Matching of Avalanche Photodiodes and Light Injection Into Scintillation Crystals Benjamin Wohlfahrt Matching of Avalanche Photodiodes and Light Injection Into Scintillation Crystals Inaugural-Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften (Dr. rer. nat.) der Justus-Liebig-Universität Gießen im Fachbereich 07 (Mathematik und Informatik, Physik, Geographie) Februar, 2019 vorgelegt von Benjamin Wohlfahrt Justus-Liebig-Universität Gießen II. Physikalisches Institut Heinrich-Buff-Ring 16 35392 Gießen Deutschland Dekan: Prof. Dr. Kai-Thomas Brinkmann Prodekan: Prof. Dr. Ludger Overbeck 1. Gutachter und Betreuer: Prof. Dr. Kai-Thomas Brinkmann 2. Gutachter: PD Dr. Jens Sören Lange 1. Prüfer: Prof. Dr. Martin Buhmann 2. Prüfer: Prof. Dr. Sangam Chatterjee Contents Zusammenfassung 1 Abstract 2 1 Fundamentals 4 1 Motivation 4 2 FAIR 4 3 Antiproton production 7 3.1 Collector Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 High Energy Storage Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 PANDA-experiment 9 4.1 Physics at PANDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1.1 Charmonium spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.1.2 Gluons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.1.3 Hadrons in nuclear matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.1.4 Hypernuclear physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 PANDA-Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2.1 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2.2 Micro Vertex Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2.3 Central Straw Tube Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.2.4 Time-Of-Flight Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2.5 DIRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2.6 Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2.7 Muon Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2.8 Tracking and Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5 Electromagnetic Calorimeter 24 5.1 Interactions of radiation with matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.1.1 Photon interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.1.1.1 The photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.1.1.2 Compton effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.1.1.3 Pair production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.1.2 Charged particle interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.1.2.1 Bremsstrahlung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.1.2.2 Cherenkov radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.1.2.3 Transition radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.1.3 Electromagnetic shower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.1.4 Scintillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.2 PANDA Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.2.1 Design concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.2.2 PWO-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.2.3 Avalanche Photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.2.4 Preamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.2.5 Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2 Matching 53 6 APD Parameters 53 6.1 APD screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.1.1 Cluster analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.2 Parameter extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6.2.1 Diode regression modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6.2.1.1 Estimation methods and coefficients of determination . . . . . . . . . . . . . . 59 6.2.1.2 Empirical relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.2.1.3 Polynomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.3.1 Polynomial degree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.3.2 Numerical convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6.3.3 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.3.4 Q-point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.3.5 Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.3.6 Breakdown voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.3.7 Data pool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 7 Assignment & Matching 99 7.1 Similarity measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 7.1.1 Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7.2 Greedy algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.3 Hungarian algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.3.1 Adjustment to a single set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.4 Edmond’s algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.4.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 7.5 Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.6.1 Basic network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.6.1.1 Blossom algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.6.1.2 Greedy algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.6.1.3 Pool influence on the similarity measurement . . . . . . . . . . . . . . . . . . 116 7.6.1.4 Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.6.1.5 Parameter deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.6.1.5.1 Voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.6.1.5.2 Slopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.6.2 Modified network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.6.2.1 Distance limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.6.2.1.1 Optimal distance threshold . . . . . . . . . . . . . . . . . . . . . . . . 131 7.6.2.2 Slope limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 7.6.2.2.1 Optimal slope threshold . . . . . . . . . . . . . . . . . . . . . . . . . . 142 7.6.2.3 Voltage limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.6.2.3.1 Optimal voltage threshold: . . . . . . . . . . . . . . . . . . . . . . . . 150 7.6.2.4 Comparison between all optima . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 7.6.2.5 Group APD pairings to a cluster of four pairings . . . . . . . . . . . . . . . . . . 153 7.6.2.5.1 Assigning the APD groupings via Mahalanobis . . . . . . . . . . . . . 154 7.6.2.5.2 Assigning the APD pairings via voltage limits . . . . . . . . . . . . . . 156 7.6.3 Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 3 Light coupling for the monitoring system of the Electromagnetic calorimeter 161 8 Experimental setup 163 8.1 Stability test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.2 Material analysis for coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 8.3 Position study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 8.4 Energy injection at various positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 8.5 Absolute light yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 8.6 Polishing dependency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 9 Simulation & Implementation 174 9.1 SLitrani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 9.2 Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 9.3 Geometrical and optical parameters of the components . . . . . . . . . . . . . . . . . . . . . . . 175 9.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 9.4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 9.4.2 Angle study at origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 9.4.3 Angle study at specific coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 9.4.4 Efficiency map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 9.4.5 Elapsed time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 9.4.6 Elapsed distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 9.4.7 Interaction study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 9.4.8 Correlations between the propagation quantities . . . . . . . . . . . . . . . . . . . . . . 187 9.4.9 APD ratio during rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 9.4.10 APD ratio during x translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 9.4.11 Type scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 9.4.12 Position impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 10 Conclusion and outlook 194 4 Appendix 195 11 Background 196 11.1 Crystal geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 12 Matching 197 12.1 APD Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 12.1.1 Share of wafers in data points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 12.1.2 APD 711006317 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 12.1.3 Linear mixed model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 12.1.4 Influence of single APDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 12.1.5 Residual plot of the lots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 12.1.6 Q-point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 12.1.7 Breakdown voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 12.1.8 Parameters against lots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 12.1.9 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 12.2 Assignment & Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 12.2.1 Similarity measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 12.2.2 Influence of irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 12.3 Graph theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 12.4 Adjustment to a single set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 12.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 12.5.1 Distance scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 12.5.2 Voltage scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 12.5.3 Reduced graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 12.6 List of APDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 13 Beam time with Proto120 in Main 232 13.1 Mainzer Mikrotron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 13.1.1 A2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 13.1.2 Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 13.1.3 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 13.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 13.2.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 13.2.2 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 13.2.3 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 13.2.4 Cosmic single calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 13.2.5 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 13.2.6 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 13.2.7 Readout cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 13.2.8 Light pulser fiber coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 14 Light coupling 248 14.1 Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 14.2 Experimental settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 14.3 Slitrani settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 14.3.1 Geometrical and optical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 14.3.2 Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 14.3.3 Cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 14.3.4 Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 14.3.5 Wrapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 14.3.6 Glue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 14.3.7 Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 14.3.8 APD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 14.3.9 Best angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Data sheets References 15.1 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zusammenfassung Das zur Zeit im Bau befindliche PANDA-Experiment an der FAIR-Einrichtung in Darmstadt, Deutschland, er- fordert ein elektromagnetisches Kalorimeter mit einem sehr niedrigen Schwellenwert von 3 MeV pro Kristall und 10MeV pro Cluster. Dieses Kalorimeter hat die Form eines Fasses und wird drei Einheiten umfassen: Zwei Endkappen und das Fass selbst. Insgesamt werden 15552 Kristalle verwendet, wobei das Fass den Hauptteil mit 11360 Kristallen darstellt. Die Szintillationskristalle werden aus einer zweiten Generation von Blei-Wolframat (PbWO4-II) hergestellt, die eine sehr schnelle Abklingzeit von etwa τ = 15 ns bieten. Das erzeugte Licht wird anschliessend von zwei Lawinenphotodektoren, APDs, ausgelesen, die auf der Rückseite der Kristalle ange- bracht sind. Diese Photodioden werden von Hamamatsu hergestellt und ähneln den APDs, die bereits im CMS-Experiment am CERN zum Einsatz kommen, besitzen aber eine größere aktive Fläche und eine leicht modifizierte innere Struktur. Ein den APDs nachfolgender Vorverstärker, der APFEL ASIC, basierend auf 350 nm CMOS-Technologie, formt das Signal mit Hilfe eines Pulsformers dritter Ordnung und wird von 14-bit SADCs ausgelesen. Um ein bestmögliches Auslesesignal zu erhalten, ist ein bestimmter Arbeitspunkt der Lawinenphotodektoren bei einer Verstärkung vonM = 150 vorgesehen. Die APDs werden von dem Photosensor-Laboratory in Darm- stadt vermessen, im Strahlenzentrum inGießenmit Photonen bei einer Dosis von 30Gy bestrahlt und inDarm- stadt erneut vermessen. Dabei wird je eine Kennlinienkurve VerstärkungM gegen SpannungU gemessen. Der Arbeitspunkt ist durch eine individuelle Betriebsspannung vorgegeben undweist einen bestimmten Anstieg an diesemPunkt auf. Umdiesen Arbeitspunkt so genauwiemöglich zu bestimmen, werden imRahmen dieser Ar- beit mehrere Interpolationsmethoden mit Hilfe statistischer Mittel untersucht, da das in der Standardliteratur üblicherweise verwendete Modell, der sogenannte Miller-Fit, bei hohen Verstärkungsspannungen (ab etwa M = 50) keine präzisen Vorhersagen mehr liefert. Ausgangspunkt ist daher ein polynomiales Regressions- modell, dessen Ordnung, Anzahl verwendeter Datenpunkte und konkrete Implementierung, beispielsweise als gemischtes Modell als Referenz, analysiert werden. Ein einfaches Polynom dritten Grades bei einer An- zahl von insgesamt sechs verwendeten Datenpunkte (je drei Datenpunkte über- und unterhalb der anvisierten Verstärkung von M = 150) erweist sich letztlich am effizientesten. Darüber hinaus zeigt sich, dass sich eine Transformation des Datenbereiches in eine doppelt-logarithmische Skala als nützlich erweist. Da zwei APDs pro Kristall zum Einsatz kommen werden, um das selbe Signal zu detektieren, ist es wichtig, jedem Kristall die beiden gemäß ihrer Betriebsparameter ähnlichsten APDs aus dem verfügbaren Pool so zuzuordnen, dass die Summe der zuweisbaren APDs so hoch wie möglich ist. Dazu ist zunächst ein geeignetes Werkzeug erforderlich, um die Ähnlichkeit der Parameter bestimmen zu können. Dafür wird dieMahalanobis- Distanz verwendet, die sich für kontinuierliche, multivariate Räume eignet. Solch eines wird hier durch vier Dimensionen aufgespannt, die jeweils einen Betriebsparameter einer APD repräsentieren. Diese lässt sich auch verwenden, um festzustellen, wie sehr sich die APDs als Kollektiv ähneln. Dazu zählen beispielsweise Korrelationen zwischen den Detektoren und deren Parametern, das Temperaturverhalten, die Bestimmung der Durchbruchspannung oder Parameteränderungen durch Bestrahlung. Die Zuordnung der APDs erfolgt mittels einer Implementierung des Blossom V-Algorithmus, der ein perfektes minimal-gewichtetes Matching erzeugt. Die Beeinflussung dieses durch das Einfügen von Limits bezüglich etwaiger Parameterunterschiede innerhalb der 2er-Gruppierungen wird mit Auswirkung auf die resultierende Gesamtanzahl der Gruppierungen ausführlich untersucht. Die Hochspannungsversorgung der APDs erfolgt über eine Platine, die insgesamt acht APDs zu regulieren vermag. Für solch ein Multi-Matching existiert bislang kein Ansatz, daher erfolgt das Gruppieren von vier 2er-Paaren zu einem 8er-Paar über sogenannte virtuelle APDs, womit sich der schon zuvor verwendete Blos- som V-Algorithmus wieder verwenden lässt. Eine virtuelle APD repräsentiert dabei ein 2er-Paar über deren Mittelwerte in den Betriebsparametern. Die Spannungsauflösung der Versorgungsplatine beträgt gemäß des verwendeten 10-bit DACs 100 mV und weist einen Spannungsbereich von voraussichtlich etwa 50 V auf. Die Quartetts und auch schlussendlich die Oktetts müssen ebenfalls entsprechend zugeordnet werden, dass sie den entsprechenden Spannungsbereich erfüllen. Nutzt man für diese jeweils nur die Spannungswerte als Dis- tanzfunktion, reduziert sich der maximale Spannungsunterschied innerhalb einer Hochspannungsplatine auf weniger als 5 Volt. 1 Um eine Online-Überwachung der APDs zu ermöglichen, wird ein Lichtpulser verwendet, der Licht in die Kristalle einkoppelt. Dieses wird von den APDs in entsprechende Signale umgewandelt. Aufgrund des gerin- gen freien Volumens im mechanischen Träger des Kalorimeters ist es nicht möglich, diesen dort direkt zu installieren. Deshalb wird das Licht über eine Lichtfaser vom Lichtpulser zum jeweiligen Kristall geleitet. Dort ist wiederum eine spezielle Befestigung für die Faser erforderlich, die Einfluß auf die eingekoppelte Licht- menge hat. Aktuell werden mehrere Designvorschläge untersucht, von denen in dieser Arbeit der erste Proto- typ analysiert wurde. Dieser stellt eine kuppelartige Kappe aus Polyamid 12 dar und wird an der Vorderseite des Kristalls angebracht. Diese Methode bietet einige Freiheitsgrade wie unter anderem den Kopplungswinkel und die -tiefe der Faser. Der Einfluß dieser Parameter auf die eingekoppelte Lichtmenge wird experimentell mithilfe eines PANDA-Szintillationskristalls und eines Photomultipliers als Detektor untersucht. Um die re- flektiven Eigenschaften zu verbessern, wurde die Kappemit Bariumsulfat beschichtet und dessen Strahlenhärte und Auftragsart untersucht. Darüber hinaus wurde die Lichteinkopplung mithilfe einer Simulation in SLitrani für zwei APDs als Detektoren analysiert. Abstract The PANDA-experiment currently under construction at the FAIR facility in Darmstadt, Germany, requires an electromagnetic calorimeter with a very low threshold of 3 MeV per crystal and 10 MeV per cluster. This calorimeter has a shape of a barrel and will comprise three units: Two end caps and the barrel itself. A total of 15552 crystals will be used, with the barrel representing the main part with 11360 crystals. The scintillation crystals are made from a second generation of lead tungstate (PbWO4-II), which have a very fast decay time of about τ = 15 ns bid. The generated light will be read out by two Avalanche Photodetectors, APDs, which are attached to the back of the crystals. These photodiodes are manufactured by Hamamatsu and are similar to the APDs already used in the CMS experiment at CERN, but provide a larger active area and a slightly modified inner structure. A preamplifier following the APDs, the APFEL ASIC based on 350 nmCMOS technology, forms the signal with the help of a third-order pulse shaper and is read out by 14-bit SADCs. In order to obtain the best possible readout signal, an operating point of the avalanche photodetectors with a gain of M = 150 is foreseen. The APDs will be measured by the Photosensor Laboratory in Darmstadt, irradiated with photons at a dose of 30Gy at the Strahlenzentrum in Giessen andmeasured again in Darmstadt. Each time, a characteristic curve with gainM is measured against voltage V . The operating point is defined by an individual operating voltage and shows a certain increase at this point. In order to determine this operating point as accurately as possible, several interpolation methods are investigated in this work with the aid of statistical means, since the model commonly used in standard literature, the so-called Miller-Fit, used at high amplification gains (from about M = 50) does not longer provide accurate predictions. The starting point is a polynomial regression model whose order, number of data points used and concrete implementation, for example a mixed model as a reference model, are analyzed. A simple third-degree polynomial with a total of six data points (three data points each above and below the targeted gain ofM = 150) ultimately proves to be the most efficient. Since two APDs per crystal will be used to detect the same signal, it is important to assign to each crystal the two most similar APDs from the available pool according to their operating parameters so that the sum of the assignable APDs is as high as possible. This requires a suitable tool to determine the similarity of the parameters. For this reason, theMahalanobis distance is used, which is suitable for continuous multivariate spaces. This is spanned by four dimensions, each representing one operating parameter of an APD. This distance function can also be used to determine how similar the APDs behave as a collective. This includes, for example, correlations between the detectors and their parameters, the temperature behavior, the determination of the breakdown voltage or parameter changes due to irradiation. TheAPDs are assigned using an implementation of the BlossomValgorithm, which produces a perfectminimum- weighted matching. The influence of it through the introduction of limits regarding possible parameter differ- ences within the 2-groupings is examined in detail with effects on the resulting total number of pairings. The high-voltage supply of the APDs is provided by a circuit board which is capable of regulating a total of eight APDs. For such a multi-matching no approach exists as of this writing. Therefore, the grouping of four 2 2-pairings to an 8-pair is performed via so-called virtual APDs, which allow the previously used Blossom V algorithm to be reused. A virtual APD represents the APDs of a pairing via their mean values of their operating parameters.. The voltage resolution of the supply board is according to the used 10-bit DACs 100 mV and provides a voltage range of presumably about 50 V. The quartets and finally the octets must also be assigned accordingly so that they fulfill the corresponding voltage range. If only the voltage values are used as a distance function for the octets, the maximum voltage difference within a high voltage board is less than 5 Volt. In order to enable an online monitoring of the APDs, a light pulser is used to couple light into the crystals. This light will be converted by the APDs into corresponding signals. Due to the small free volume in the mechanical carrier of the calorimeter, it is not possible to install it directly there. Therefore, the light is guided via a light fiber from the light pulser to the respective crystal. There is a special attachment for the fiber necessary, which has an influence on the coupled light quantity. Several design proposals are currently being investigated, of which the first prototype is analyzed in this work. The prototype is a dome-shaped cap made of polyamide 12 and is mounted at the front of the crystal. This method provides some degrees of freedom such as the coupling angle and the depth of the fiber. The influence of these parameters on the amount of coupled light is experimentally investigated using a PANDA-scintillation crystal and a photomultiplier as a detector. In order to improve the reflective properties, the cap is coated with barium sulfate and its radiation tolerance and application method are investigated. In addition, the light injection is simulated in SLitrani with two APDs as detectors. 3 Part 1 Fundamentals „The Standard Model is working too well‘‘ Richard P. Feynman 1 Motivation Pursuing the principle of simplification, the foundation of physics nowadays is based on four fundamental forces. The Standard Model unifies three of them and is, at the present, the most complete theory to describe nature. It is an effective field theory built upon major gauge theories and is, in return, a gauge quantum field theory itself. The Standard Model provides a deep insight into interactions as well as the structure of matter. Especially the former is subject of interest since all incidents in nature are understood as interactions: Among particles, forces, fields or other things, depending on the point of view. Unfortunately, at this stage, the Standard Model falls short of explaining ‘‘everything’’ successfully. A few violations and contradictions have been noticed and some questions still remain open, for example: Why are there exactly three families of particles? The elementary particles can be divided into three families which differ almost only in mass Why is there an imbalance in the mass scale of subatomic particles? Particles gain mass through the Higgs mechanism but why do they couple in different ways? Why is the matter-antimatter ratio unequal? Beginning with the Big Bang, there should be a symmetric matter-antimatter ratio Why does the potential of the strong force include a repulsive part? Models of the effective nuclear force including short-range repulsion tend to fit experimental data better compared to those which are purely attractive How did the universe evolve (horizon problem)? There are two possibilities: Expansion inflationary or cyclic In order to help answer some of these questions, a new international science facility is currently being con- structed: The FAIR1 research center. 2 FAIR FAIR will be a new accelerator complex, located at the GSI2 in Darmstadt, Hessen, Germany. Contributing crucial discoveries to physics, the GSI became a significant part of the national and international research landscape. Up to the present day, this research facility plays a major role in a vast range of scientific areas, for example, from nuclear physics over space research to cancer treatment. To drive forth the progress in numerous open research fields, the GSI will be extended by creating the adjoining FAIR3 facility. The resulting complex will harbor a lot of new experiments under the aegis of major ones like CBM4, PANDA5, NuStar6 1Facility for Antiproton and Ion Research 2Gesellschaft für Schwerionenphysik mbH 3Facility for Antiproton and Ion Research 4Compressed Baryonic Matter 5antiProton ANnihilation at DArmstadt 6Nuclear Structure, Astrophysics and Reactions 4 and APPA7. A detailed summary of the research projects can be found in [73]. Physics at FAIR is related to antiprotons together with ions of all kinds over a large energy spectrum. The key component of FAIR is the accelerator SIS1008. In case of ions, it uses the GSI ion accelerator Unilac9 as one of two pre-stages which will be modernized to fulfill the requirements for FAIR. Subsequently to the Unilac, ions will be injected into the second pre-accelerator, the SIS18, with an energy of 11MeV/u at a pulsed current of 15mA [69]. Figure 1: The modernized universal ion linear accelerator (Unilac) [71]. It will provide an energy of 11.4MeV/u for or 238U28+-ions at a current of 15mA. Ions, mostly 238U4+, can be produced by a range of ion sources based on different mechanisms like electron-cyclotron-resonance, Penning ionization gauge and multi cusp ion source [61]. Along a 9m radiofrequency quadrupole, the bunches will achieve an energy of 120 keV/u at a frequency of 36MHz. Afterwards, the ions will pass two IH-cavities and enter an Alvarez with an energy of 1.4MeV/u. A gaseous stripper will then remove all Uranium isotopes different from 238U28+. After leaving the subsequent post stripper, a current of 15mA is achieved at an energy of 11.4MeV/u. The transfer line (TK) to the SIS18 consists of a foil stripper and a further charge state separator system (e.g. 73+ for Uranium). In addition, a dedicated accelerator will be built for protons only, the so-called p-linac. Figure 2: The new proton linear accelerator (p-linac) [70]. It comprises a proton source, a radiofrequency- quadrupole and a Cross-bar H-Type Drift Tube (CH-DTL) linac. The ion source provides a current of 100 mA together with an extraction energy of 95 keV. After the radiofrequency quadrupole, the particles achieve an energy of 3 MeV before they accelerate up to 70 MeV by the drift tube. Afterwards, they are injected into the SIS18 at a current of 70 mA. It will be capable of injecting protons up to 70MeV in pulses of 70mA at 4Hz into the subsequent synchrotron SIS18 [69]. The SIS18 will extract protons up to 4.5GeV and ions with an energy of 200MeV/u and into the SIS100 (see fig. 4), each at a repetition rate of 2.7Hz [68, 69]. With a magnetic rigidity of 100Tm, it brings up the protons to an energy of nearly 30GeV and ions up to 1.5GeV/u. In contrast to other large particle accelerators which focus on high beam energies, FAIR is designed for high 7Atomic, Plasma Physics and Application 8Schwerionensynchrotron 9Universal Linear Accelerator 5 beam intensities: In case of ions 4 · 1011/s and in case of protons 2 · 1013/s. The figure below depicts the global parameters of the PANDA accelerators: Ions: Protons: Figure 3: Extraction parameters of the main accelerator SIS100 [118]: Ions like 238U28+ will be produced by the Unilac and extracted with 11.4MeV/u into the SIS18. There, ions will be accelerated up to 200MeV/u and injected into the SIS100. In the main accelerator ring, the ions will be accumulated and extracted with an intensity of 4 · 1011/s at 1.5GeV/u. Protons will be prepared by the p-Linac. Injected into the SIS18 with an energy of 70MeV, they will afterwards be pulled out into the SIS100 at an energy of 4GeV. Finally, leaving the SIS100 with an intensity of 2 · 1013/s, they will have achieved an energy of nearly 30GeV. For lower beam momenta, the particles with their quantities received from the SIS18, can bypass the main accelerator SIS100 and be guided directly to the experimental halls, storage and cooler rings. CRYRING UNILAC p‐LINAC SIS18 SIS100 HESR PANDA CBM Rare Isotope Production Target SUPER‐FRS (NuSTAR) Antiproton Production Target Plasma physics Atomic physics CR Figure 4: Sketch of the existing GSI facility (blue) and of the planned FAIR facility (red) [17]. Ions will be produced by the upgraded Unilac and protons will be generated by the new p-Linac. Then, both pre-accelerators extract into the next pre-accelerator, the SIS18, before the particles will receive their maximum energy in the main accelerator SIS100. From there on, the particles can be guided to various experimental areas. Some of the experiments require a preceding preparation of the particles to obtain their final properties. 6 The research at FAIR will cover a wide spectrum and can be divided into three general topics: A deeper inves- tigation of matter, an advanced research of the evolution of the universe as well as the utilization of ions in technology and applied research. These studies will be representedmainly by fourmajor experiments [114, 158]: • APPA: Research at FAIR will study plasma at unknown states. Heavy ions will be used to analyze the possible influence of cosmic radiation on crew and components for upcoming inter-planetary flights. Obtained information can be used for space flight- as well as for QED-experiments. • CBM: At extreme energy densities, confinement10 is assumed to vanish resulting in quarks and gluons moving freely. The required conditions for such a state can be achieved through heating and compressing occurring in high-energy nucleus-nucleus collisions. On this basis, it is foreseen to explore an unobserved part of the phase diagram of nuclear matter. • NUSTAR: Primary heavy ionswill break into fragmentswhenhitting a target. Afterwards, these fragments will be separated magnetically to be extracted in secondary beams. Such particles can be tailored for all kinds of experiments to investigate the nuclear configuration of various isotopes together with heavy elements and their processes. • PANDA: See the dedicated section PANDA-experiment on page 9. With respect to the PANDA-experiment, the production of antiprotons will now be described in detail. 3 Antiproton production The p-linac is designed to produce antiprotons out of protons after leaving the accelerator chain. It is feasible to produce antiprotons by the Unilac too, but resulting in plenty of fission fragments at a lower luminosity. At FAIR, protons from the accelerators SIS18 and SIS100 will be available in a range of 1.5 − 29 GeV/c. At these momenta, the protons will hit the antiproton production target in bunches of 50ns to generate antiprotons of up to 3GeV in a flux of 107/s [158]. Figure 5: Production of antiprotons [42]. Protons extracted from SIS18 or SIS100 will hit a metal target and result in the preparation of a secondary beam that contains antiprotons of 3 GeV/c. With the help of a separator, all other kinds of particles will be removed. About 98 % of the produced antiprotons will be discarded due to a large bending angle θ or momentum p. Afterwards, they will pass a magnetic horn which focuses the beam. An antiproton separator, a beamline of 100m length with a very high acceptance, will isolate antiprotons above all from protons as well as from all other kinds of particles. Next to the separator, the antiprotons will be ejected and cooled by the CR. When using a primary proton beam, antiprotons can only be produced via inelastic reactions due to baryon 10Phenomenon that quarks and gluons cannot be observed singularly 7 number conservation: p + A + Ekin 7→ X + p, where A is the target and X represents all particles in any allowed final quantum state. The kinetic threshold energy for an antiproton production is 6 ·mpc 2 ≈ 5.63 GeV. The cross section for the production of antiprotons varies from about 50 to 100 mb, according to the related momentum range. 3.1 Collector Ring The purpose of a collector ring is to improve and to ensure the quality properties of a beam, viz by minimizing themomentum spread and emittance. This will be done in two different ways: Bunch rotation and stochastic cooling. Antiprotons in bunches of 108 will be injected into the CR and caught by 1.3MHz radiofrequency- quadrupoles. Applying a bunch rotation in the longitudinal phase space will reduce the momentum spread by a factor of 3. During stochastic cooling, bunch rotation will be disabled but it will also reduce the momentum spread. It is noteworthy that such a process is not following the Liouville’s theorem. The principle of stochastic cooling works in such a way that the orbit of the beam is measured and compared to its ideal orbit. In case of a deviation it will be ‘‘kicked back’’ according to a phase shift of π(n+ 1/2) between the signal pick up and the kicker, an electromagnetic device. The cooling time for antiprotons will be about 10 s and in case of ions 1.5 s. The bandwidth will start at 1− 2GHz but will be extended later to 2− 4GHz [115]. Figure 6: Collector ring [115]. The CR is the first stage after the production of antiprotons. It aims at cooling and fixing them at 3GeV by the use of stochastic cooling and will reduce the relative momentum spread of antiprotons by a factor of about 10. The CR has to prepare the particles for a further extraction to the HESR. Above all, the antiprotons have to be fixed at a velocity of 0.97 c corresponding to p = 3GeV/c, whereas isotopes will be fixed at 0.83 c corresponding to 740MeV/u. Antiprotons will enter the CR with a momentum spread of 4p/p = 3% and leave at 4p/p = 0.2%, ions will be injected into the CR with 4p/p = 1.5% and ejected with 4p/p = 0.1% [41]. Finally, the antiprotons enter the HESR to be prepared for the PANDA-experiment. 8 3.2 High Energy Storage Ring Storage rings improve the quality of the beams by providing energy sharpness and focusing. Within the HESR, this will be achieved through electron cooling and stochastic cooling, longitudinally as well as transver- sally. Electron cooling works via superposition of cold intense electron beams which interfere with the antipro- tons at the same velocity. The injected beamwill be de- or accelerated by about 0.1GeV/cs and themomentum will be transferred via Coulomb collisions. The HESR has to ensure the cooling of antiprotons in a momentum range from 1.5 to 15 GeV/c. Two technical modes can be chosen: A high luminosity mode with luminosities up to L=1032 cm−2s−1and a high resolution mode with a relative momentum resolution up to 4p p ≤ 10−5. Figure 7: High energy storage ring [98]. Antiprotons of 3.8GeV/c from the CR will be cooled and accelerated up to 15GeV/c at the HESR. Cooling will be realized by a combination of electron and stochastic cooling. Cooled antiprotons at 3.8 GeV/c from the CR will be transferred adiabatically in bunches to the HESR which is capable of accepting antiprotons with twice a momentum spread and emittance of the CR extraction parame- ters. Cooling already causes a loss of 30% of antiprotons but with the help of stochastic cooling and a barrier bucket system, this amount can be reduced. Finally, the aniprotons will be accumulated until a number of 108 antiprotons is available. Antiprotons traversing the target, respectively not impinging the target material, are recirculated in the storage ring for about 500, 000 times. Meanwhile, the particles will be cooled by elec- tron cooling to ensure a compensation of any energy loss. HESR will provide a high reaction rate and a high resolution of 30keV to enable the study of rare production processes at PANDA-experiment. 4 PANDA-experiment The PANDA-experiment is located at the HESR and represents the main pillar of hadron physics at FAIR. Hadrons are compounds of quarks, elementary particles which are subject to the strong force. Its mediators are gluons and, up to the present, neither the interaction of quarks or gluons is fully understood nor in which all combination quarks and gluons can occur. PANDAwill help to deepen the knowledge about the strong force by its particular kinematical region. Especially the charm region is of high interest to investigate confinement and the origin of hadron masses. Antiprotons will annihilate with target protons to produce a variety of composite particles. HESR utilizes antiprotons for its physics program because of several reasons [1, 83]: 9 High angular momenta directly accessible e+e−-processes lead to charmonium states limited by the quantum number of the virtual photon, JPC=1−−. Unfortunately, even in this indirect case, different vector spin-parity states remain unobtainable due to the angular-momentum barrier. In contrast, pp-reactions enable direct formation of all quantum states: e+e− → Ψ ′ ↪→ γχ1,2 ↪→ γγ J/ψ ↪→ γγe+e− p̄p → χ1,2 ↪→ γ J/ψ ↪→ γ e+e− Unlike formation processes as e+e−, a direct production provides a distinct background to identify charmo- nium states. While formation processes will produce charm as well as non-charm hybrids with high cross sections, production processes will generate charm-hybrids plus a different particle, e.g. π and η [95]. Antiproton-reactions are rich of gluons The investigation of gluonic excitations is much easier when a lot of gluons are present. This happens easily in antiproton-proton reactions. Heavy glueballs could also be observed but are hard to identify due to their mixing (see Gluons on page 14). Furthermore, the PANDA-detector provides additional useful aspects: Very high resolution in formation reactions The advantage of resonance scans through beam stepping is given by their much better resolution compared to an invariant mass reconstruction which depends on the detector resolution. PANDA makes it possible to discover the mass width of very narrow states through energy scans with a precision better than 100 keV. Large mass-scale coverage The PANDA-experiment provides CM-energies from 2 to 5.5GeV/c which enable studies of hadronic states consisting of light, strange and charm quarks. High hadronic production rates By taking advantage of large production cross sections in case of antiproton-proton reactions compared with electromagnetic probes, PANDA will provide a high statistic accuracy. These aspects allow advanced investigations with respect to baryon and meson spectroscopy, reaction dynam- ics with possible CP violation as well as deeper insight into the hadron structure and more. FAIR will provide very similar operation parameters to the previous AAC (LEAR Experiment, see table 1) but with the support of on-hand theories and investigation targets which were not available in the AAC’s uptime. The CERN Antiproton accumulator has already been shutdown in the early 90’s, whereas Fermilab’s Tevatron stopped in 2011. For that reason, PANDA will come into play and aim at specific objects of investigation, de- picted in fig. 8: 10 Figure 8: Observable hadrons at HESR [73]. The figure depicts the accessible hadrons as a function of the antiproton momentum provided by the HESR. The arrow indicates the energy range studied within LEAR at CERN, the successor of the AAC. The following table holds a comparison of accelerators using antiprotons: Proton beam CERN (AAC) Fermilab FAIR Kinetic energy / [GeV] 25 120 29 Maximum number of protons per cycle 1.45 x 1013 8 x 1012 2 x 1013 Transverse beam emittance h/v / [π·mm/mrad] - - 3 / 1 Cycle time / [s] 4.8 2.2 10 Pulse length of one bunch / [ns] 400 1600 50 Antiproton beam Kinetic energy / [GeV] 2.7 8 3 Momentum spread / [%] 6 4.5 6 Transverse emittance h=v 210 35 240 Yield per proton 5.4 x 10−6 2.8 x 10−5 5 x 10−6 Maximum yield per cycle 7 x 107 2.6 x 108 1 x 108 Maximum possible stacking rate / [1/h] 5.3 x 1010 2.1 x 1011 3.5 x 1010 Table 1: Comparisonof antiprotonaccelerators according to different facilities [42]. FAIR is able to deliver the highest number of protons per cycle and also the most intense beam. 11 4.1 Physics at PANDA Most of all, PANDA embodies the hadron physics program at FAIR. The single subjects are in the first instance charmonium spectroscopy, hybrids and glueballs. The rules that dictate the quarks how to freeze out into hadrons are determined by theQCD11. Present fundamental models of the strong interaction reproduce physics phenomena only at distances much shorter than the size of a nucleon. In this region, perturbation theory can be applied and yields high precision results and predictions but these are not applicable in the hadron region. The program of PANDA addresses specific aspects of non-perturbative QCD by making use of the interaction potential of cc which can be computed with the help of effective field theories and LQCD12. Due to the charm quark’s heavy mass, in contrast to up, down and strange quarks, a non-relativistic treatment is more feasible and its corresponding kinematical region is crucial for a better understanding of quark confinement and mass generation. After all, the physics at PANDA is on the whole linked to QCD. Its coupling constant gQCD determines the particle’s interaction strength via the running coupling αs = g2/4π. This constant is not completely constant and depends on the characteristic energy scale of the underlying process. Noteworthy it goes logarithmically: αs ( q2 ) = 12π (33− 2nf ) log (q2/Λ2) (1.1) with Λ as the scaling parameter, nf for the number of quark flavors to take part in self-loops and q2 as the four-momentum transfer This constant αs(q 2) behaves very differently for q2 than other coupling constants do since αs(q 2) increases with q2 and results in powerful interaction processes - in case of large distances. The scaling parameter Λ describes the region in which q2 becomes ineffective, respectively, this happens when Λ2 is greater than q2 inducing quarks and gluons to participate only in weak processes (related to ‘‘asymptotic freedom’’). The other way around, it is difficult to study this special situation because αs(q 2) will oblige quarks and gluons to form hadrons. Therefore, up to now, it is not possible to observe free quarks. This attributes the scaling parameter Λ the capability to set a boundary between a world of quasi-free quarks and gluons on the one hand and a world of hadrons on the other hand. Important to emphasize: Λ is a free parameter and, thus, not predictable by theory. Thus, it has to be determined by experiments [49]. Overall, αs describes how much a particle participates in strong interaction processes and occurs in the phe- nomenological potential of the strong force: V (r) = −4 3 αs r + kr (1.2) with r representing the qq gap αs has been determined experimentally as αs=0.1185 at √ s = 91 GeV, the mass of the Z boson. The strong potential does not decrease with the distance like other forces do, instead it increases at a rate of about 1 GeV/fm. Further researches on the Quantum Chromodynamics promise to yield a better understanding of the generation of hadronic masses which is connected to the confinement of quarks and to the spontaneous breaking of chiral symmetry. Additional general questions are the fundamental degrees of freedom of a bayron and gluonic excitations. 11Quantum chromodynamics 12Lattice Quantum Chromodynamics 12 4.1.1 Charmonium spectroscopy Charmonium13 is the bound state of a charm together with an anticharm quark. Its charm flavors compensate each other resulting in a so-called ‘‘hidden-charm’’. Charmonium is someway special because of its sepctrum. One of these states is J/Ψ which is the most prominent state as it is the proof for the fourth quark (c), back in the 1970s. Figure 9: Charmonium states [106]. The spectrum highlights experimentally observed states in black and theoretically predicted ones in colours (distinguished by their angularmomenta JPC). The open charm threshold (DD) is at about 3750MeV/c2 and sets a boundary between the upper and lower region, each with a different density. All eight states below the open charm threshold are experimentally well studied. The ηc denotes the ground state of charmonium. Furthermore, the spectra of charmonium (below the open charm threshold) and positronium resemble each other. This promotes the assumption that the model of the strong interaction is similar to the electroweak theory which provides the subtle difference of a 1/r Couloumb-potential to replace the linear confinement part in the strong potential. This property of separated energy scales makes the cc-spectrum an ideal probe for confinement researches. While the masses below the DD-threshold14 have been quite accurately measured, the region above is well unknown up to now, except of the ψ-states, especially ψ(3770), which have already been observed by e+e−- colliders. Nevertheless, its excited states 4040, 4160 and 4415 require further investigation. hc has also already been observed by E835 (pp → hc → J/ψπ0) and CLEO (hc → ηcγ) [12] but further observations have a very high priority because the data is inconsistent up to now. Besides, former experiments studied the lower region only in large energy steps. In contrast to the states above the open charm threshold, strong decay modes are suppressed which result in long life times and very narrow 13cc 14D mesons contain exactly one charm quark as the heaviest one 13 widths. At the moment, the low-lying states are already well described theoretically but current models fail at higher levels. Being located below the open charm-threshold (e.g. the D-mesons, the so-called ‘‘hydrogen- QCD analogue’’), they cause the charmonium region to be a vital opportunity for QCD-tests and the region above this threshold will extend the knowledge of the strong interaction in general. 4.1.2 Gluons In the naive quark model, the nucleons are made up of three quarks and the mesons are built of a quark and an antiquark. These models do not display the real world but they have the merit of giving an image of it though neglecting the admixture of gluons as well as of see quarks. However, reality is more complex, for example, such that the gluons, force carrier of the strong force, are in principle allowed to build up hadrons too. Figure 10: Glueball spectrum [30]. The colours in- dicate the spin quantum number. One of the most promising candidate is f0(1500), which has a flavor- blind decay width of Γ = 110MeV. Hybrids: Beside a quark and an antiquark, hybrids contain excited gluons too (qq̄g). Glueballs: Gluons are subject to their own force and confinement requires that particles must not exist which are not color-neutral. Thus, because gluons carry color charge, they should be able to create compounds which are colorless. An important aspect of the research of gluonic mat- ter is that glueballs and hybrids are allowed to have exotic quantumnumbers (called ‘‘oddballs’’), for example JPC = 0−−, 0+−, ... These states are promising opportunities to distinguish between pure quark-states and those with a gluonic part. Glueballs have characteristic decays such that the decay width is quite narrow and that they are fla- vor blind since valence quarks do not occur. Be- low 3.6 GeV/c2, the dominant channels will likely be φφ and φη. The decays J/ψφ and J/ψη are the best candidates to observe heavy glueballs [12]. The f0 state at about 1500MeV/c2 represents the sup- posed glueball groundstate, while the lowest glue- ball with exotic quantumnumbers (2++) is assumed to be at about 2.4GeV/c2. In formation processes, pp hadronic systems only allownon-exotic quantum numbers whereas in production processes even exotic quantum numbers can be generated, typically with a π or a η as a recoil particle. Experiments at LEAR hint that pp-reactions produce numerous particles with gluonic degrees of freedom in a direct way. The charmonium mass range provides a field where gluonic matter is expected to be less mixed with regular mesons since cc requires its quark content to annihilate with each other. 14 4.1.3 Hadrons in nuclear matter The QCD expectation value of hadrons is assumed to be dif- ferent in hadronic environment compared to vacuum. By transitioning, a mass-shift of hadrons can occur, in some cases larger than their natural width. However, Fermi mo- tion will already cause broadenings up to 250MeV which will make it rather difficult to measure modifications below 100MeV. Mass shifts of states with a charm flavour can in- duce decays of neighbouring states and, therefore, facilitate mass changes to be observed. Hayashigaki supposed that the shifts of D and D̄ could decrease the DD-threshold enabling charmonium decays into DD [21]. The investigation of medium modifications can be bridged to the origin of masses in the context of spontaneous chiral symmetry breaking in QCD. In this context, the Goldstone theorem plays a major role by determining that, at any time a continueous symmetry is sponanteously broken, a mass- less scalar appears. This spontaneous breaking of the chiral symmetry is a good method to investige the low-energy phe- nomena of the strong interaction and is well defined for the light quarks in the QCD. Up to now, experiments have only studied the light quark re- gion. Thanks to its high intensity p-beam at the HESR, it will be possible to augment this section by the contribution of the charm region. Vaccum Nuclear medium Figure 11: Hadrons in nuclear matter [74]. While hadron mass shifts in case of the non-charmed pseudoscalar and vector mesons will be studied at HADES and CBM, the mass shifts of charm mesons will be in- vestigated at PANDA. 4.1.4 Hypernuclear physics Nucleons are solely built of light quarks and are regularly only fragile towards the weak force which enables the generation of strong bonds among each other and results in a comparatively very long lifetime. On this basis, hypernuclei are nuclei with at least one nucleon being a hyperon Λ15. Such nuclei have barely been sufficiently measured up to now. The investigation of hadrons including a strange part is essential to understand the low-energy regime of QCD due to the additional degree of freedom because it is yet unknown how the nuclear force emerges from QCD [80]. In comparison to hadrons without strangeness, hyperons are not limited in the population of nuclear states as they avoid Pauli blocking due to their quantum number strangeness. When a strange quark takes a light quark’s place within a nucleus, the nuclear structure will change by producing a system of a hyperon together with the core of the remaing nucleons. Hypernuclei offer the possibility to study the structure of nuclei as well as its properties. With the help of a stored antiproton beam, Ξ-hyperons16 will be copiously produced in the PANDA-experiment via: p̄p → Ξ−Ξ+ p̄n → Ξ−Ξ̄0 p p p p π π π π Λ Ξ Λ Ξ - + - + + - At first, the antiprotons will hit primary nuclear targets and then produce double hypernuclei in formation processes because secondary targets will catch the Ξ-particles. Among all hyperons, Λ are the only ‘‘conve- nient’’ systems to investigate the strong nuclear interaction. Λ are produced at a secondary target through 15Baryon with at least one strange quark but without a heavy quark 16Hyperons comprising two strange quark and one light quarks 15 e.g. Ξ−p → ΛΛ. This channel will likely decay into pπ− and then finally emit γ. Therefore, high-precision γ-spectroscopy of double strange systems will be enabled by the Electromagnetic Calorimeter (see Electro- magnetic Calorimeter on page 24). 4.2 PANDA-Detector As previously described in section 4.1, Physics at PANDA, the PANDA-experiment is foreseen to perform high- precision tests of the hadron structure as well as of the nature of the strong interaction. The detector has to meet some demanding requirements[95][83]: • The detection of low energy photons plays an important role (see Electromagnetic Calorimeter on page 24) • A momentum resolution of 1 % to reconstruct invariant masses • An excellent vertex resolution in the order of 100 µm is relevant to reconstruct open-charm states, e.g. D-mesons • High interaction count rates up to 20MHzhave to be handled, connectedwith an efficient event selection • Radiation tolerance is mandatory due to the presence of intense radiation fields • Since PANDA is a fixed target-experiment, it has to manage the detection of the resulting forward boost together with a 4π -scope for reactions with large opening angles due to their high transverse momenta like charmed hadron decays • Studies of hidden-charm and of exotics require the reliable and simultaneous detection of dilepton pairs as well as a good kaon identification • In case of e.g. hyperon studies, a good detection of antihyperons and low momentumK+ in the forward region is mandatory together with a solid state tracker to track hyperons at large angles The detector of the PANDA-experiment will be placed within the HESR. It comprises an extensive symmetric target spectrometer and a large acceptance dipole spectrometer to cover the forward region. On basis of stochastic cooling, the HESR will ensure the beam quality and provide excellent parameters such as a high luminosity of L = 1032 cm−2s−1 at a maximum momentum spread of δp/p = 10−4. In case of high-precision spectroscopy, electron cooling will enable a high resolution mode for momenta up to 8 GeV/c at a momentum spread of δp/p = 10−5. However, the required precision of the measurement of resonancemasses and widths depends on the precision of the beam energy, respectively, the resolution of the line shape depends on the phase space cooledmomentum distribution and not on the detector resolution. Therefore, an excellent resonance mass resolution of 30 keV is feasible. A telling example to show the capability of PANDA is the measurement of X(3872) which has already been confirmed by BELLE and several other experiments. Its natural width is less than 1.2MeV and simulations predict for PANDA a Breit-Wigner response of 100 keV at a precision of 20 % [83]. And in case of Y(3940) PANDA is expected to observe thousands events per day, whereas e.g. BELLE and BaBar needed several years for a lower statistic [161]. Since PANDA is designed as a beam-target experiment (see fig. 12), many particles will go into the forward direction. Therefore, the Foward Spectrometer contains a dipole magnet that bends the antiproton beam to allow a positioning of the subdetectors in a 0°-direction. Overall, the forward angles will be covered by Drift Chambers located in both Spectrometers. Additionally, this will be supported by a DIRC17 in the Target Spectrometer together with a muon detector. 17Detection of Internally Reflected Cherenkov Light 16 TOF Micro Vertex Detector Electromagnetic Calorimeter Muon Detection Central Straw Tube Tracker DIRC Forward Straw Tube Tracker Shashlyk Electromagnetic Calorimeter Muon Range System RICH TOF Dipole Target Production Target Spectrometer Forward Spectrometer Figure 12: PANDA-Detector [65]. The envisaged physics program requires a 4 π coverage of the solid angle together with a good particle identification. Hence, a high angular and energy resolution for photons and charged particles is mandatory. The detector contains two spectrometers: The Target Spectrometer which covers the interaction point and the Forward Spectrometer that analyzes the momentum of the forward-going particles. Both contain several subdetectors with arrangements that follow the onion principle. In the following, the subdetectors of the Target Spectrometer will be explained in detail. Target Spectrometer The innermost detector is the Micro Vertex Detector which is of great importance in reconstructing vertices and providing tracking andmomentum information together with the Straw Tube Tracker and the Gas Electron Multiplier Detector. The DIRC detector provides particle identification and the Electromagnetic Calorimeter delivers energy information. The complete Target Spectrometer is surrounded by a solenoid magnet and per- pendicular to each other, both the beam pipe and the target pipe cross all subdetectors. The Target Spectrometer covers the interaction point and provides a 4π acceptance. Thus, it is particularly designed for the detection of transverse reaction processes. It contains a superconducting solenoid magnet with a field homogeneity of better than 2% to measure high transverse momentum tracks of charged particles. Overall, the Target Spectrometer is designed modularly to ensure different setup possibilites without the need of a full assembly. Moreover, the detector will be arranged in three sections: • the forward part covers vertical angles down to 5° and horizontal angles down to 10°, • the barrel part spans the angles between 22° and 140° and • the backward part detects signals between 145° and 170°. 17 Beampipe Solenoid Micro Vertex Detector Electromagnetic Calorimeter Muon Detection Central Straw Tube Tracker DIRC Target Production Target Spectrometer Interaction point Gas Electron Multiplier Stations Scintillator Tile Target recovery Figure 13: Target Spectrometer [65]. The Target Spectrometer is constructed according to the onion-shell principle. Through injection pipes, the target material will cross the beam pipe. Radiant from the interaction point, the subdetectors are arranged from the inside to the outside as follows: 4.2.1 Target The internal target concept of PANDA pursues two different drafts: Frozen pellet targets and cluster-jet targets. The requirements of the targets are on the one hand to provide a pure material with as few as possible admixtures and on the other hand to provide an areal target density below ρ = 1016 nucleons/cm−2 [34]. The first is able to reduce background signals, the latter is important to avoid multi-scattering and beam heating. Nonetheless, the target must be thick enough to provide the foreseen high luminosity of L = 1032 cm−2s−1. Therefore, a thickness of about 1 ·1015 atoms/cm2 is required for 1011 stored antiprotons in the HESR. The two major concepts are: Cluster-jets: Agas is injected through a nozzle into vacuumand, while passing, the gas cools down to form a supersonic beam. At certain conditions, condensation can occur to convert the gas into nano-particles of which the cluster-jets are made up with up to 1015 atoms/cm2. The advantages of a cluster beam are its homogeneous volume density together with a sharp boundary and a constant angular divergence. This results in a time-independent beam-target injection. Hence, the parameters like the cluster-jet thickness can be easily modified during operation. The substance will be mostly Hydrogen but it can be replaced by Deuterium, Nitrogen, Neon and other even heavier gases. Pellet-targets are composed of frozen Hydrogen microspheres which pass the beam pipe as a stream of about 10, 000 pellets/s at 70m/s. Their size depends on the injection nozzle but is between 20 µm and 40 µm. The stream has a position uncertainty of ± 1mm at a diameter of 3mm, corresponding to 1015 atoms/cm2. 18 Beampipe Interaction point Target recovery Target Production H2 p _ Figure 14: Target system [62]. Two different main systems will be used for distinct applications: The cluster-jet target and the pellet-beam target. Their applications depend on specific conditions. On the one hand the cluster target which is designed for a high precision, whereas, on the other hand, the pellet target will be used to provide a high luminosity. The targets will traverse the beam laterally through a pipe. Due to a lack of momentum in beam direction, the targets can be regarded as fixed. Compared to each other, the pellet targets have a higher maximum density and a better point-like interaction zone. In contrast, the cluster target provides an adjustable and homogenous target density plus a better time structure. In the end, it depends on the specific experiment which target is more suitable. For a • high luminosity up to L = 1032 1 cm2s and 4p p = 10−4 with 1011 p̄, it is the pellet target and for a • high precision with L = 1031 1 cm2s and 4p p = 10−5 with 1010 p̄, it is the cluster target. Both concepts share the same devices. Target material that did not interact with the beam will be recovered by the target beam dump. 4.2.2 Micro Vertex Detector The MVD18 is designed to track charged particles and delivers track and time information. A minimum of at least four track points is necessary to reconstruct a particle’s trajectory [142]. On this basis, it will strongly improve the transverse momentum resolution. Hence, to meet all the requirements of the according physics tasks, it will be capable of reconstructing displaced vertices. It is the very first detector around the interaction point due to its purpose to resolve primary interaction vertices on the one hand and secondary vertices of short- lived particles such as D-mesons and hyperons on the other hand, plus to provide a maximum acceptance close to the interaction point. The MVD has a length of 40 cm and a radius of 15 cm [33]. The vertex reconstruction will have a spatial resolution of < 100µm and a time resolution of ≤ 6.43ns. Mainly, the detector consists of two different parts: Four barrels of silicon detectors, of which two layers are radiation hard hybrid silicon pixel detectors and two layers are double-sided silicon strip sensors as well as six forward disks made of a mixture of the former ones. The spatial resolution is given by the pitch19, which is, e.g. 45 µm for the barrel layout and 70 µm for the disk layout. Ideally, the Micro Vertex Detector influences traversing particles as little as possible to leave the particles unaffected for the subsequent detectors. Right after the Micro Vertex Detector, further tracking information will be gathered by straw tubes or by the time projection chamber. 18Micro Vertex Detector 19Gap between strips 19 Figure 15: Micro Vertex Detector [22]. The Micro Vertex Detector is responsible to provide tracking and time information of charged particles. Furthermore, it has to detect primary and secondary vertices. Therefore, it comprises several layers of hybrid silicon pixel detectors and double-sided silicon strip detectors to cover a polar angle of 3° up to 150°. Additionally, six discs will be installed in the forward direction of which four are hybrid silicon pixel detectors and two are a mixture of a pixel and a double-sided strip detector. 4.2.3 Central Straw Tube Tracker Besides the Micro Vertex Detector, the Central Straw Tube Tracker is another device to track charged parti- cles. Hence, it will also measure particle energy losses with a resolution of σE ≤ 10% for momenta up to 1 GeV/c [66]. PANDA provides two of such tube track- ers. The one in the Target Spectrometerwill be installed around the Micro Vertex Detector and will consist of 4636 self-supporting straw tube modules. These straw tubes are about 1 cm in diameter each and operated at over-pressure. Furthermore, the tubes will be glued to- gether to form planar multi-layers. Then, these layers will form a hexagonal layout within the cylindrical vol- ume. The tubes are skewed with respect to the beam axis enabling a position resolution of 2.9 mm in beam direction. The cathode is made of an aluminizedmylar filmwith a thickness of 27 µm, whereas the anode is a gold-plated tungsten-rhenium wire of 20 µm diameter. Argon will be used together with 10%CO2 as quencher because of its good behaviour in high-rate hadronic environments since it does not react with the installed components. In consequence of the presence of the beam pipe, the detector is divided into two halves. Finally, the trans- versemomentum resolution will be about 1.2% and a spatial resolution of ≤ 100 µm is expected [137]. Figure 16: Straw Tube Tracker [63]. The Central Straw Tube Tracker detects charged particles outside the Micro Vertex Detector. It consists of 4636 straw tubes which act like a gaseous ionisation chamber. The tubes are ar- ranged hexagonally around the Micro Vertex Detector. 20 4.2.4 Time-Of-Flight Detector The main purpose of the TOF-detector is to measure the particles’ velocity to discriminate different particles by their accordingmasses. The detector itself will be a scintillating tile hodoscope containing 1920 small scin- tillating tiles read out by 15360 Silicon Pho- tomultipliers. The Barrel TOF will comprise 16 segments and, in turn, each segment will contain 120 scintillating tiles. A scintillator will be read out on two sides by four SiPMs connected in series [93]. The time is deter- mined when particles propagate through a very fast organic scintillator. The time of flight, respectively the collision time t0, will be reconstructed by using track and velocity information of other subdetectors resulting in a resolution of about 55 ps, while t0 will have a resolution of 2.3 ns. A time resolution of better than 100 ps is required together with an acceptance angle from 22° up to 140°. Figure 17: Time-of-Flight detector [94]. The collision time t0 of the particle is recalculated via track and velocity infor- mation from other subdetectors. The time itself is measured when a particle traverses one of the 1920 scintillators which are read out by eight SiPMs each. 4.2.5 DIRC The task of the DIRC20-detector is to identify particles via Cherenkov radiation. Charged particles propagating through amediumwith β > 1/nwill emit Cherenkov radiation at an angle ofΘc = arccos (1/βn). The detector comprises two parts, both housed within the Target Spectrometer: A barrel shaped detector to cover light at a polar angle between 22° and 140° and a planar end cap detector in forward direction for a polar angle down Figure 18: DIRC Detector. The DIRC detector uses time-of-propagation to extract the angular information of theCherenkov photons traversing the radiator. It com- prises 200 synthetic fused silica radiators with a thick- ness of 1.7 cm [64]. to 5°. It is necessary to design the DIRC- detector as thin as possible since it will be placed in front of the Electromagnetic Calorimeter. The barrel part contains 200 ra- diators with a thickness of 1.7 cm which are aligned in beam direction at a radius of 48 cm. These radiators are made of synthetic fused silica with a refraction index of n = 1.47 and guide the Cherenkov photons lengthways to a regular aerogel ring imaging cherenkov counter-system via internal total reflections. Particles at about β ≈1 within such a radiator with n = √ 2 might always be reflected in to- tal internally. Finally, the photons exit the ra- diator through focusing elements into an ex- pansion volume which has a different refrac- tion index. This causes a widening of the ini- tial angle. There, the photons will be gathered by a photon detector array of micro-channel- photomultipliers which are usable within the magnetic field [137]. 20Detection of Internally Reflected Cherenkov Light 21 With the help of the hit position on the photon detectors, their initial direction can be calculated. The angle of the Cherenkov photons is determined via a comparison of the track of the detected photon and the direction of the particle’s track from another detector. The larger the propagation time of the particles the larger the dif- ference between photons generated by pions and kaons [108]. The concept design is close to the DIRC-detector of BaBaR but provides some improvements like a more compact geometry, a focusing system and a fast photon timing. The DIRC will have a time resolution of about 100 ps [100]. 4.2.6 Electromagnetic Calorimeter The Electromagnetic calorimeter is described in detail in section 5, Electromagnetic Calorimeter. 4.2.7 Muon Detection The muon tracker will be the most outward detector and it will comprise an inner barrel with four planes and an outer barrel with six planes wrapped around the iron yoke. Each plane will consist of 3 cm thick layers of iron interleaved with MDTs21. Therefore, the yoke of the Target Spectrometer is segmented in thirteen layers in total. All together, the muon system will be made up of 3751MDTs [19]. A MDT is built up of eight anode wires while the cathode is made of an aluminum comb-like profile. The signals will be read out by external strip electrodes [82]. Absorbed muons are an important probe for e.g. J/ψ-decays and D-mesons. The muon system aims at identifying primary muons as well as those from the background. Therefore, the muon detection has to fulfill an important and complicated task. The spatial accuray will be about 0.5mm and a longitudinal accuracy of better than 200 µm. Figure 19: The Muon Tracker [44]. The Muon detection is based on a segmentation of the iron yoke and contains thirteen layers interleavedwith MDTs. Plastic scintillators behind the iron yoke will cover a polar angle in the lab system from 60° down to the dipole’s opening angle. Muons at larger angles will be stopped by the iron yoke. 4.2.8 Tracking and Particle Identification All information of the subdetectors have to be gathered to extract physics signatures for analysis purposes. This is not possible in a single process and, therefore, it is necessary to merge several signal inputs together to form a whole entity. Thus, the previously described subdectors can be grouped into four main categories: • the Target system: Pellet beam target, cluster beam target or nuclear target • the Tracking System: Micro Vertex Detector, Central Tracking Detector and Forward Mini Drift Chamber Stations • the Electromagnetic Calorimeter and • the Particle Identification: DIRC-detector, TOF-detector and the Muon Chamber 21Mini Drift Tubes 22 Figure 20: Tracking&particle identification [45]. The information of the particles can be adressed to various domains each of which is covered by a specific subdetector: Tracking aims at gathering the momentum and is done by the Micro Vertex Detector, Central Tracking Detector and Forward Mini Drift Chamber Stations. Particle identification is settled mainly by the DIRC detector, TOF detector and the Muon Chamber but also with small contributions from the Straw Tube Tracker. The Electromagnetic Calorimeter delivers crucial energy information. Overall, the PANDA-detector requires a highmomentum resolution as well as a high dynamic range for γ- detection plus a very goodparticle identification from electrons over pions up to protons since pions are often more abundant than kaons. Some benchmark channels highlight the importance of a good π/K separation as well as the need for an excellent γ-detection since even a single γ can represent another reaction process [32], [100]: p̄p → π0π0η p̄p → ηc → γγ p̄p → ψ (3770)→ D+D−K−π+π+ + cc̄ p̄p → ψ (4040)→ D∗+D∗− → D0π+D̄0π− → D0 → K−π+/K−π+π−π+ PANDA requires a separation of 3σ to separate π from K in the momentum range from 0.5GeV/c up to 3.5GeV/c. Moreover, an identification of particles is generally needed for momenta up to 12GeV/c. The efficiency of the DIRC detector to separate pions from kaons is almost 100 % [138]. Furthermore, pions will be the most dominant background channel and thus, a e+/−/π+/− discrimination is crucial and, among others, done by the TOF-detector. The TOF can only measure relative times of flight between charged particles compared to each other since it consists of only a single depletion layer that is not located near the interaction point. There, the Micro Vertex Detector will play the role to determine vertices of very short-lived particles like D-mesons with a position resolution of less than 100 µm. In addition, the Straw Tube Tracker provides a position tracking resolution of less than 150 µm and a momentum resolution of about 2%. Tthe DIRC-detector identifies particles with momenta > 1GeV/c. Together with the velocity information de- rived from the Cherenkov angle Θc, the mass of detected slower particles can be determined. On the basis of this, likelihoods for e, µ, π,K and p are feasible. 23 The energy of the particles will be determined by the Electromagnetic Calorimeter with a resolution of about 2%. The mainly produced particles decay into γγ, forcing the need of a detection of the γ’s as best as possible. The muon identification will be done primarily by the muon tracker but the Electromagnetic Calorimeter, the TOF-detector and the DIRC-detector can also improve the identification. Nevertheless, the muon system will enable information of the total path of the muons traversing the absorbers plus their according energy losses. Muons with energies below < 1GeV will not reach the tracker and have to be covered by the DIRC and Electromagnetic Calorimeter. 5 Electromagnetic Calorimeter Calorimetry is the detection of particles within a given material through total absorption. The benefit of such devices is to obtain energy information. A major aspect in designing detectors which contain a calorimeter is that, typically, these subdetectors absorb respectively dissipate all the particles to be measured - except of the muons. Since the particles will not be available anymore for further investigation done by other subdectors, a calorimeter is usually placed at or close to the end of the subdetector chain (see Target Spectrometer on page 18). The PANDA Electromagnetic Calorimeter, for example, is made out of (inorganic) semiconductor crystals which offer very good properties in gaining time and energy information. Their detection principle is based on electromagnetic showers (see Electromagnetic shower on page 30) which are generated when incident particles interact with the detector material. The performance of an electromagnetic calorimeter is given through several aspects: The most important one is the so-called calorimeter response which describes ‘‘the average calorimeter signal divided by the energy of the particle that caused it’’ [131]. An electromagnetic calorimeter should have a constant response for a given particle energy and the global response should be a linear function of energy. An additional significant aspect is the energy resolution, quantifying the precision of measuring the deposited energy. Though a linear response is an absolute necessity, the energy resolution is the most discussed facet. It is influenced by fluctuations of the energy deposition within the detector material and by the specific utilized read out devices. These factors can be expressed in a parameterized equation: σE E = a√ E ⊕ b E ⊕ c (1.3) It includes several aspects which behave uncorrelated and thus, they affect the energy resolution σE E . The co- efficient a represents the fluctuations which are stochastic and almost unavoidable. Cardinally, fluctations in signal productions caused by particles are assumed to follow a Poissonian behaviour. The coefficient b de- scribes fluctuations, for example, generated by electronic noise and pile-up which are energy independent. c contains non-uniformities, for example, caused by the light propagation inside the crystal, imperfections due to the manufacturing processes, inter-calibration errors or shower leakages such as lateral and longitudinal energy losses. The latter coefficient c is the most dominant term. Overall, the formula describes the fact that the energy resolution improves with the energy due to a better statistic since more deposited energy generates more photoelectrons in the readout device. Further calorimeter aspects are the time and position resolution as well as the ability to discriminate particles from each other. In homogenous calorimeters such as the PANDA Electromagnetic Calorimeter, the detector material is at the same time the absorber and detector. Various materials possess different dominant signal production mech- anisms, for example, in case of BGO, BaF2 and PbWO4, the signal is producedmainly by scintillation while lead glassmakes use of Cherenkov light and detectors operating with noble gases are based on ioniziation processes. 5.1 Interactions of radiation with matter Particles can only be measured when they interact with the material of the detector. This requires a long enough lifetime but the majority of the particles of interest is short-lived. Hence, the ECAL will only be able to measure the final products and, with the help of the other subdetectors, the initial particles can be recon- 24 structed. In general, radiation interacts with matter in a wide scope and, in case of calorimeters, the informa- tion sought is their deposition of energy dE/dx. To determine a particle’s energy, the kind of material (atomic number, thickness,..) the particle interacts with plays an important role. Hence, the possible processes can be separated into interactions of photons on the one hand and into interactions of charged particles on the other hand. One main difference is the absorption which results almost in a local drop in intensity in case of charged particles and in an exponential decrease in case of photons. All these processes result in an energy loss along the particle’s trajectory and are always connected to an ion- ization or excitation of the absorber material. The target particles can be almost considered at rest and the radiation processes as a two-body scattering. Then, the possible maximum energy transfer W will occur in head-on collisions and is found by Wmax = (p2c2)/( 12mec 2 + 1 2 ((m/me)c 2 + √ p2c2 +m2c4)), under the as- sumption that the target particle is an electron. When the incident particles are massive like p, K, π and in a high relativistic region, the maximum energy transfer simplifies toWmax ≈ pc ≈ Ei [29]. Figure 21: Overview of interaction processes of particles with matter. The possible interaction processes can be subdivided into those involving photons and into those involving charged particles. In case of photons, the energy is deposited completely in a single process except in case of the Compton effect. In contrast, the energy of charged particles decreases continuously along the trajectory. Charged particles interact mostly via ionization processes and, with respect to their mass, also via radiation emissions. As a thumb of rule, measuring charged particles is often less difficult than measuring photons. An electromagnetic calorimeter can only detect particles which interact electromagnetically. Photon interac- tions can take place via the Photoelectric Effect, Compton scattering and Pair Production while charged particles interact mostly via ionization processes and radiation emissions. In the following, the interactions which are likely to occur within an electromagnetic calorimeter, will be described through some terms: The mass attenuation coefficient µ/ρ, the cross section σ and the ionization density dE/dx. The attenuation of a photon beam behaves exponentially as I (x) = I0 exp (−µx), where µ is the absorption coefficient, also called linear attenuation coefficient. It represents the fraction µ = Nσtot of N absorbed pho- tons per cm within the material. 25 The mass attenuation coefficient µ/ρ is a normalization of the linear attenuation coefficient µ per unit density ρ. It takes into account different magnitudes of absorption of different materials ρ. In return, the mass atten- uation coefficient µ/ρ is similar to the cross section σ which uses the effective area per unit mass instead of particle numbers. The cross section is the probability of an interaction process: dN/dx = −Nnσ, where N is the number of particles, n the number of target scatterers and σ the cross section. It is connected with the scattering length λ = 1/ (nσ) for a certain cross section. To consider all possible final states, the total cross section can be defined but, commonly, the differential cross section dσ/dΩ is used because it considers the dependency of the scattering angle θ with respect to the possi- bility to detect the particle within a given area. 5.1.1 Photon interactions 5.1.1.1 The photoelectric effect eliminates the incidient particle and transfers all its energy Eγ to the atom,ET = Eγ . The photonwill wrest an (photo-)electron from an atom only if its energy exceeds the binding energy I of the electron I ≈ Z2 · 13.6 eV (with Z as the atomic number). Secondary effects like characteristic X-rays and Auger electrons can happen. The cross section τK of the photoelectric effect can be described as τK = 8 3 πr2e4 √ 2 Z5 1374 ( mc2 hν )7/2 (1.4) with re representing the classical electron radius by using the born approximation22 [29]. Through a more handy expression it can be simplified to τ = Zn Em γ with n = 4 andm = 3 for the K-shell and applied in an energy region of E u 100 keV. K-shell electrons are the most tightly bound electrons, thus being the most important contribution to the cross section of the photoelectric effect since the K-edge absorption probability prevails other shells when the photon energy exceeds the K- electron’s binding energy. 5.1.1.2 Compton effect describes the increase of the wavelength (λ0 → λ) of a photon due to scattering at an electron under the angle ϑ. Contrary to the photoelectric effect, the photon is not absorbed by the electron in this process. Instead, it is deflected because the Compton effect is not an elastic scattering but an elastic collision process. The energies of the scattered photon Eγ and of the electron Ee read Eγ = hν0 1 + (hν0/mc2) (1− cosθ) Ee = mec 2 2 (hν0) 2 cos2 φ (hν0 +mec2) 2 − (hν0) 2 cos2 φ (1.5) with hν0 as the energy of the incident photon and hν as energy of the scattered photon At a collision angle of 180°, the Compton-edge, the energy transfer between photon and electron is maximum. There, the scattered photon remains with Eγ = 1 2mc². The cross section σ of the Compton Effect is obtained by the Klein-Nishina formula which is based on Dirac’s relativistic theory. The total cross section is given by σC = πr2e 2 ln ( 2 ( hν/mec 2 ) + 1 ) hν/mec2 (1.6) in case of unpolarized radiation and when the reduced photon energy hν/mec 2 � 1 can be applied. This is a good approximation for photons with an energy of Eγ > 1MeV and a material with a low Z. Equation eq. (1.6) already takes into account binding corrections but is not complete. An extensive description can be found in [79][29]. The Klein-Nishina formula shows a decreasing cross section when the photon energy increases. 22The Born approximation is the first term in the Born expansion and takes into account only the incident particle’s field, e.g. neglects induced emissions. This is a valid assumption when 2πZe2 ~ζ � 1, where ζ = {v, v0} with v being the electron velocity after and v0 before photon emission 26 The low-energy limit of Compton scattering is known as Thomson scattering and can be applied as long as the photon energy is much less than the electron energy: hν � mec 2. Its cross section is given by dσ dΩ = r2e ( 1 + cos2 ϕ ) /2 [51] and together with the resonant and the Rayleigh-scattering it is one of the elastic scat- tering processes. These three processes occur when radiation perturbates electrons at ω0 = 2πν0 and differ in principle only in the compelled oscillator frequency: ω � w0 : Thomson scattering, ω ' w0 : resonant scattering, ω � w0 : Rayleigh scattering. 5.1.1.3 Pair production is the most important interaction to an electromagnetic calorimeter due to its domi-nance at energies of Eγ > 10MeV. Pair production converts a photon in the Coulomb field of a nucleus into an electron-positron pair above an energy threshold E ≥ 2mec 2 + 2 m2 ec 2 mnucleus . The created particles will produce Bremsstrahlung as well as they will cause ionizations along their paths. In contrast to the electron, which is rather fast absorbed by an ion, the positron annihilates with an electron. Afterwards, two photons sharing twice the electron’s rest mass will be produced. By taking into account screening effects [29], the cross section κ is κ = αZ2r2e [ 28 9 ln ( 183Z−1/3 ) − 2 27 ] (1.7) with α = e2/ (~c) For different energy regions the equation above can be split into simplified expressions as follows: low photon energy high photon energy κ ∼ ln (hν) κ ∼ 7 9 ( A/X0NA ) In case of photons with an initial energy of Eγ = 1GeV and Pb as target material, the difference between both approximations is about 7% [79][11]. The cross section increases with the particle’s energy and is connected to the radiation length X0 (see Charged particle interactions on the following page) [131]. The probability that a photon undergoes a conversion within one radiation length is given by P ≈ σPair( ρNA A )X0 ≈ 7/9. Each process has a separate contribution to the mass attenuation coefficient µ/ρ. Therefore, the cross section of attenuation of a photon beam can be written as σ = τ + σC + κ (1.8) photonuclear reactions like Rayleigh scattering are neglected due to the negligable energy transfer Finally, it has to be noted that the cross sections of the interactions between photons and matter are much smaller than those of charged particles and matter. Therefore, for example, X-rays and γ-rays are more pene- trating than charged particles. The separate cross sections are: Process Order Incident photon energy Photoelectric effect τ ∝ Z4/E3 ≤ 1 MeV Compton effect σC ∝ Z/E 1MeV ≤ Eγ ≤ 10 MeV Pair production κ ∝ Z2 ln (E) ≥ 10 MeV Table 2: Comparison of interaction processes of light with matter The dependency in Eγ and Z reveals the situation that it is, e.g., easier to cover against 10− 20MeV photons than against 3MeV. 27 Even though the dependency of a cross section is always given in Z, the interactions also depend on the elec- tron density (∼ Z) which is not strongly related to the atomic number Z of the medium since an increasing amount of electrons can cause a lower electron density due to Coulomb repulsion. Furthermore, though the cross sections of the different mechanisms are energy dependent, they do not re- veal how much energy will be transferred. While the Compton effect transfers only a fraction of the photon’s energy according to ET = Eγ/(1 + (E/mec 2 (1− cos θ)), the photopeak results in a complete transfer of the energy ET = Eγ . In fig. 22 is the mass attenuation and the photon cross sections for the according interaction processes given: Figure 22: Mass attenua- tion and photon cross section of PbWO4. The photon interac- tions at lead tungstate represent very well their general energy de- pendence: The photoelectric ef- fect is dominant at energies up to about 0.5 MeV while scat- tering processes prevail within a rather small energy region from 0.5 − 6 MeV and from there on pair production is the most ma- jor interaction. The mass at- tenuation of PbWO4 [111] is con- verted into the cross section via σ = µ ρ · mA NA with mA, = 455.0376 g mol [35]. 5.1.2 Charged particle interactions Mainly, charged particles interact with matter electromagnetically whereas neutral particles require the de- tection of charged secondary particles. The interactions of charged particles can generally be subdivided into electrons/positrons on the one hand and heavy particles such as µ, π, K, p, d and α on the other hand. The latter are mostly based on inelastic collisions with shell electrons, causing an ionization or excitation of the atom. Starting with massive particles, Bohr was the first to describe the energy loss of charged particles. Bethe and Bloch extended this description quantum mechanically while Sternheimer added correction terms to consider effects of the shell electrons: dE dx = 2πz2e4 mv2e ρNA Z A [ ln ( 2mv2eWmax I2 (1− β2) ) − 2β2 − δ − U ] (1.9) ρ as the target density, Z representing the atomic number, I is the material dependent mean ionization potential, Wmax the maximum of the transferable energy which is W ≈ 2me (cβγ) 2, ze indicates the incident charge, δ takes into account electric field corrections and U considers inner shell corrections This expression is very accurate in an energy range of 0.1 < βγ < 100 and the energy loss depends mainly on the velocity of incident particles, their charge and on the target material density. Above formula can be split up into three regions: A negative slope proportional to (1/β) 2 due to the fact that slow particles undergo more electric forces of atoms until they reach approximately βγ ≈ 3.5 as well as a positive, logarithmic slope due to relativistic effects in which Lorentz transformations increase the transversal electric field according toE → γE 28 and a Fermi plateau at high energies as a result of polarization effects. Within a local minimum at βγ ≈ 3.5, different particles suffer a very similar energy loss. There, the particles are calledMIPs23 and their energy loss is nearly independent of the material with approximately 2MeV/ ( g/cm2 ) . It is a meaningful property because particles with different mass but same momentum have different β and γ according to p = γmc. Typically, the energy loss is normalized to the absorber density ρ to − 1 ρ dE dx . The energy loss against the penetration depth is given by the so-called Bragg curve which indicates that the number of collisions increases with the remaining energy of a particle. Also, collisions with atomic electrons are much more likely than such with a nucleus. Thus, a low energy transfer is more likely than higher ones. Energy losses are a statistical process since the number of collisions N of a traversing particle varies with √ N , according to a Poissonian distribution. Therefore, the energy loss varies typically with the thickness of the material: The energy loss in thin layers follows mainly a Poissonian behaviour while thick layers result rather in a Gaussian distribution. Especially in thin layers the calculated energy loss is less than assumed. This discrepancy becomes visible at higher energies above about p = 100MeV/c but remains nearly the same from there on [103]. This is considered by the Landau distribution which represents almost a Gaussian behaviour but with an asymmetric tail at high energies. At very high energies, the energy loss is predominantly caused by Bremsstrahlung and less by ionization. However, electrons suffer energy losses foremost by the former process. 5.1.2.1 Bremsstrahlung is the emission of a photon when an electrically charged particle traverses mat- ter. Such a particle will radiate in the vicinity of an electromagnetic field of a nucleus and atomic electrons due to deceleration. The emitted energy is converted into a photon and is proportional to the charged particle’s energy loss. While radiation emission is almost negligible for heavy particles, it plays a significant role for electrons where this process is dominant at energies above ≥ 10MeV. The point at which Bremsstrahlung prevails over ionization is called critical energyEC which can be parameterized byEC = 610MeV/ (Z + 1.24), applicable in case of solids and liquids. A comparison between electrons and muons indicates the fact that the energy loss of electrons is much higher according to dE/dx α E/m2 [131]. The energy loss is as follows − ( dE dx )rad = nAE05.8 −28Z2 [ 4 ln ( 183 Z1/3 ) + 2 9 − f (Z) ] (1.10) with nA = Nρ/A as the number of atoms per cm³ and f (Z) = { 1.2021 (αZ)2 for low-Z 0.925 (αZ)2 for high-Z But an exact expression has to take into account screening effects[29]. The angle of emissionΘ depends also on the particle’s energy E0 throughΘ = mc2/E0 and forms at high energies a bunched cone in forward direction. In contrast to ionization processes, where energy losses are almost continuous along the trajectory, energy reduced by Bremsstrahlung can be emitted already by one or two photons and results in large fluctuations. In this context, the radiation lengthX0 characterizes the distance an