Determination of αs via the Differential 2-Jet-Rate with ATLAS at LHC Dissertation der Fakultat¨ fur¨ Physik der Ludwig-Maximilians-Universitat¨ Munchen¨ vorgelegt von Markus Lichtnecker geboren in Pfarrkirchen M¨unchen, den 20.04.2011 Erstgutachter: Prof. Dr. Otmar Biebel Zweitgutachter: Prof. Dr. Wolfgang D¨unnweber Tag der m¨undlichen Pr¨ufung: 09.06.2011 It’s just like flying a spaceship. You push some buttons and see what happens. Zapp Brannigan (FUTURAMA) Have you tried turning it off and on again? Roy Trenneman (The IT Crowd) Abstract The first determination of the strong coupling constant αs via the differential 2-jet-rate in pp 1 collisions at the LHC (at a center-of-mass-energy of 7 TeV) is presented. Data ( L dt = 700 nb− ) gathered by the ATLAS experiment are fitted by next-to-leading order (NLO) perturbative QCD R predictions from calculations with the program NLOJET++. As an observable, the jet-flip-parameter from 3 to 2 reconstructed jets is investigated, using the infrared and collinear safe kT jet algorithm in the exclusive reconstruction mode. The jet-flip-parameters from real data are compared to simulated data from Monte Carlo generators. For the determination of αs, real data have been corrected for the jet-energy-scale, whereas the calculations from NLOJET++ have been corrected for the influence of hadronization effects as well as the impact of the Underlying Event by applying bin-by-bin corrections. The fit between real data and the calculations from NLOJET++ yields a value of αs(MZ)= 0.120 0.001(stat.) 0.005(syst.), which is in very good agreement with the current world average. ± ± Zusammenfassung In dieser Arbeit wird die erste Messung der starken Kopplungskonstanten αs mithilfe der differen- tiellen 2-Jet-Rate bei pp Kollisionen am LHC (bei einer Schwerpunktsenergie von 7 TeV) vorgestellt. 1 An Daten ( L dt = 700 nb− ) aus dem ATLAS Experiment werden dabei die Theorierechnungen in n¨achst-f¨uhrender Ordnung (NLO) in der St¨orungsrechnung der QCD aus dem Programm NLOJET++ R angepasst. Als Observable wird der Jet-Flip-Parameter untersucht, der den Ubergang¨ von 3 nach 2 rekonstruierten Jets beschreibt. Hierbei wird der infrarot- und kollinear-sichere kT Jet Algorithmus im exklusiven Rekonstruktionsmodus verwendet. Die Jet-Flip-Parameter aus echten Daten werden mit simulierten Daten aus Monte Carlo Generatoren verglichen. F¨ur die Bestimmung von αs werden einerseits die echten Daten um den Einfluss der Jet-Energie-Skala bereinigt und andererseits die Berechnungen aus NLOJET++ um den Einfluss der Hadronisierung und des Underlying Events korrigiert, indem die Eintr¨age Bin f¨ur Bin korrigiert werden. Durch einen Fit zwischen echten Daten und den Berechnungen aus NLOJET++ ergibt sich ein Wert von αs(MZ)= 0, 120 0, 001(stat.) 0, 005(syst.), der sehr gut mit dem Weltmittelwert ¨ubereinstimmt. ± ± Contents 1 Introduction 1 2 Theory 3 2.1 StandardModel................................... 3 2.2 QuantumChromoDynamics . ... 5 2.2.1 Color-charge .................................. 6 2.2.2 Strong Coupling Constant αs .......................... 7 2.3 Hadronization................................... ... 8 2.4 Determination of αs ................................... 10 2.5 Parton Distribution Functions . ......... 12 2.6 BackgroundProcesses ..... ..... ...... ...... ..... .. 13 2.6.1 MinimumBias ................................. 13 2.6.2 UnderlyingEvent............................... 14 2.6.3 Pile-up ..................................... 16 3 LHCandATLAS 17 3.1 LHC........................................... 17 3.2 ATLAS ......................................... 18 3.2.1 CoordinateSystem .............................. 19 3.2.2 MagnetSystem................................. 20 3.2.3 InnerDetector ................................. 21 3.2.4 Calorimeter................................... 22 3.2.5 MuonSpectrometer... ..... ...... ...... ..... ..... 22 3.2.6 Trigger ..................................... 23 3.3 Data&ComputingGrid .............................. 25 4 Jets 27 4.1 JetProduction................................... 27 4.2 ConeAlgorithm................................... 27 4.3 kT Algorithm ...................................... 29 4.3.1 InclusiveMode ................................. 30 4.3.2 ExclusiveMode................................. 30 4.3.3 Anti-kT Algorithm ............................... 31 4.4 Inputs to Jet Reconstruction . ........ 32 4.5 JetCorrection ................................... 33 4.5.1 Correcting for Calorimeter Response . ....... 33 4.5.2 Jet-Energy-Scale .... ..... ...... ...... ..... .... 33 4.5.3 JetCleaning................................... 34 1 5 Analysis Software 37 5.1 NLOJET++....................................... 37 5.2 PYTHIA and Underlying Event Models . ...... 38 5.2.1 PYTHIA .................................... 39 5.2.2 Underlying Event Models . 40 5.3 HERWIG ........................................ 42 5.4 ATHENA ........................................ 45 6 Differential 2-Jet-Rate 47 6.1 Motivation...................................... 47 6.2 StudieswithNLOJET++ ...... ..... ...... ..... ...... 47 6.2.1 d23 Distributions of 2-Parton-Events . 48 6.2.2 d23 Distributions of 3-Parton-Events . 50 6.2.3 d23 Distributions of 4-Parton-Events . 52 6.2.4 Comparison between BORN and FULL “minus” NLO . 54 6.3 RealDataAnalysis ................................ 56 6.3.1 Datasets..................................... 56 6.3.2 JetCleaning................................... 58 6.3.3 Separation from 4-Jet-Events . ...... 62 6.4 Comparison to Simulations . ...... 64 6.4.1 Comparison between Data and PYTHIA . 64 6.4.2 Comparison between Data and NLOJET++ . 67 6.4.3 Comparison between PYTHIA and NLOJET++ . 68 7 Corrections 71 7.1 Jet-Energy-Scale ................................ 71 7.2 Hadronization................................... 71 7.3 UnderlyingEvent ................................. 76 7.4 Low-pT Method..................................... 79 8 αs-Fit and Systematic Uncertainties 87 8.1 αs-Fit .......................................... 87 8.1.1 LO αs ...................................... 88 8.1.2 NLO αs ..................................... 89 8.2 Systematic Uncertainties . ....... 91 8.2.1 JESUncertainty ................................ 91 8.2.2 Impurity due to 4-Jet-Events . ..... 94 8.2.3 Renormalization Scale Uncertainty . ....... 94 8.2.4 PDFUncertainty ................................ 95 8.2.5 Hadronization Uncertainty . ..... 98 8.2.6 Underlying Event Uncertainty . 100 8.3 FinalResults .................................... 101 9 Summary 103 Bibliography 105 Chapter 1 Introduction Since ancient times matter and its structure have been investigated by mankind. Beginning with thought experiments of philosophers, the science led to the biggest experiments on earth. Elementary particle physics uses experiments with cosmic rays as well as huge particle accelerators, like the Large Hadron Collider (LHC) at CERN1 near Geneva, Switzerland, to study the properties and interactions of matter. The LHC (and with it the ATLAS2 experiment) started its operation in September 2009. It has been designed to collide protons at a center-of-mass energy3 of √s = 14 TeV (currently, the LHC is operating at √s = 7 TeV) with a final instantaneous luminosity of up to 34 2 1 L = 10 cm− s− . At such high energies, it is now possible to find (or exclude) predicted particles, which have not been observed yet due to their very large mass. Nonetheless, before new particles can be discovered, and thereby new theoretical models confirmed, a good understanding of the Standard Model (SM) at LHC scale is crucial. All known elementary particles and interaction forces (excluding the gravitation) are included in this powerful model: the electromagnetic, the weak and the strong interaction. The latter 15 describes the force between quarks and gluons and has a range of about 10− m. The interaction force is conveyed by eight gluons, being discovered in 1979 via 3-jet-events at PETRA4 at DESY5. The strength of the strong interaction is described by the strong coupling constant αs. By combining many different measurements, the world average was set to αs(MZ) = 0.1184 0.0007 with a Z ± boson mass of MZ = 91.1876 0.00021 GeV (values are taken from [1]), which is about two orders ± of magnitudes above the electromagnetic force. When starting a new experiment, first of all the detector has to be understood and it has to be shown that the experiment works well, reproduces the results from former colliders and is consistent with the theoretical extrapolation to the high collision energies of the LHC. Sophisticated technical innovations and improved analysis techniques make it possible to measure several properties of particles and their couplings with an accuracy and precision that are second to none [2]. A basic quantity for testing the Standard Model and especially Quantum Chromo Dynamics (QCD) is the strong coupling constant αs, describing the strength gluons couple to colored particles. As αs is not a constant - contrary to the misleading name - but varies with the transfer of momenta Q, it opens the opportunity to compare its value with former experiments and, in addition, to determine it in regions of Q not yet investigated. As a test of QCD, this thesis deals with the determination of αs via the ratio of 3-jet-events to 2-jet-events. The jets are reconstructed using the kT jet algorithm in the exclusive mode, with the algorithm being forced to find 3 jets in the final state. The differential 2-jet-rate is measured via the jet-flip-values, describing