Institut fur¨ Theoretische Physik Fakult¨at Mathematik und Naturwissenschaften Technische Universit¨at Dresden Event generation at hadron colliders Dissertation zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr.rer.nat.) vorgelegt von Andreas Sch¨alicke Dresden 2005 Dedicated to the memory of Prof. Gerhard Soff, 1949 - 2004. Eingereicht am 31. M¨arz 2005 1. Gutachter: Prof. Dr. R. Ketzmerick 2. Gutachter: Prof. Dr. B. R. Webber 3. Gutachter: Prof. Dr. M. L. Mangano Verteidigt am 15. Juli 2005 Kurzfassung Diese Arbeit befasst sich mit der Simulation von hochenergetischen Hadron- Kollisionsexperimenten, wie sie im Moment am Tevatron (Fermilab) durchgefuhrt¨ werden und in naher Zukunft am Large Hadron Collider (LHC) am CERN zu er- warten sind. Fur¨ die Beschreibung dieser Experimente wird ein Algorithmus un- tersucht, der es erm¨oglicht, exakte Multijet-Matrixelemente auf Baumgraphen- niveau in die Simulation einzubeziehen und so die Qualit¨at der Vorhersage deut- lich zu verbessern. Die Implementierung dieses Algorithmus in den Eventgenera- tor \SHERPA" [1] und die Erweiterung des Parton Showers in diesem Programm ist das Hauptthema dieser Arbeit. Die Ergebnisse werden mit experimentellen Daten und mit anderen Simulationen verglichen. Abstract This work deals with the accurate simulation of high energy hadron{hadron{ collision experiments, as they are currently performed at Fermilab Tevatron or as they are expected at the Large Hadron Collider at CERN. For a precise de- scription of these experiments an algorithm is investigated, which enables the inclusion of exact multi-jet matrix elements in the simulation. The implementa- tion of this algorithm in the event generator \SHERPA" [1] and the extension of its parton shower is the main topic of this work. The results are compared with those of other simulation programs and with experimental data. Contents 1 Introduction . 1 1.1 The Large Hadron Collider . 2 1.2 New tools for high energy physics . 3 1.3 The Monte Carlo Event generator SHERPA . 4 1.4 Outline of this thesis . 6 2 Calculation of cross sections. 7 2.1 The matrix element generator AMEGIC++ . 9 2.2 Results . 11 2.2.1 Cross sections for the NLC . 12 2.2.2 Matrix elements for the LHC . 20 2.3 Summary . 23 3 Parton Shower . 27 3.1 APACIC++ { A PArton Cascade In C++ . 28 3.1.1 Basics of parton showering . 28 3.1.2 Variables in APACIC++ . 30 3.1.3 Colour treatment . 34 3.1.4 Initialisation of the parton shower . 34 3.1.5 Merging issues . 36 3.2 Results . 37 3.2.1 Comparison with analytic Sudakov form factors . 37 3.2.2 Comparison of shower and hadron level: Hadronisation corrections . 41 3.2.3 Comparison with experimental data from LEP . 43 3.2.4 Comparison with experimental data from Tevatron . 48 3.3 Summary . 51 4 Merging matrix elements and parton showers. 53 4.1 NLL jet rates and Sudakov form factors . 54 4.2 The algorithm . 57 4.2.1 Combination of matrix elements . 58 4.2.2 Pseudo parton shower history . 59 4.2.3 Starting the parton shower . 62 4.3 Examples . 63 + 4.3.1 Example I { e e− jets . 64 ! 4.3.2 Example II { pp¯ W + jets . 65 ! 4.3.3 Example III { pp¯ jets . 69 ! ii Contents + 4.3.4 Example IV { e e− dd¯uu¯(g) . 70 ! 4.4 Results . 72 + 4.4.1 Results for e e− jets at LEP1 . 72 ! 4.4.2 Results for pp¯ W + jets at Tevatron, Run I . 75 ! 4.4.3 Results for pp¯ jets at Tevatron, Run I . 79 + ! 4.4.4 Results for e e− dd¯uu¯(g) at LEP2 . 82 ! 4.5 Summary . 87 5 Applications { Results . 89 5.1 Hadron production at LEP1 . 89 5.2 Hadron production at LEP2 . 96 5.3 W=Z + jets production at the Fermilab Tevatron . 101 5.3.1 Input parameters and phase-space cuts . 102 5.3.2 Consistency checks . 103 5.3.3 SHERPA vs. data and other MCs . 109 5.4 W=Z + jets production at the CERN LHC . 118 5.4.1 Input parameters and phase-space cuts . 118 5.4.2 Consistency checks . 119 5.4.3 SHERPA vs. NLO results . 126 5.4.4 SHERPA vs. MC@NLO and PYTHIA . 130 5.5 W-pair production at the Fermilab Tevatron . 134 5.5.1 Input parameters and phase-space cuts . 135 5.5.2 Consistency checks . 135 5.5.3 SHERPA vs. NLO results . 141 5.5.4 SHERPA vs. MC@NLO and PYTHIA . 147 5.6 Summary . 153 6 Summary . 155 A Observables . 157 A.1 Definitions of event shapes . 157 A.2 Topological structure of four-jet events . 159 B Parton shower details . 161 B.1 Splitting kinematics . 161 B.1.1 Kinematics of the final state shower . 161 B.1.2 Kinematics of the initial state shower . 163 B.2 The DGLAP evolution equation . 166 C NLL jet rates. 169 C.1 The differential four-quark rate . 169 C.2 The differential five-jet rate . 170 Contents iii D Brief program documentation . 173 D.1 The parton shower module APACIC++ . 173 D.1.1 Implementation . 173 D.1.2 The interface with SHERPA . 176 D.1.3 Running the showers . 177 D.1.4 Splitting functions & Sudakov form factors . 179 D.1.5 Kinematics . 180 D.1.6 Basic structures . 181 D.1.7 Altarelli{Parisi splitting functions . 181 D.2 The merging module . 182 D.2.1 Implementation . 183 D.2.2 Steering . 185 D.2.3 Clustering . 189 D.2.4 Weighting . 191 5 Publication list . 195 Bibliography. 197 1 Introduction To a large amount, modern particle physics centres around accelerator experiments, where high-energetic particles are brought to collision. Examples of such collider experiments are: the Large Electron Positron collider (LEP) at CERN, where until November 2000 + e e−{collisions at centre-of-mass energies up to 207 GeV took place, or the Tevatron at Fermilab, where proton{anti-proton{collisions at 1960 GeV centre-of-mass energy are cur- rently investigated. To confront the resulting experimental data with theoretical models, a systematic understanding of such multi-particle production processes is of paramount im- portance. A full, quantum-mechanically correct, treatment is, at the moment, out of reach. There are two reasons for this: First of all, there only is a limited understanding of the non- perturbative phase of QCD, or, in other words, of how colourless hadrons are built from the coloured quarks and gluons. This is especially true for phenomena such as hadronisation or for questions related to the impact of the partonic substructure of the colliding hadrons on the pattern of multiple interactions. In all such cases, phenomenological models for the transition from hadrons to partons or vice versa have to be applied with parameters to be fitted. This clearly puts a constraint on a conceptual understanding of high-energy particle production processes. On the other hand, even considering the, in principle, well-understood perturbative phase of scattering processes alone, there are limits on present technical abili- ties to calculate all amplitudes that contribute to a given process. This is due to the fact that even at the tree-level the number of Feynman diagrams grows factorially with the number of particles involved. Moreover, at higher orders of the perturbative evolution new difficulties arise, which are connected for instance with the evaluation of multi-leg loop integrals. This failure necessitates other, approximate solutions, such as simulation programs, usu- ally called event generators. These event generators decompose the full.