ACTA UNIVERSITATIS UPSALIENSIS Uppsala Dissertations from the Faculty of Science and Technology 101 Multi-Strange and Charmed Antihyperon- Hyperon Physics for PANDA Erik Thomé Dissertation presented at Uppsala University to be publicly examined in Häggsalen, Ångström- laboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, November 23, 2012 at 10:15 for the degree of Doctor of Philosophy. The examination will be conducted in English Abstract Thomé, E. 2012. Multi-Strange and Charmed Antihyperon-Hyperon Physics for PANDA. Acta Universitatis Upsaliensis. Uppsala Dissertations from the Faculty of Science and Technology 101. 151 pp. Uppsala. ISBN 978-91-554-8497-2. The thesis concerns the prospects of studying multi-strange and charmed antihyperon-hyperon physics and CP violation in hyperon decays in the upcoming PANDA experiment. The angular distribution dependence on polarisation parameters in the decay of the spin 3/2 Omega hyperon was calculated using the density matrix formalism. Expressions for the angular distributions in both the W ! LK and the subsequent L ! pp were obtained. ¯ + − ¯ + − ¯ − + Simulations were performed for the pp¯ ! X X , pp¯ ! W W and pp¯ ! Lc Lc . The beam momenta were 4, 12 and 12 GeV/c, respectively. Special attention was given to the reconstruc- tion of spin variables. For the pp¯ ! X¯ +X− reaction PANDA will give tens of events/s, which should be compared to the previously existing data of a handfull of events for this reaction. For the other two reactions the event rates will be lower but still reasonably high, considering that this will be the first measurements of these reactions. It was also shown that spin variables can be reconstructed in all three reactions for all production angles of the hyperons. Simulations concerning the possibility to measure CP violation parameters in hyperon de- cays were also performed for the reactions pp¯ ! LL¯ and pp¯ ! X¯ +X−. It was found that false signals from detector asymmetries disappears if no particle identification criterium is used and the analysis is restricted to events were the hyperon decays occur close to the beam axis. The effect of the magnetic field in the PANDA detector on the measurement of hyperon spin variables was investigated for the case of pp¯ ! LL¯ . The effect was observed to be small for polarisation and negligible for spin correlations. Keywords: PANDA, FAIR, antiproton, hyperon, strangeness, charm, polarisation, spin correlation, CP violation Erik Thomé, Uppsala University, Department of Physics and Astronomy, Nuclear Physics, Box 516, SE-751 20 Uppsala, Sweden. c Erik Thomé 2012 ISSN 1104-2516 ISBN 978-91-554-8497-2 urn:nbn:se:uu:diva-182450 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-182450) Printed by Elanders Sverige AB, 2012 Till Alva och Lovisa Contents 1 Introduction . ........................................ 11 1.1 Standard Model of Particle Physics . .................... 11 1.2 Quarks and Gluons ................................. 13 1.3 Hadrons .......................................... 14 1.4 Hyperons . ...................................... 16 1.5 Hyperon Physics in Antiproton-Proton Collisions and the PANDA experiment . .............................. 18 1.6 CP Violation ...................................... 19 1.7 Thesis Disposition .................................. 20 2 PANDA............................................. 23 2.1 The FAIR Facility .................................. 23 2.2 The PANDA Detector . ............................. 25 2.2.1 Target Spectrometer . ............................ 26 2.2.2 Forward Spectrometer . ........................ 32 2.3 PANDA Physics . .................................. 34 3 The pp¯ → YY¯ Reaction . ................................ 37 3.1 Spin Variables . .................................. 37 3.1.1 The Density Matrix . ............................ 37 3.1.2 Hyperon Density Matrices ........................ 39 3.1.3 Angular Distributions for Hyperon Decays . .......... 44 3.1.4 Spin Variables in the pp¯ → YY¯ Reaction . ............ 50 3.1.5 Hyperon Rest Systems and Symmetry Constraints on Spin Variables ................................. 53 3.1.6 Restrictions on Spin Variables from Theoretical Consid- erations . ..................................... 54 3.2 CP Violation Parameters ............................. 56 4 Existing Data and Theoretical Predictions . ................. 59 4.1 Prior Knowledge on the pp¯ → YY¯ Reaction . ............. 60 4.2 Hyperon Channels for This Thesis . .................... 65 4.2.1 The pp¯ → Ξ¯ +Ξ− Reaction ........................ 65 4.2.2 The pp¯ → Ω¯ +Ω− Reaction ........................ 67 → Λ¯ −Λ+ 4.2.3 The pp¯ c c Reaction ........................ 69 4.3 CP Violation ...................................... 69 5 Analysis Methods . ................................... 71 5.1 Spin Variables for the Spin 1/2 Hyperons . ................ 71 5.2 Polarisation and Asymmetry Parameters of the Ω Hyperon . 73 5.3 Methods to Compensate for Angular Dependence of Recon- struction Efficiency . .............................. 76 5.3.1 Method Using Monte Carlo Based Acceptance Functions . 76 5.3.2 Method Without the Use of Monte Carlo Based Accep- tance functions ................................. 76 5.4 CP violation parameters . ............................. 80 6 Simulations of Multi-Strange and Charmed pp¯ → YY¯ Reactions . 85 6.1 The Simulation Framework . ......................... 85 6.1.1 Digitisation . ................................. 86 6.1.2 Track Reconstruction ............................ 87 6.1.3 Charged Particle Identification . ................... 87 6.1.4 Analysis ..................................... 90 6.1.5 Ongoing Software Development . ................... 90 6.2 The pp¯ → Ξ¯ +Ξ− Reaction . ......................... 92 6.2.1 Data Generation ................................ 92 6.2.2 Event Reconstruction ............................ 92 6.2.3 Reconstruction Efficiency and Background . .......... 93 6.2.4 Reconstruction Efficiency as a Function of the Ξ¯ + Pro- duction Angle ................................. 93 6.2.5 Reconstruction of Decay Vertices ................... 94 6.2.6 Ξ− Lifetime Reconstruction . ..................... 94 6.2.7 Invariant Mass ................................. 95 6.2.8 Correction for the Bending of the Ξ¯ + and Ξ− Trajectories in the Magnetic Field ............................ 96 6.2.9 Reconstruction Efficiency as a Function of the Λ¯ Decay Angle in the Ξ¯ + rest frame . ..................... 97 6.2.10 Comparison Between the Methods for Calculation of Spin Variables ................................. 98 6.3 The pp¯ → Ω¯ +Ω− Reaction . ......................... 104 6.3.1 Data Generation ................................ 104 6.3.2 Event Reconstruction ............................ 104 6.3.3 Reconstruction Efficiency and Background . .......... 105 6.3.4 Reconstruction Efficiency as a Function of the Ω¯ + Pro- duction Angle ................................. 106 6.3.5 Reconstruction of Decay Vertices ................... 106 6.3.6 Ω− Lifetime Reconstruction . ..................... 107 6.3.7 Invariant Mass ................................. 107 6.3.8 Reconstruction of Polarisation and Asymmetry Parameters 108 → Λ¯ −Λ+ 6.4 The pp¯ c c Reaction . ......................... 111 6.4.1 Data Generation ................................ 111 6.4.2 Reconstruction ................................. 111 6.4.3 Reconstruction Efficiency and Background . .......... 111 Λ¯ − 6.4.4 Acceptance as a Function of the c Production Angle . 112 6.4.5 Reconstruction of Decay Vertices ................... 113 6.4.6 Invariant Mass ................................. 113 6.4.7 Reconstruction of Spin Variables ................... 114 6.4.8 Other Charmed Hyperons ........................ 114 6.5 CP Violation in Hyperon Decay ........................ 116 6.5.1 General Experimental Considerations . ............... 116 6.5.2 Reconstruction of the CP Violation Parameter A for the pp¯ → ΛΛ¯ Reaction .............................. 116 6.5.3 Reconstruction of CP Violation Parameters for the pp¯ → Ξ¯ +Ξ− Reaction . ............................... 119 7 Precession of the Hyperon Polarisation Vector in the Magnetic Field of the PANDA Detector . ............................... 123 7.1 Precession of Polarisation Vectors in a Magnetic Field ....... 123 7.2 Effect on the measurement of Λ Polarisation . ........... 125 7.3 Effect on the measurement of ΛΛ¯ Spin Correlations . ....... 127 7.4 Other Hyperons . .................................. 130 8 Conclusions and Outlook . .............................. 133 8.1 Calculations of Decay Angular Distributions for the Spin 3/2 Ω Hyperon . ...................................... 133 8.2 Simulations of Multi-Strange and Charmed pp¯ → YY¯ Reactions 134 8.3 Effect of Magnetic Field on Measurement of Hyperon Spin Variables . ...................................... 135 8.4 Outlook .......................................... 136 9 Svensk sammanfattning . .............................. 137 10 Acknowledgements . ................................... 143 11 Bibliography . ....................................... 145 1. Introduction Three quarks for Muster Mark! Sure he hasn’t got much of a bark And sure any he has it’s all beside the mark. James Joyce “Finnegans Wake’ The topic of this thesis is within the field of hadron physics. A hadron is a composite particle built up by quarks and held together by the strong in- teraction. The most important aim of hadron physics is to understand how the strong interaction binds the quarks into composite particles. This is the