Studies of PWO Crystals and Simulations of the p̅p →Λ̅Λ, Λ̅Σ0 Reactions for the PANDA Experiment

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(1)ACTA UNIVERSITATIS UPSALIENSIS Uppsala Dissertations from the Faculty of Science and Technology 88.

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(3) Sophie Grape. Studies of PWO Crystals and ¯ ΛΣ ¯ 0 Simulations of the pp ¯ → ΛΛ, Reactions for the PANDA Experiment.

(4) Dissertation presented at Uppsala University to be publicly examined in Polhemsalen, Lägerhyddsvägen 1, Ångströmlaboratoriet, Friday, October 30, 2009 at 10:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Abstract Grape, S. 2009. Studies of PWO Crystals and Simulations of the ¯pp ¯, ¯0 Reactions for the PANDA Experiment. Acta Universitatis Upsaliensis. Uppsala Dissertations from the Faculty of Science and Technology 88. 229 pp. Uppsala. ISBN 978-91-554-7605-2. The thesis comprises investigations of two topics related to the PANDA experiment at the upcoming FAIR facility in Darmstadt, Germany. The first part is dedicated to energy resolution and light yield uniformity studies of PWO crystals for the electromagnetic calorimeter. The second part of the thesis is dedicated to simulation studies of the ¯pp ¯ and the pp ¯ ¯ 0 reaction channels. Photon response measurements with one 3×3 crystal matrix of non-tapered crystals and one 5×5 matrix with tapered crystals have been performed at the MAX-Lab synchrotron facility in Lund, Sweden. Photon energies in the range of 13-84 MeV were used. GEANT4 simulations were performed in order to find the most suitable method for adding the energy contributions and for calibration purposes. The widths of the resulting experimental summed energy peaks were fitted using Novosibirsk distributions. The results show that the electromagnetic shower at 84 MeV is completely contained in transversal direction by the 5×5 matrix. Studies of the light yield uniformity were performed for crystals of three different shapes and different wrapping materials. The light yield as a function of distance between the point of energy deposition and the PM tube, was shown to be closely related to the crystal shape and the wrapping material. The ¯ pp ¯ channel was studied at beam momenta of 1.64 GeV/c, 4 GeV/c and 15 GeV/c, while ¯ pp ¯0 was studied at 4 GeV/c. In the simulations, both isotropic differential cross sections and forward peaked differential cross sections were used as input. The purpose of the simulations was to investigate how well the reaction channels can be reconstructed in the detector. Special interest was paid to the polarisation and spin correlations of the hyperons. The result is that there is acceptance for all values of cos over the full momentum range of the HESR for both channels. Using isotropic differential cross sections, the polarisation of ¯ and 0 as well as spin correlations between ¯ and ¯0 can be well reconstructed. Using the forward peaked differential cross section, the particles are more likely to go forwards in their respective directions in the CM-system, which makes it less likely to obtain events over the full angular range at high beam momenta.. Keywords: PANDA, antiproton, PWO, hyperon, lambda, simulation, polarisation, spin correlation. Sophie Grape, Department of Physics and Astronomy, Box 516, Uppsala University, SE-751 20 Uppsala, Sweden © Sophie Grape 2009. ISSN 1104-2516 ISBN 978-91-554-7605-2 urn:nbn:se:uu:diva-108441 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-108441) Printed in Sweden by Distribution: Uppsala University Library, Box 510, SE-751 20 Uppsala.

(5) Contents. 1. 2. 3. 4. 5. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 The Fermions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 The Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 The Constituent Quark Model . . . . . . . . . . . . . . . . . . . . . 1.2 PANDA Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Thesis Disposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The FAIR Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The FAIR Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Experimental Programs at FAIR . . . . . . . . . . . . . . . . . . . . . . . . The PANDA Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Target Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 The Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 The Micro Vertex Detector . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Central Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Charged Particle Identification . . . . . . . . . . . . . . . . . . . . . 3.1.5 The Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . 3.1.6 The Solenoid Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.7 The Muon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.8 Hypernuclei Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Forward Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The Dipole Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Forward Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Forward Particle Identification . . . . . . . . . . . . . . . . . . . . . 3.2.4 Forward Electromagnetic Calorimeter . . . . . . . . . . . . . . . 3.2.5 Forward Muon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . Electromagnetic Interaction in Matter and Crystal Energy Resolution 4.1 Interactions with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Energy Losses of Electrons and Positrons in Matter . . . . . 4.1.2 Photon Interactions with Matter . . . . . . . . . . . . . . . . . . . . 4.2 PbWO4 Scintillator Characteristics . . . . . . . . . . . . . . . . . . . . . 4.3 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Energy Resolution for PANDA . . . . . . . . . . . . . . . . . . . . . . . . Simulated Response of a Crystal Matrix . . . . . . . . . . . . . . . . . . . . . 5.1 Crystal Geometry and Simulations . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Fitting Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9 9 9 11 12 13 14 17 17 19 21 21 22 23 24 25 26 27 28 28 28 29 29 30 30 30 31 31 31 33 36 37 40 43 43 44.

(6) 5.2 Examples of Energy Depositions . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Raw and Summed Depositions of a 5×5 Matrix . . . . . . . . 5.2.2 The Effect of Noise and Threshold . . . . . . . . . . . . . . . . . . 5.2.3 The Effect of Wrapping Material . . . . . . . . . . . . . . . . . . . 5.3 Conclusions from the Simulated Responses . . . . . . . . . . . . . . . 6 Energy Resolution Measurements with PWO Matrices . . . . . . . . . . 6.1 Photon Beam Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 The MAX-Lab Facility . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 The MAMI Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Measurement Set-Ups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Set-Ups for the MAX-Lab Measurements . . . . . . . . . . . . 6.2.2 Set-Ups for the MAMI Measurements . . . . . . . . . . . . . . . 6.3 Read-Out Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Read-Out Electronics and Data Acquisition at MAX-Lab . 6.3.2 Read-Out Electronics and Data Acquisition at MAMI . . . 6.4 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Energy Ranges and Runs at MAX-Lab . . . . . . . . . . . . . . . 6.4.2 Energy Ranges and Runs at MAMI . . . . . . . . . . . . . . . . . 6.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Analysis of the 3×3 Matrix Data at MAX-Lab . . . . . . . . . 6.5.2 Analysis of the 5×5 Matrix Data at MAX-Lab . . . . . . . . . 6.5.3 Reanalysis of the 3×3 Matrix Data at MAMI . . . . . . . . . . 6.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Results from the 3×3 Matrix at MAX-Lab . . . . . . . . . . . . 6.6.2 Results from the 5×5 Matrix at MAX-Lab . . . . . . . . . . . . 6.6.3 Results of the MAMI Measurements . . . . . . . . . . . . . . . . 7 Light Yield Uniformity Tests of PWO Crystals . . . . . . . . . . . . . . . . 7.1 Set-Up for Uniformity Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Light Yield Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Pulse Height Scale Calibration for Old PANDA Crystals . 7.2.2 PM Tube Calibration for Forward Endcap Crystals . . . . . . 7.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Analysis Approach for Old PANDA Crystals . . . . . . . . . . 7.3.2 Analysis Approach for Forward Endcap Crystals . . . . . . . 7.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Old Type PANDA Crystals . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Forward Endcap Crystals . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Light Yield Uniformity Improvements . . . . . . . . . . . . . . . . . . . 7.6 Implications of αNH for the Energy Resolution . . . . . . . . . . . . . 8 Hyperon Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Hyperon Production Mechanisms . . . . . . . . . . . . . . . . . . . . . . 8.2 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Differential Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . ¯ Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Λ. 46 46 50 53 55 57 57 57 59 60 60 61 62 62 64 64 64 65 65 66 72 78 81 82 90 104 109 109 111 112 113 114 114 115 117 117 120 125 127 131 132 133 135 135.

(7) ¯ .............................. 8.4 Spin Observables in ΛΛ 8.5 The Software Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6 Data Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.1 Criteria and Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8.1 Detector and Detection Efficiency . . . . . . . . . . . . . . . . . . 8.8.2 Invariant Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ¯.................... 8.8.3 Differential Cross Sections of Λ 8.8.4 Reconstruction of Decay Vertices . . . . . . . . . . . . . . . . . . . ¯ ......... 8.8.5 Momentum and Vertex Reconstruction of ΛΛ 8.8.6 Reconstruction of cτ . . . . . . . . . . . . . . . . . . . . . . . . . . . . ¯ Polarisation Reconstruction . . . . . . . . . . . . . . . . . . . . . 8.8.7 Λ ¯ 8.8.8 ΛΛ Spin Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8.9 Σ0 Polarisation Reconstruction . . . . . . . . . . . . . . . . . . . . . 9 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Crystal Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Hyperon Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Summary in Swedish - Svensk sammanfattning . . . . . . . . . . . . . . . 10.1 Vad är hadronfysik? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 PANDA-experimentet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Avhandlingens innehåll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ¯ .................. A.1 Acceptance Distributions for pp ¯ → ΛΛ ¯ 0 ................. A.2 Acceptance Distributions for pp ¯ → ΛΣ Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 137 140 140 141 142 142 142 145 146 150 154 162 165 176 179 187 187 189 190 191 191 192 192 195 195 214 223 225.

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(9) 1. Introduction. Hadron physics deals with one of the most challenging and fascinating problems in contemporary physics: the understanding of the strong force that binds together the elementary constituents (the quarks) into the particles we observe around us. Protons and neutrons are the most familiar examples of hadrons; they are composite objects that build the atomic nucleus. The PANDA (antiProton ANnihilation at DArmstadt) detector is a state-ofthe-art detector that will allow studies of the strong interaction [1]. It will be located at FAIR (Facility for Antiproton and Ion Research) [2], a future international science centre located outside of Darmstadt, Germany. The PANDA collaboration includes over 50 institutes in 16 countries with more than 400 physicists, all working to get the detector in shape for commissioning in late 2014. The FAIR accelerator complex will include a High Energy Storage Ring (HESR) [3] for antiprotons where the PANDA detector will be installed.. 1.1. Theoretical Background. The Standard Model (SM) is a theory that describes the 12 fundamental particles that we know of and three of the four known interactions between them. It has been very successful at describing, explaining and predicting many experimental observations. This chapter aims at describing some of the content of this model.. 1.1.1. The Fermions. The Standard Model contains three generations of fundamental particles with half-integer spin, also known as f ermions. The fermions are subdivided into two groups, called quarks and leptons. Properties of these particles are listed in table 1.1 and 1.2, respectively. The first generation of fermions contains the up (u) and the down (d) quark, two quarks with opposite electric charge. They constitute the proton (a uudconfiguration) and the neutron (a udd-configuration), the building blocks of matter around us. The charges of the proton and the neutron lead to the conclusion that the charge of the up quark must be +2e/3 and the charge of the down quark -e/3. The atomic nucleus, made up of protons and neutrons, is surrounded by a cloud of electrons. The electrons, together with the electron. 9.

(10) neutrino (νe ), also belong to the first generation of fermions and both are examples of so-called leptons. The electron neutrinos are very light particles that are created and annihilated together with the electrons. The neutrinos interact weakly and are created in outer space, in the atmosphere or via radioactive decays. The second generation of fermions comprises the charm (c) and the strange (s) quarks together with the muon (μ− ) and the muon neutrino (νμ ). The two quarks have the same electric charge as the up and the down quark, respectively, but much larger masses, see table 1.1. Also the muon is heavier than the electron. The third fermion generation is made up of the top (t) and the bottom (b) quarks as well as the tau (τ− ) and the tau neutrino (ντ ). The fermions of this generation are much heavier than the fermions in the second generation. Each fermion has a corresponding antifermion with the same properties as the fermion, but with opposite electric charge.. Table 1.1: The six quarks with some of their properties [4]. The masses cannot be measured directly due to confinement, but are determined through their influence on hadronic processes.. Generation. Name. 1. Up (u) Down (d) Charm (c) Strange (s) Top (t) Bottom (b). 2 3. Charge (e). Mass [GeV/c2 ]. Spin. +2/3 -1/3 +2/3 -1/3 +2/3 -1/3. 0.0015-0.0033 0.0035-0.006 1.16-1.34 0.07-0.13 171.3±1.1±1.2 4.13-4.37. 1/2 1/2 1/2 1/2 1/2 1/2. Table 1.2: The six leptons and some of their properties [4].. Generation. Name. 1. Electron (e− ) Electron neutrino (νe ) Muon (μ− ) Muon neutrino (νμ ) Tau (τ− ) Tau neutrino (ντ ). 2 3. 10. Charge (e). Mass [MeV/c2 ]. Spin. -1 0 -1 0 -1 0. 0.511 < 2 · 10−6 105.7 < 0.19 1777 < 0.0182. 1/2 1/2 1/2 1/2 1/2 1/2.

(11) 1.1.2. The Interactions. The SM describes three of the four fundamental interactions between the particles listed in table 1.1-1.2: the strong, the weak and the electromagnetic interaction. The fourth interaction, gravity, is not included, based on it being (by far) the weakest of them at the level of hadron physics. The exchange particles of the weak force are the massive neutral Z boson and the charged flavour changing W ± bosons. This force is perhaps most widely known for causing radioactive β-decay and is important only at small distances due to the large mass of the mediating bosons. The time scales of particles decaying with the weak force are of the order of 10−7 − 10−13 s. The electromagnetic force has infinite range, acts between electrically charged objects and is mediated by the massless photon. This force is responsible for keeping the electrons in orbit around the nucleus as well as for binding atoms together in molecules. States which decay by this mechanism usually have lifetimes around 10−16 − 10−21 s. The strong force is responsible for keeping together the quarks in the nucleons, and the nucleus itself. It is mediated by the massless gluons and acts on a charge called colour. Colour charge is only carried by the quarks and the gluons and it comes in three varieties named red, green and blue (or anti-red, anti-green and anti-blue). Quarks carry colour while gluons carry both colour and anticolour. This type of charge explains how the Ω− -baryon with three s-quarks and the Δ++ with three u-quarks can exist. With spin 3/2 and relative angular momentum equal to 0, the wave function for these states is completely symmetric and thus forbidden by the Pauli exclusion principle1 . An antisymmetric state can only be created with the three, otherwise identical, quarks if they are in different colour states. The quantum theory that describes this interaction is called Quantum Chromo Dynamics (QCD). In contrast to the electromagnetic force where the mediating photons are electrically neutral, the mediating bosons of the strong force are able to interact with themselves. The strength of the interaction is dependent on the energy scale. At high energies and small distances, the quarks in the hadrons only feel a very weak force and experience what is called asymptotic freedom. In this scenario, a perturbative treatment of QCD as a theory of the strong interaction is possible. At low energies and distances comparable to the hadronic scale (10−15 m), the quarks are confined in composite objects, hadrons, and a non-perturbative treatment of the theory is necessary. The range of the strong force is about 10−15 m and the decay times are typically 10−22 − 10−24 s. At the hadronic scale, processes are dominated by the strong interaction. Effects of the weak force are only visible if the strong and electromagnetic interactions are forbidden due to conservation laws. 1 The. Pauli exclusion principle applies to all fermions and says that identical such particles can not occupy the same quantum state simultaneously.. 11.

(12) 1.1.3. The Constituent Quark Model. Only colour neutral objects are observed in nature; a free quark or a single gluon has never been seen. The constituent quark model offers a description of how quarks can be combined into colour neutral objects, hadrons. There are two families of hadrons, distinguishable by their valence quark content. The mesons are made up of one quark and one antiquark (qq) ¯ and hence carry integer spin, while the baryons are made up of either three quarks or three antiquarks (qqq or q¯q¯q) ¯ and therefore carry half-integer spin. The proton and the neutron are two examples of baryons. 1.1.3.1 Symmetries and Conservation Laws There are quantum numbers and corresponding conservation laws that define the allowed configurations for the hadrons. Much like in atomic physics, hadronic systems are described by these numbers. Some examples are the principal quantum number (for radial excitations) n, the angular momentum of the system L, the intrinsic spin S and the total spin J. These can be combined to the spectroscopic notation 2S +1 L J . Other quantum numbers are the isospin T, the parity P (which describes the symmetry under spatial inversion) and the charge conjugation C that describes the symmetry under charge inversion. Given the opposite parity between fermions and antifermions, the total parity of a system of two or more particles is given by Pmeson = (−1)L+1 , Pbaryon = (−1)L12 +L3 ,. (1.1). with L12 and L3 being the internal angular momentum between two arbitrarily chosen quarks and the orbital angular momentum of the third quark about the center of mass of the pair, respectively. Similarly, the charge conjugation values for a system of two or more particles are given by Cboson = (−1)L , Cfermion = (−1)L+S .. (1.2). These quantum numbers can be used together with the total spin J to restrict the accessible quantum numbers for a hadronic system according to T (J PC ). If one were to discover particles having quantum numbers that cannot be explained by composite systems of the SM (qq ¯ and qqq/q¯q¯q), ¯ they would be referred to as “exotic”. Though many physicists believe they exist, no such particles have as of today been firmly established. One example of a possible exotic state is a glueball (a bound gluonic state), which may exist due to the self-interaction of the gluons. Another example is a hybrid, a qq-pair ¯ with an excited gluon. A conservation law exists because of a certain symmetry. The three forces in the SM have different symmetries and hence obey different conservation laws. The strong, electromagnetic and weak interactions conserve electric charge, 12.

(13) energy, momentum, angular momentum and baryon number. The strong and the electromagnetic interactions also conserve strangeness S (the number of squarks), parity P, time reversal T and charge conjugation C. Parity and charge conjugation is, however, not conserved in the weak interaction and even small violations of CP have been seen [5]. In addition, flavour and the third component of the strong isospin in the case of light quarks are not conserved by the weak process.. 1.2. PANDA Physics. PANDA is a general-purpose detector and there is a broad spectrum of physics objectives for future experiments. Performing hadronic spectroscopy in the non-perturbative regime is one of the main goals. This will be done using antiproton-proton collisions in a kinetic energy range from 0.8 GeV to 14 GeV, a scale which covers the transition region where quark-gluon degrees of freedom turn into hadronic degrees of freedom in the description of the strong interaction. This regime is poorly understood and PANDA is therefore well suited to address this question. Measurements at PANDA will benefit from the collisions with p¯ and p, allowing the observation of possible non-exotic states accessible already via formation mode where a resonance, which then decays to several particles is formed. This is a huge advantage compared to performing this type of experiments with an e+ e− -collider, where the quantum numbers of the intermediate photon, J PC = 1−− , determines that only states with the same quantum numbers can be directly created. Possible exotic states can be formed in production mode (directly together with other particles). The appearance of a state in this mode but not in formation mode is a clear sign of a state with exotic quantum numbers. Hybrids (qq ¯ pairs with an excited gluon) and glueballs (bound state entirely made of glue) are the simplest forms of possible exotic matter. The search for exotic states like glueballs [6] and hybrids [7] [8] in the charmonium mass region have a high priority since there are predictions that low lying exotic states could exist in this region. In charmonium, the bound state of c¯c, quark masses are comparable to the mass of the bound state (in contrast to states composed of only u-, d- and s-quarks). This makes it possible to apply non-relativistic QCD calculations. Perturbative calculations can also be performed for the system since the strong coupling constant αs is around 0.3 at this scale and hence small. The states are in addition generally narrow with small mixing effects below the threshold of open charm production, where the charmed quark pair must annihilate to create lighter quarks. The narrowness of the state is a huge advantage in searches for new and possibly exotic states [9]. In the last years, B-factories have reported so-called alphabet states (X-, 13.

(14) ¯ Y- and Z-states) above the DD-threshold [10] [11] [12] which do not seem to entirely fit into our present understanding of the charmonium spectrum based on the naive quark model where states are made up of either three quarks or a quark and an antiquark. Possible explanations for such states are hybrids, glueballs, di-quarks (a weakly bound system of two colour-singlet mesons in a wave function with an extension much greater than the mesonic radius [13]), molecular states (two loosely bound mesons [14]) and probably other configurations as well. Other aspects, besides c¯c-spectroscopy, of the PANDA scientific program are: • Interactions of charmed hadrons in the nuclear medium. State masses may change as a modification of the chiral symmetry breaking pattern of QCD due to the presence of the nuclear medium [15], • Non-perturbative dynamics including spin degrees of freedom in the hyperon sector [16], • Studies of single and double Λ hypernuclei to gain a better understanding for nuclear structure and the ΛΛ-interaction [17], • Studies of the time-like form factors of the nucleons and of the transverse parton distributions in Drell-Yan production [18], • Possibly at a later stage, also studies of direct CP-violation in hyperon decays and CP violation and mixing in the charm sector [19] [20] [21] [22].. Hypernuclei are nuclei where at least one nucleon has been replaced with a hyperon. Besides being a well-suited probe for nucleon structure (the hyperon is in contrast to the other nucleons not restricted by the Pauli principle in populating possible nuclear states) the structure of hypernuclei provides unique information about the spin-dependent hyperon-nucleon interaction. The investigation of double hypernuclei will allow an exploration of the hyperonhyperon interaction.. 1.3. Thesis Disposition. This thesis treats two topics in preparation for the first physics experiments with the PANDA detector. One is investigations of energy resolution and light yield homogeneity for PbWO4 -crystals. This type of crystal has been selected for use in both the barrel and endcap sections of the electromagnetic calorimeter. Its performance is very important to all physics channels where photons (with low as well as high energy) must be detected with high precision. One such example is the reconstruction of radiative decays of excited hyperons to light Λ and Σ0 states and excited hyperon decays to final states involving more than one photon. Another prerequisite for such experiments is the reconstruction of ground state Λ and Σ0 hyperons, which 14.

(15) is studied in the second part of this thesis. Simulations involve hyperon reconstruction and studies of hyperon spin observables. The thesis composition is presented below. Chapter 2-4 summarises the work done by others, while chapter 5-8 and the Appendix contains work done by the author. Chapter 2: The FAIR Facility The chapter presents the existing GSI and the upcoming FAIR facilities and mentions some of the experimental programs. Chapter 3: The PANDA Detector The PANDA detector layout with the target and forward spectrometers as well as the subdetectors therein is presented. Chapter 4: Electromagnetic Interaction in Matter and Crystal Energy Resolution The interactions of electrons and photons with matter are discussed and the scintillator material of the PANDA electromagnetic calorimeter is presented. The chapter also contains a section on possible contributions to the energy resolution when performing measurements with scintillating crystals. Chapter 5: Simulated Response of a Crystal Matrix This chapter contains simulations of response measurements with a 5×5 PWO matrix. The goal is to show what factors that influence the energy resolutions and what the results may be. Chapter 6: Energy Resolution Measurements with PWO Matrices This chapter describes energy resolution measurements performed and the results from those measurements. Two of the measurements were conducted at MAX-Lab in Lund, using a 3×3 and a 5×5 matrix, respectively. The third type of measurements were performed at MAMI in 2004 and a reanalysis of those measurements is done. Chapter 7: Light Yield Homogeneity Tests of PWO Crystals Here, the measurements and results of light yield homogeneity tests of PWO crystals are described. The data was analysed using two different methods and the results as well as a comparison between the methods are presented. Chapter 8: Hyperon Simulations ¯ and This chapter deals with simulations and reconstruction of the p¯p → ΛΛ 0 ¯ p¯p → ΛΣ channels, with emphasis on the spin observables. The chapter includes a reaction motivation and a description of how the simulations were performed, as well as the results of the analysis. Chapter 9: Summary and Conclusion This chapter summarises the work done in this thesis and contains both a conclusion and an outlook. Chapter 10: Summary in Swedish - Svensk sammanfattning This chapter contains a short, popularised version of the thesis summary. Appendix The Appendix contains a collection of acceptance figures from chapter 8. 15.

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(17) 2. The FAIR Facility. The FAIR acronym stands for Facility for Antiproton and Ion Research, and the project is today well on its way to becoming an international accelerator complex, located outside of Darmstadt in Germany, at the site of the existing GSI facility (figure 2.1). FAIR will comprise an integrated system of particle accelerators of high energy and high intensity beams for elements ranging from protons to heavy elements as uranium. FAIR is presently the largest research infrastructure on its way within Europe. The construction is planned to begin in 2010, with the commissioning of the facility and first experiments scheduled for 2014. The experimental programs will reach their full performance in 2016 with the completion of the facility [2].. Figure 2.1: Photograph of the existing GSI facility with surroundings in Darmstadt [23].. 2.1. The FAIR Facility. Today, the existing GSI facility includes a 120 m long UNILAC (a linear accelerator), a heavy-ion synchrotron called SIS18 and an experimental storage ring, ESR, for storing stable and radioactive beams, see figure 2.2. The synchrotron has a circumference of 216 m and 18 Tm maximum bending power. It can accelerate protons up to 4.5 GeV and the highly charged U78+ and Ne10+ up to 1.07 GeV/u and 1.92 GeV/u, respectively. For more information see [24]. 17.

(18) Figure 2.2: The existing GSI facility (shown in blue) with its UNILAC, SIS 18 and ESR, as well as the future FAIR facility (shown in red) [23].. The future facility will host two dedicated synchrotron rings (SIS100 and SIS300) with identical circumferences of 1100 m. They will be placed in the same tunnel 17 m below ground and have magnetic rigidities of 100 Tm and 300 Tm, respectively. The two rings will provide intensities of 3 · 1011 ions per second at energies of 1 GeV/u for heavy ions. SIS100 will be able to produce a pulsed uranium beam having approximately 5 · 1013 ions per pulse at 1 GeV/u, and a pulsed proton beam with an energy of 29 GeV and roughly 4 · 1013 particles per pulse. It is planned to operate this ring at a repetition rate of 1 Hz, i.e. with ramp rates of up to 4 T/s of the bending magnets for the high intensity mode. SIS300 will give high energy ion beams of energies up to 45 GeV/u for Ne10+ and almost 35 GeV/u for fully stripped U92+ beams. The new accelerator complex will house four additional storage rings: the Collector Ring (CR), the Accumulator Ring (RESR), the New Experimental Storage Ring (NESR) and the High-Energy Storage Ring (HESR). Antiprotons will be produced in inelastic collisions between high intensity proton beams from SIS100 having energies of 29 GeV and a target nucleus at rest. The target will be made of nickel, iridium or copper. Every ten seconds, 2 · 1013 protons will strike the target with a duration of 50 ns [25]. The CR will be used for storing beams created at the production targets (antiprotons up to 3 GeV) and nuclei with a mass/charge-ratio, A/q, equal to 2.7 at 0.7 GeV/u. The RESR will be used for containing and decelerating the antiprotons after they have been precooled in the CR. The NESR will have electron cooling of the radioactive and antiproton beams and extract them to the FLAIR experi18.

(19) ments [27]. The HESR, where PANDA will be located, can be operated in a momentum range from 1.5 GeV/c to 15 GeV/c. In this ring, the antiprotons will be cooled with electrons up to 8.9 GeV/c and stochastically up to their maximum momentum of 15 GeV/c [26]. For the high resolution and high luminosity modes, the momentum resolution is expected to be δp/p < 4 · 10−5 and < 10−4 , respectively [3]. A whole new generation of physics experiments will be conducted at FAIR. The radioactive beam intensities will, in conjunction with the new fragment separator, increase with a factor of 10 000 compared to today (at the SuperFRS) and the beam energies by a factor of 20. This translates into beams ranging from 0.4 to 1.5 GeV/u for all elements up to uranium. Plasma and atomic physics researchers will receive beam energies of 0.4-1 GeV/u ions and 1-10 GeV/u ions, respectively.. 2.2. Experimental Programs at FAIR. In the future, FAIR will provide thousands of scientists with the opportunity to study the following diversified fields [2]: • Hadron physics with antiprotons. This is where the PANDA experiment will be active, studying aspects of the strong interaction by investigating reactions where antiprotons are colliding with protons and nuclei, with the expectation of observing many new states and measuring masses and lifetimes (widths) of these and other strange- and charm states with unprecedented precision. Another collaboration which will be dealing with hadron physics is PAX [28]. They intend to use polarised antiprotons produced by spin filtering from an internal polarised gas target to study the transversity distributions of the proton valence quarks (the probability to find a transversally polarised quark inside a transversally polarised proton [29]). The FLAIR (Facility for Low-energy Antiproton and Ion Research) collaboration will perform spectroscopy of antiprotonic atoms for QED and CPT tests and nuclear structure studies with antiprotons as hadronic source. • Nuclear structure physics. The nucleus provides a unique opportunity for structure studies of complex systems where the strong, electromagnetic and weak forces are present. The structure studies will be conducted with rare radioactive isotope beams with unmatched intensity and composition. The NUSTAR collaboration aims at developing, constructing and operating the Super-FRS rare isotope beam facility and the related experimental set-ups. The Super-FRS is a superconducting fragment separator followed by experimental branches including a storage ring system. This system contains both the CR and the NESR, allowing for precision mass and lifetime measurements. Some of the experiments foreseen for the Super-FRS are:. 19.

(20) • R3 B (Reactions with Relativistic Radioactive Beams). Studies of nuclear reactions with exotic nuclei far from stability including shell structure and valence nucleon wave functions, nucleon matter radii and densities. It also includes astrophysical reactions inverse to those relevant for astrophysical r- and rp-processes (nucleosynthesis by rapid neutron and consecutive rapid proton captures) by using electromagnetic excitations at high beam energies. • HISPEC/DESPEC. Studies of the classical shell gaps and magic numbers with radioactive ion beams directed onto neutron- and proton-rich nuclei. • ELISe. The project that aims at supplementing the NESR with an intersecting electron ion ring to scatter 125-500 MeV electrons off exotic nuclei to perform elastic, inelastic and quasielastic scattering off shortlived radioactive isotopes for the first time. • Physics of nuclear matter under extreme conditions. This aspect of physics deals with what happens to matter as temperature and particle density change in such a way that a quark gluon plasma may be created. This type of physics will be the focus of CBM [31]. • Physics of the atomic shell. There are many (unconfirmed) predictions of the behaviour of the atomic shell under extreme conditions. Testing of the QED formalism at very strong electromagnetic fields can be done using highly-charged heavy ions. Antihydrogen will also be studied in order to investigate the relationship between matter and antimatter. The SPARC (Stored Particles Atomic Physics Research Collaboration) collaboration will perform investigations of extreme atomic conditions with highly-charged very heavy ions in an energy regime ranging from rest to relativistic energies. • Plasma physics. Bombarding solid materials with high-intensity pulsed heavy-ion beams or laser beams will make it possible to create plasma temperatures and densities similar to conditions in giant planets like Jupiter. This allows for a study of the bulk matter in the high density plasma states addressing fundamental questions of inertial confinement fusion [30].. 20.

(21) 3. The PANDA Detector. The PANDA-detector will be located at the HESR and is planned to be commissioned in 2014. It will have almost 4π acceptance and high resolution for track reconstruction and particle identification. The detector will be split into two parts, a target spectrometer (TS) and a f orward spectrometer (FS) for an optimum momentum resolution. The former will be surrounded by a superconducting solenoid magnet and measure large scattering angles, while the latter will use a dipole magnet for forward going tracks. Both spectrometers will provide charged particle identification, electromagnetic calorimetry and muon identification. The detector layout can be seen in Figure 3.1. Detailed information on the detector layout and expected performance is found in [32] and [33].. Figure 3.1: Layout of the PANDA detector with the target and forward spectrometers [33].. 3.1. The Target Spectrometer. The target spectrometer (figure 3.2) has a cylindrical geometry and will measure charged tracks and detect neutral particles using several subdetectors 21.

(22) placed in an onion configuration with a magnetic solenoid field of 2 T, provided by a superconducting solenoid. The central part will cover tracks with opening angles between 22◦ and 140◦ in the vertical plane. There is an endcap in the forward direction that covers the region down to 5◦ in the vertical and 10◦ in the horizontal plane.. Figure 3.2: Layout of the target spectrometer with the subdetectors marked [34].. The target spectrometer comprises several parts: internal target, solenoid magnet, Micro Vertex Detector (MVD), Straw Tube Tracker (STT) or Time Projection Chamber (TPC), Gas Electron Multiplier (GEM) detectors, Cherenkov detector/Time of Flight (ToF) system, Detector for Internally Reflected Cherenkov light (DIRC), an Electromagnetic Calorimeter (EMC) and a Muon Detector. The target spectrometer has an outer radius of about 2 m and will be almost 6 m long.. 3.1.1. The Target. The compact geometry of the TS leaves very little space for the target installation. Despite this, the target should have a thickness which together with the beam intensity provides the (design) luminosity of 2 · 1032 cm−2 s−1 . This requires a target thickness of 4 · 1015 hydrogen atoms per cm2 combined with 22.

(23) 1011 stored antiprotons in the HESR. At the moment, two complementary target techniques are being developed simultaneously: a hydrogen pellet target and a cluster jet target. Both are expected to fulfil the luminosity criteria. However, they have different effect on the beam quality and give different vertex resolutions. The pellet target features frozen droplets of hydrogen (pellets) that traverse the antiproton beam vertically. Hydrogen gas is liquefied and cooled down before being injected into a low-pressure helium environment in form of a jet, which later breaks up to a train of droplets. The technique was developed at TSL in Uppsala, Sweden, and has been successfully used in the WASA experiment [35] by both the CELSIUS/WASA collaboration [36] and the WASA-atCOSY collaboration [37]. This type of target gives a very well defined interaction point and one should be able to reach a precision of a few hundred μm with an optical pellet tracking device [38]. The cluster jet target is based on the principle of having pressurized cold hydrogen gas condensate in a nozzle, forming jets of hydrogen clusters. Compared to the pellet option, it gives a more diluted target. Development is going into increasing the target density and to minimising the spread of the hydrogen clusters in order to get a more precise vertex determination. The present lateral spread, given by the hydrogen clusters, is around 10 mm. The advantage with this solution is the continuous flow and homogeneous density profile.. 3.1.2. The Micro Vertex Detector. The main purpose of the micro vertex detector is to detect secondary vertices from D-meson and hyperon decays close to the interaction point and provide precision tracking for emerging particles. For low particle momenta where the energy loss in the MVD is dependent on the particle type, it can also be used for particle identification and separation (p/π, K/p and K/π) [39]. The barrel detector part is located between -17 cm and 14 cm in z-direction and stretches from 2.5 cm to 13 cm in radial direction, see Figure 3.3. Due to its location close to the interaction point it must be a very radiation hard detector. It will consist of two silicon pixel layers closest to the target and two outer layers of silicon strip detectors. In addition to the barrel layers, there will be eight detector wheels located perpendicular to the beam direction. All discs are made in a sandwich structure with active sensors on both sides of a support and cooling structure. The two innermost discs, located at a longitudinal distance of 22 mm and 44 mm, will be of pixel type. Next come three additional pixel discs, followed by two strip discs and one additional pixel disc at the end. The first three pixel discs are located at 72 mm, 102 mm and 150 mm. The two strip detectors come in a sandwich structure with the electronics for both disks between and are positioned at 162.5 mm and 207.5 mm. The last pixel disc sits at a longitudinal distance of 228 mm. The discs which have a relatively large distance to the 23.

(24) Figure 3.3: Layout of the Micro Vertex Detector with the barrel section and the six pixel and two strip discs.. vertex are intended for detection of hyperon cascades. The pixel size will be (100×100) μm2 , leading to a spatial resolution in the order of 10 μm. There is also a suggestion to have two additional discs at distances of 40 cm and 60 cm, respectively. This will be investigated further before a decision is made.. 3.1.3. Central Tracking. The central tracking will be made with either a Straw Tube Tracker (STT) or a Time Projection Chamber (TPC) together with three sets of GEM trackers for forward angles. The subdetector will cover the radial region between 15 cm and 42 cm from the beam pipe. The STT is proposed to consist of 24 layers of self-supporting aluminised mylar tubes with a total length of 150 cm. The diameter of all the 4200 straws is 10 mm and they will be filled with a gas mixture of Argon and CO2 and operated at 1 bar overpressure. The expected resolution in the xy-plane is 0.15 mm. To ensure a tracking ability down to 3 mm in longitudinal direction, the innermost 8 layers are skewed. The detector is based on the principle that charged particles will enter the detector and thereby produce negative electrons and positive ions that drift in opposite directions due to an applied electric field. In the strong field close to the wire, held at positive voltage, an avalanche amplification will occur, producing secondary electrons. These electrons will be collected here while the ions drift towards the cathode. The xy-track coordinates are given by the drift time of the electrons in the tubes and the longitudinal coordinate is either obtained by the charge division technique or by using the geometry of the skewed straws. The former is based on a length-dependent wire resistivity that affects the amplitude of the output pulse which is read out in both ends of the straw. This gives a worse resolution 24.

(25) compared to using skewed straws. The drift time in the detector depends on the gas mixture filling the straws, but varies between tens of nano seconds up to a few hundred nano seconds. The TPC is a far more challenging subdetector but it also gives a superior track resolution. It is split in two half-cylinders, each being a closed gas filled volume with an electric field applied in the direction of the beam pipe. Traversing charged particles will give rise to electrons and positive ions and as the electrons drift towards the anode at the upstream end face, they will create an avalanche with the charge amplification, most likely, coming from GEM detectors. This will provide xy-coordinates for the event. The z-coordinate is given by the drift time of each primary electron cluster. At present, further work on the R&D of the TPC is being done before a decision will be made. In addition to the central tracker, there will be three double layers of GEM detectors covering emission angles below 22◦ . A GEM detector is a metalcoated polymer plate, pierced by many small holes. When a high voltage is applied across the detector, the field in the holes becomes so strong that single electrons that pass through create an avalanche of new electrons, thereby amplifying the signal. The GEM detectors will be placed 1.1 m, 1.4 m and 1.9 m downstream of the target. Drift chambers are not considered here since they would suffer from ageing and have too high occupancy.. 3.1.4. Charged Particle Identification. It is very important to correctly identify the particles created in the reactions. For low velocities, particle identification by dE/dx can be done with the TPC or the STT, but the energy loss resolution of the latter is worse since there are considerably fewer measurements per traversing track. This results in large fluctuations of the measured quantity. Above 1 GeV/c, the primary detectors for this purpose will be the Cherenkov detectors, which measure the velocity of the particles. There are two DIRC detectors, one barrel shaped and one in the forward endcap. Both operate on the same principle - that charged particles in a medium emit radiation in an angle that depends on the particle’s velocity and the refractive index of the material. The materials chosen for this detector must have high optical quality so that the angle of the emitted Cherenkov light is preserved. One can obtain a measure of the particle mass by combining the information on the velocity with the momentum information from the tracking detectors. The barrel DIRC will detect particles emitted at angles between 22◦ and 140◦ using 1.7 cm thick quartz slabs at a radial distance of 45 cm to 54 cm from the beam pipe. The reflected light will be focussed onto micro channel plate photomultiplier tubes (MCP PMTs), an electron multiplier device that provides a very good time resolution also in the presence of strong magnetic fields. What is observed are so-called Cherenkov rings, from which the 25.

(26) Cherenkov angles can be calculated. The detection principle is the same for the forward disc, but the geometry is different. The detector will focus its light at the rim using mirroring quartz elements that reflect the light onto MCP PMTs. For both detectors, two space coordinates as well as the propagation time will be read-out. Fused silica provides pion-kaon separation from momenta of 800 MeV/c up to about 5 GeV/c. There will also be a barrel shaped time-of-flight detector for slow particles emitted at large polar angles, located just outside of the STT/TPC. A very good time resolution (50-100 ps) is needed, as the flight path in the target spectrometer is rather short. There will be no absolute time recorded, instead a relative timing will be provided between two or more traversing particles. The material of the detector will either be scintillator bars or multi-gap resistive plates.. 3.1.5. The Electromagnetic Calorimeter. A suitable detector material for an electromagnetic calorimeter must be both dense and fast to facilitate the collection of the electromagnetic radiation and the read-out of the signals before the next event is registered. The expected time resolution for the PANDA electromagnetic calorimeter is about 3 ns. For PANDA, the calorimeter is the single most expensive subdetector, comprising three units and in total approximately 15 500 scintillating crystals. The chosen material is lead tungstate, or PbWO4 (PWO), which is a very dense and radiation hard material with short radiation length, Molière radius (a measure of the transversal shower spread) and decay time of the scintillation process. These are very important properties as the count rates are expected to be high and the dynamic range includes low energy photons of a few MeV as well as high energy photons up to some GeV. The disadvantage of PWO is the relatively low light yield. It can however be increased with a factor of four by cooling the scintillators down to -25◦ C. For more information on the detector material, see section 4.2. The central part of the electromagnetic calorimeter (EMC) is the barrel (figure 3.4) with its 11 360 crystals, a 2.5 m long detector with an inner radius of close to 60 cm. It will consist of rings, each having 16 slices of crystals. A small tilt of approximately 4◦ with respect to the interaction region has been introduced in order to avoid having particles travelling between two detectors. The two additional pieces are the forward and backward endcaps, located 2.1 m downstream and 1 m upstream of the target. The forward endcap will have a diameter of 2 m and contain 3600 crystals. The backward endcap will have a diameter of 0.8 m and contain 592 detectors. In total, eleven various crystal shapes will be used in the barrel part. The backward endcap crystals are rectangular whereas the other crystals have truncated pyramid shapes. The degree of tapering varies depending on the exact location of the scintillator within the barrel. All crystals will have the same 26.

(27) Figure 3.4: The barrel EMC with the forward endcap.. length of 200 mm (≈ 22 radiation lengths). For the readout, a combination of avalanche photo diodes (APDs) and vacuum photo triodes (VPTs) will be used. Both types of sensors have a high resistance to radiation damages; in addition the APDs have a high internal gain. This is very important because of the low light yield of the scintillators. For the barrel crystals the read-out will be APDs, or rather Large Area APDs (LAAPDs), which have an active area of 10×10 mm2 for a better light collection. During the development phase, rectangular shaped LAAPDs have also been investigated as they allow for two read-out sensors to be placed on the back of each crystal. The forward endcap, with is subjected to a higher rate due to the forward boost of the system, will be equipped with VPTs which are faster. Development of such detectors with a higher quantum efficiency than the ones existing today is ongoing.. 3.1.6. The Solenoid Magnet. The target spectrometer includes a superconducting solenoid providing a maximum magnetic field of 2 T with a field homogeneity better than 2% in the volume where the vertex detector and central tracker are present. The inner radius of the coil is 90 cm and it will have a length of 2.8 m.. 27.

(28) 3.1.7. The Muon Detectors. In order to separate muons from pions and their decay daughters, i.e. the muons, a range tracking system will be implemented in the yoke of the solenoid magnet. The tracking system will consist of interleaved layers of absorbers (lead) and tracking detectors (aluminium drift tubes) that measure the energy loss as well as kinks of possible decays. The barrel section will have 12 layers, which is enough to absorb the pions, while the forward endcap will have additional material.. 3.1.8. Hypernuclei Detection. For the case of hypernuclei studies, the backward endcap of the calorimeter will be removed and a dedicated nuclear target station will be inserted together with additional detectors for γ spectroscopy. This is shown in figure 3.5.. Figure 3.5: The target spectrometer with the detector for γ spectroscopy inserted.. These studies require a special two-step target where hyperons are created and then scattering occurs such that the hyperons are caught in a nucleus, which then forms a hypernucleus. The dedicated detector will be an existing germanium array with n-type Germanium crystals of the EUROBALL type, but the read-out and tracking algorithms will be new and are being developed. The crystals will be grouped into 15 triple clusters, complemented with new read-out electronics.. 3.2. The Forward Spectrometer. The forward spectrometer (figure 3.6) is an essential part of the detector due to the large forward boost given to all particles. The instrumentation in this region consists of a dipole magnet, a tracker system, particle identification devices, an electromagnetic calorimeter and a muon detector. 28.

(29) Figure 3.6: Layout of the forward spectrometer with its subdetectors marked [34].. 3.2.1. The Dipole Magnet. To analyse the momenta of particles with polar angles lower than ±10◦ and ±5◦ in the horizontal and vertical directions, respectively, a dipole with a gap opening (H×W) of approximately 1×3 m2 will be used in the forward region. The total length of the magnet will be approximately 2 m and it will have a bending power of 2 Tm, causing a deflection of antiprotons at 15 GeV/c of roughly 2.2◦ . The antiproton beam will be deflected back using two correcting dipole magnets.. 3.2.2. Forward Tracking. The deflections caused by the dipole magnet will be measured by three pairs of wire chambers located in front of, within and behind the dipole magnet. The wire chamber drift cells will be have a width of 1 cm. Each chamber will consist of three detection planes; one vertical and two inclined ones. The expected momentum resolution for protons with 3 GeV/c is δp/p = 0.2%. It is not yet decided if the drift cells will be of small cell size drift chamber or straw tube type. Both types of detectors are presented in section 3.1.3.. 29.

(30) 3.2.3. Forward Particle Identification. There are two systems that deal with particle identification: the RICH detector and the Time-of-Flight Wall. The RICH detector will provide a separation of pions and kaons, and kaons and protons at high momenta. The detection technique is similar to that of the DIRC-detector’s in the target spectrometer but its design will be based on the RICH detector of the HERMES experiment at DESY [40]. Here, two radiators made of silica aerogel and C4 F10 -gas are used to provide a signal separation between particles. A spherical mirror array is located at the rear of the radiators and reflects the light onto an array of photon detectors. There will be two walls of Time-of-Flight stop counters measuring the relative time between two charged particles traversing any ToF detectors. One of them will be located 7 m downstream of the target, and the other inside the dipole magnet opening for particles with low momentum. The walls will consist of plastic scintillators, read-out on both sides by fast photomultiplier tubes. A 3σ separation of pions/kaons and pion/proton is expected up to 2.8 GeV/c and 4.7 GeV/c, respectively. This assumes a time resolution of σ = 50 ps.. 3.2.4. Forward Electromagnetic Calorimeter. The forward calorimeter is planned to be a Shahlyk-type detector based on lead-scintillator layers, read-out with wavelength shifting fibres coupled to photo multipliers. The scintillators are used for detection, while the lead layers act as energy absorbers and photon converters. An energy resolution√comparable to that of the E865 experiment at BNL [41], which was 4%/ E, is expected.. 3.2.5. Forward Muon Detectors. As in the target spectrometer, the forward muon detector will consist of absorber layers interleaved with rectangular aluminium drift-tubes. The design allows for a separation of pions from muons, detection of pion decays as well as some energy determination of neutrons and antineutrons.. 30.

(31) 4. Electromagnetic Interaction in Matter and Crystal Energy Resolution. 4.1. Interactions with Matter. The interactions of electrons and photons will be treated separately in this chapter. After this introduction, comes a section that deals with energy resolution calculations and specifically what is important for the PANDA electromagnetic calorimeter.. 4.1.1. Energy Losses of Electrons and Positrons in Matter. The electromagnetic interaction can be described with the Coulomb potential. This potential results in a force which, due to the low mass of the electrons (positrons), largely deflects them. Charged particles changing their velocity either to direction or magnitude, emit bremsstrahlung. This means that the particles lose energy continuously as they travel inside a material. The Bethe-Bloch equation describes the collision and radiative losses suffered by a charged particle [42]: dE dE dE + , (4.1) = dx dx coll dx rad where . dE dx. . = . coll. e2 4π 0. 2. 2πNa Zρ mc2 β2 A. T (T + mc2 ) β2 2 + (1 − β ) − (2 1 − β2 − 1 + β2 ) ln 2 × ln 2I 2 mc2 2 1 2 + (1 − 1 − β ) (4.2) 8 . dE dx. 2. . = rad. e2 4π 0. 2. Z 2 Na (T + mc2 )ρ 2(T + mc2 ) 4 − 4ln . 137m2 c4 A mc2 3. (4.3). 31.

(32) The electron mass is denoted m, the kinetic energy of the electron T, the mean excitation energy of the atomic electrons I, Avogadro’s constant Na , the atomic number Z, the atomic weight A, the density of the material the electron interacts with ρ, the permittivity in vacuum 0 and the velocity of the particle v = βc. Due to the dependence on energy and Z, the radiative term plays a larger role than the collision term for higher energies and heavier materials. 4.1.1.1 Radiative Losses by Electrons and Positrons Electrons and positrons are the only particles for which radiation losses play an important role. This is due to the bremsstrahlung emission probability, which depends on the inverse square of the particle mass. The probability for bremsstrahlung emission is dependent on the electric field felt by the electron. Since a nucleus is surrounded by a cloud of electrons, the field strength (as seen from a distance) will appear reduced or screened. This effect can be described by the parameter ξ. This parameter affects expression for the bremsstrahlung and pair production cross sections, since the processes are very similar. ξ is defined as [43] ξ=. 100me c2 Eγ . E0 EZ 1/3. (4.4). E0 is the initial total energy of the electron (positron) and E is its energy after the bremsstrahlung emission. Eγ is the difference between the two energies, hence the energy given to the emitted photon. The screening parameter takes on values close to 0 for complete screening, and large values for no screening. The cross section for bremsstrahlung can be calculated for the cases of no and complete screening. The energy loss, −dE/dx, due to radiation is obtained when integrating the differential cross section multiplied with the photon energy over the frequency ν [44] ν0 dE dσ − =N hν (E0 , ν)dν = NE0 Φrad . (4.5) dx rad dν 0 N is the number of atoms per cm3 (N = ρNa /A; with ρ and Na defined above and A being the mole mass). The total radiation cross section, Φrad , can be written as 1 Φrad = E0. . Eγ. dσ (E0 , ν)dν dν. (4.6). with ν being the photon frequency. This relation is practically only a function of the material, since dσ/dν is approximately proportional to 1/ν.. 32.

(33) 4.1.1.2 The Radiation Length The radiation length is defined, in the high energy region with complete screening, as the distance over which the electron’s energy has been reduced by a factor 1/e due to radiation losses only. Integrating equation 4.5 gives −. dE = NΦrad dx ⇒ E = E0 e−x/X0 E. (4.7). where X0 = 1/NΦrad . For an evaluation of X0 , we use the total radiation cross section from ref. [45], Φrad =. 4Z 2 re2 α 1 [ln(183Z −1/3 ) + − f (Z)]. ν 18. (4.8). where re is the classical electron radius and f (Z) is a correction to the Born approximation, taking the Coulomb interaction of the emitting electron into account. The inverse of the radiation length becomes ρNa 2 1 = 4Z(Z + 1) (4.9) re α[ln(183Z −1/3 ) − f (Z)]. X0 A where Z 2 has been replaced by Z(Z + 1) to include also electron-electron bremsstrahlung.. 4.1.2. Photon Interactions with Matter. Photons interact with matter primarily via three different types of interactions. They are called the photoelectric effect, Compton scattering and pair production. The cross section for each process is strongly energy dependent. For the future PANDA experiment, the interesting energy regime starts at a few MeV. 4.1.2.1 Photoelectric Effect As can be seen in figure 4.1, the dominant process in the energy regime below 1 MeV is the photoelectric effect. In this process, the incoming photon interacts with an electron bound in the material, thereby giving it enough energy to be released. The kinetic energy given to the electron equals the incoming energy minus the binding energy. The cross section is strongly dependent on the atomic number Z. According to experimental investigations, the cross section per atom is proportional to [43] σph ∝. Z5 Eγ7/2. (4.10). 33.

(34) Figure 4.1: The three interaction processes photons can undergo in matter [46]. The photoelectric effect is dominant for photon energies below 1 MeV, Compton scattering for energies between 1 and 5 MeV and pair production for energies above that.. for Eγ me c2 and to σph ∝. Z5 Eγ. (4.11). for Eγ me c2 , where Eγ is the photon energy. 4.1.2.2 Compton Scattering As we move higher in energy, the photoelectric effect becomes less important and the Compton scattering process starts to dominate (see figure 4.1). In this case, the incoming photon scatters off a loosely bound electron and both particles share the energy between them according to the energy and momentum conservation laws. At low energies where relativistic effects can be neglected, the cross section for this interaction is the Thomson scattering cross section, which is used to describe scattering of electromagnetic radiation by a point charge using wave formalism. The Thomson scattering cross section can be written as dσ = dΩ. . q2 4π 0 mc2. 2 | i · f |2. (4.12). where q is the electric charge and i and f are the polarisations of the initial and final photons, respectively. At energies Eγ me c2 , relativistic effects must be included and the cross 34.

(35) section for Compton scattering (per electron) is proportional to [46] σCo ∝. Z ln Eγ . Eγ. (4.13). 4.1.2.3 Pair Production The last of the three processes is pair production. Here, the incoming photon converts into a electron-positron pair in the neighbourhood of a nucleus (to conserve momentum). This happens only when the photon has enough energy to create the two particles, Eγ ≥ 2me c2 . The pair production process is very similar to the bremsstrahlung process. When describing the processes with Feynman diagrams (see figure 4.2), it is seen that the two processes are very similar, and calculations for one process hence also give results for the other.. e+ e−. e−. e−. Figure 4.2: The bremsstrahlung process (left) and the pair production process (right) depicted with Feynman diagrams.. As for bremsstrahlung, the screening of the electric field from a nucleus by the atomic electron cloud must be taken into account using the screening parameter in equation 4.4. Analytical integration of the differential cross section per atom gives in the case of no screening [44] 2Eγ 109 2 2 7 σpair = 4Z αre − f (Z) − ln , (4.14) 9 me c2 54 and for complete screening σpair = 4Z. 2. αre2. . 1 7 1/3 (ln 183Z − f (Z)) − . 9 54. (4.15). For other cases, apart from the two extremes, the calculations must be performed numerically. 35.

(36) From the total cross section with complete screening the mean free path, λpair , for a γ-ray to perform pair production can be estimated, 1 λpair. 7 7 = Nσpair ≈ 4Z(Z + 1)Nre2 α(ln 183Z −1/3 − f (Z)) = , 9 9X0. (4.16). where the small constant term has been ignored. The factor Z(Z + 1) is used instead of Z 2 because pair production may also happen in the electric field of an atomic electron, not only in the field of an atom. An important consequence of this process is that when an incoming photon strikes matter and gives rise to pair production, an electromagnetic shower is started. The created positron will soon annihilate with an electron and two photons are emitted. This shower spreads both longitudinally and transversely in the material. The so-called Molière radius of a material is a measure of the latter. The relation between the Molière radius and the radiation length is [4] RM =. X0 E s Ec. (4.17). √ where E s is the scale energy and defined as E s = 4π/αme c2 ≈ 21 MeV and Ec is the critical energy for electrons, defined by Rossi [47]. This is the energy at which the ionisation loss per radiation length is equal to the electron energy.. 4.2. PbWO4 Scintillator Characteristics. The primary aim of the electromagnetic calorimeter of PANDA is to detect and measure the energy of photons and electrons. This puts demands on, for example, the density of the detector material, the ability of it to contain the electromagnetic shower and the read-out time of the signals. The PANDA collaboration has chosen to use the material lead tungstate, PbWO4 or PWO, in the electromagnetic calorimeter. The material was developed for the purpose of being used in the next generation high energy physics experiments at LHC, CERN. Today, the electromagnetic calorimeters of ALICE (called PHOS) and CMS are made of this material. Improvements of the crystal development and properties are ongoing and have yielded higher quality and more radiation hard samples. Also, experimenting with the crystal doping is made in order to limit reductions in optical transparency and to increase the light yield [48]. The PWO crystal is transparent, heavy and very fragile. A photograph of a sample can be seen in figure 4.3 and some of the material properties are displayed in table 4.1.. 36.

(37) Figure 4.3: One of the PWO crystals which has been delivered to Uppsala for measurements of energy resolution and light yield uniformity. Photograph by T. Thörnlund [49].. Table 4.1: Properties of the lead tungstate scintillator [32] [50].. Property. PWO. Density [g/cm3 ] Radiation length [cm] Molière radius [cm] Refractive index Decay time [ns] Light Yield (LY) relative to NaI at RT [%] Relative Light Yield at -25◦ C [%(LY NaI)] dL/dT [%/◦ C]. 8.28 0.89 2.2 2.2 6.5 0.6 2.5 -3.0. Some of the most noticeable properties mentioned in table 4.1 are the large density and the short radiation length which allow for a very compact detector. Other properties worth noticing are the high index of refraction that reduces the risk of light scattering out of the crystal, and the short decay time that facilitates fast read-out and high count rates. The light yield is the major draw back of this material. It is very low at room temperature and reasonable at -25◦ C, due to its strong temperature dependence shown in figure 4.4.. 4.3. Energy Resolution. Statistical fluctuations appear both in the light creation process inside the scintillator, in the light conversion process in the PM tube and in the electronic 37.

(38) Light output [a.u.]. 500 400 300 200 100 0 -30. -20. -10 0 Temperature [deg. C]. 10. 20. Figure 4.4: The light yield of PWO as a function of the temperature [51].. noise from the modules used to process the signals. In addition, there are fluctuations in the deposited energy due to the leakage of energy. The exact contributions will never be known, but can be estimated by measuring the total fluctuations in the detected signal under various conditions (i.e. higher and lower energy). When describing the energy resolution of calorimeters, three different terms are often included. These are normally considered to be uncorrelated. They will be described in this subsection, together with the final expression most commonly used for the quantification. One contribution to the energy resolution comes from the Poisson statistics of the light collection process. For such a distribution it is known that the variance σ2 (N) = N, where N is the number of information carriers (in this case the number of photoelectrons in the PM tube). N is related to the deposited energy through the relation as N = βE, with β being a constant describing how many photoelectrons that are emitted per unit energy. The factor β depends on the detector material, light transport and quantum efficiency of the light sensor. The uncertainty in the energy determination is 1 1 1√ E σ(E) = σ(N) = N= βE = . (4.18) β β β β The contribution from this term to the relative resolution σ/E is rather small for scintillators with a high light yield. For PWO, this is not the case, and it is thus very important to secure a high efficiency in collecting the created light. This can be done by using a highly reflective wrapping material around the crystal together with a good optical coupling between scintillator and readout device. 38.

(39) In this simple description, it is assumed that there is one unique β-value for a crystal. In reality, β can vary between different regions of the scintillator, the light yield is said to be non-uniform. This leads to the number of emitted photoelectrons being dependent on where in the crystal the interaction takes place. In the calorimeter, with only one light sensor on each crystal, the position of the energy deposition is not possible to reconstruct. Therefore, a non-uniformity of the light yield will impair the energy resolution. An investigation of the light yield uniformity among some PWO-crystals is presented in chapter 7. A second contribution comes from the electronic noise that is generated in the modules in the read-out chain, including the high voltage that directly influences the signal amplitude. However, this type of noise is considered independent of the measured energy and is therefore described by the expression σN = b.. (4.19). It should be noticed that although the noise contribution in one crystal is energy independent, the total noise that is measured when using a crystal matrix is dependent on the energy. This is due to the fact that a higher photon energy induces a larger shower in the array and hence more crystals (and more noise) contribute. A study of this effect on the result is done in section 6.6.2. The third contribution to the energy resolution comes from properties that are related to the specific crystal type as well as leakage of energy. This includes effects such as non-uniformity of the produced light inside the crystals, temperature gradients, detector ageing, radiation damage etc. In this term, also effects related to the detector system are included. This means that if more than one detector is used, any uncertainties in their intercalibration will contribute to the final uncertainty of the energy resolution. The fluctuations caused by these effects are proportional to the signal strength and thus to the energy: σC (E) = c · E.. (4.20). This term is assumed linear in energy and as such important at higher energies because it is usually relatively large compared to the other two contributions, unless special care has been taken to reduce leakage and aging effects of the crystals as well as to improving the intercalibration between them [50]. The general expression for the square of the sum of these three contributions is thus σ2 = σP (E)2 + σ2N + σC (E)2 = a2 E + b2 + c2 E 2. (4.21). 39.

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