the liquid deuterium target cell. Photo takem from [5] recommended to look for the corresponding section in the dissertation of D.Werthmüller ("Experimental Study of nucleon resonance contributions to η-photoproduction on the neutron") [17]. All the detectors and corresponding PMTs produce an analog signal. The data acquisition system stores all information provided by the detectors, digitalizes them, and finally stores them to digital files. Electronics are also needed for the experimental trigger, which decides if an event should be stored or not. Trigger The data acquisition system cannot record the data continuously. A finite time is needed for the readout and the digitalization. A trigger, which decides whether or not an event should be recorded, can keep the event rate and therefore the dead time of the detector system at a reasonable level. The dead time of the detector is the time window in which the integration process for the digitalization is running. During this time win- 29 CHAPTER 3. EXPERIMENTAL SETUP