Jet Physics at High Energy Colliders The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Chien, Yang-Ting. 2013. Jet Physics at High Energy Colliders. Doctoral dissertation, Harvard University. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:11181071 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Jet Physics at High Energy Colliders A dissertation presented by Yang-Ting Chien to The Physics Department in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts May 2013 c 2013 - Yang-Ting Chien All rights reserved. Dissertation Advisor: Professor Matthew Schwartz Yang-Ting Chien Jet Physics at High Energy Colliders Abstract The future of new physics searches at the LHC will be to look for hadronic signals with jets. In order to distinguish a hadronic signal from its background, it is important to develop advanced collider physics techniques that make accurate theoretical predictions. This work centers on phenomenological and formal studies of Quantum Chromodynamics (QCD), including resummation of hadronic observables using Soft Collinear Effective Theory (SCET), calculating anomalous dimensions of multi-Wilson line operators in AdS, and improving jet physics analysis using multiple event interpretations. Hadronic observables usually involve physics at different energy scales, and the calculations depend on large logarithms of the energy ratios. We can prove factorization theorems of observ- ables and resum large logarithms using renormalization-group techniques. The heavy jet mass distribution for e+e− collisions is calculated at next-to-next-to-next-to leading logarithmic order (N3LL), and we measure the strong coupling constant at 0.3% accuracy. We also calculate the jet-mass distribution at partial N2LL in γ + jet events at the LHC. The effect of non-global logarithms in resummation estimated, and it is significant only at the peak region. Soft QCD interactions among jets can be described by multi-Wilson line operators, with each Wilson line pointing along one of the jet directions. The anomalous dimensions of these operators are key for higher-order resummation. We study these operators using radial quanti- zation and conformal gauge, which leads to a drastic simplification of the two-loop anomalous dimension calculation. We also find that the anomalous dimension calculation is closely related to a corresponding Witten diagram calculation. Jets are complicated objects to identify in high energy collider experiments. A single inter- pretation of each event can only extract a limited amount of information. We propose telescoping jet algorithms which give multiple event interpretations by varying the parameter R in the jet definition. We can redefine the weight of each event in a counting experiment to be the fraction of interpretations passing the experimental cuts, and we get a 46% improvement in the statistical significance for the Higgs search with an associated Z boson at the 8 TeV LHC. iii Contents 1 Introduction 1 2 Precision Jet Physics using Effective Field Theory 6 2.1 Resummation of Heavy Jet Mass and Comparison to LEP Data .... 6 2.1.1 ThrustandHeavyJetMassinSCET . 8 2.1.2 Hemisphere Soft Function and Comparison to Fixed Order ........ 12 2.1.3 αs extractionanderroranalysis . 21 2.1.4 Non-perturbative effects and quark mass corrections . .......... 27 2.1.5 Conclusions .................................. 32 2.2 Resummation of Jet Mass at Hadron Colliders ............... 39 2.2.1 KinematicsandtheObservable . .... 42 HadronicandPartonicKinematics . 42 Theobservable ................................. 44 2.2.2 Differential Cross Sections and Factorization Theorem ........... 47 Factorization of the partonic cross section . ..... 48 One-loopsoftfunction . 51 2.2.3 Refactorization of the Soft Function . ....... 55 ComparingwithpQCDresult. 58 2.2.4 ScaleChoices .................................. 59 2.2.5 Results ..................................... 62 2.2.6 The Role of Non-Global Logarithms . .... 64 2.2.7 Conclusions................................... 69 3 Jet Physics from Static Charges in AdS 72 3.1 ConformalCoordinates. ..... 81 3.2 ClassicalAdSenergies . .. .. .. .. .. .. .. .. ..... 85 3.3 One-loopresults ................................. 90 3.4 Lightlikelimit.................................. .... 91 3.5 Conformalgauges................................. 95 3.5.1 Derivation of Conformal Gauge in d-dimensions. 97 3.5.2 Comparisontoradialgauge . 100 iv 3.6 ThreeWilsonLinesatTwo-Loops . ..... 101 3.7 Relation to Witten Diagrams in the Lightlike Limit . ............ 106 3.8 Conclusions ..................................... 108 4 Telescoping Jets: Multiple Event Interpretations with Multiple R’s 110 4.1 JetClusteringAlgorithms . ...... 110 4.2 Jet Algorithms with Multiple R’s........................... 112 4.3 AlgorithmandAnalysis . .. .. .. .. .. .. .. .. .... 114 4.4 Results......................................... 116 A heavy jet mass 118 A.1 Softfunction .................................... 118 A.2 Expandedsoftfunction . .. .. .. .. .. .. .. .. .... 120 A.3 Singular terms in the heavy jet mass distribution . ............ 121 A.4 Gij expansion...................................... 122 B conformal gauge 124 B.1 GeneralClassofConformalGauges. ....... 124 B.2 GhostsinConformalGauge . .... 126 References 128 v List of Figures 2.1 Comparison of the full fixed-order calculations and expanded SCET at NLO for heavyjetmassdistribution. .... 15 2.2 Extraction of the two-loop constants in the hemisphere softfunction. 15 2.3 Comparison of the full NNLO heavy jet mass distribution and the singular terms. 17 2.4 Difference between the full NNLO heavy jet mass distribution and the singular terms. .......................................... 18 2.5 Relative error for best fit to aleph heavy jet mass data at 91.2 GeV. 22 2.6 Convergence of resummed and fixed-order heavy jet mass distributions. 23 2.7 Perturbative uncertainty of the heavy jet mass distribution at Q = 91.2 GeV. 24 2.8 Best fit values for αs(mZ). .............................. 26 2.9 Hadronization and mass corrections to the heavy jet mass distribution with pythia. 29 2.10 Contours of 2σ and 5σ confidence in the simultaneous fit of αs and a non- perturbative shift parameter ΛNP to the thrust and heavy jet mass aleph data. 31 2.11 Update of Figure 2.1 with cutoff y = 10−12 in B(ρ) from event 2......... 35 2.12 Update of Figure 2.2 with cutoff y = 10−12 in B(ρ) from event 2......... 36 −7 2.13 Update of Fig 2.3 with cutoff y0 = 10 in C(ρ). .................. 37 −7 2.14 Update of Fig 2.4 with cutoff y0 = 10 in C(ρ). .................. 38 2.15 Event topology of direct photon production. ............ 42 2.16 Kinematics of the hardest jet in events with a high pT photon. .. .. 46 2.17 Illustration of dynamical threshold enhancement. ............... 47 2.18 Diagrams that contribute to the one-loop soft function in direct photon production. 51 2.19 Renormalization-group evolution of the hard, jet and softfunctions. 60 2.20 NLO corrections of the hard, jet and soft functions to the jet mass distribution as a function of the renormalization scale. ........ 61 2.21 Jet and softin scales as a function of jet mass with two different cone sizes. 62 2.22 Comparison of the leading order jet mass distribution calculated with MCFM and the prediction from expanding the resummed result to leadingorder. .. 63 2.23 Comparison of the jet mass distributions with different orders of precision to pythia.......................................... 64 2.24 Scale uncertainties of the jet mass distribution for pT = 500 GeV and R = 0.5. 65 2.25 Scale uncertainties of the jet mass distribution for pT = 2 TeV and R = 0.4. 66 vi 2.26 Resummed NLL jet mass distribution for different cone sizes for pT = 500 GeV and 2 TeV compared to pythia. ........................... 67 2.27 Estimation of the effect of leading non-global log resummation. .. .. 69 3.1 Definitions for the cusp angles β12 and γ12. ..................... 77 3.2 A coordinate change maps Minkowski space to R AdS............... 80 × 3.3 In radial quantization, final state lines map to a copy of AdS3 at positive Minkowski times, while initial state lines map to a second copy of AdS3 at negative Minkowski times. .......................................... 84 3.4 The naive solution to Laplace’s equation on the Euclidean cylinder represents the potential in the presence of additional phantom charges. ........... 86 3.5 Electric field lines for two charges in flat space and in AdS. ............ 92 3.6 2-loop graphs contributing to the coefficient F (γij, γjk, γki) of the antisymmetric color structure in Γcusp(vi). .............................. 102 3.7 Dimensional reduction from R AdS to AdS and Witten diagrams. 106 × 4.1 Cartoon calorimeter plot distinguishing the width of the localized energy distri- bution of a jet from the parameter R in the anti-kT algorithm. 111 4.2 Two b jets with the same partonic kinematics but different widths. ....... 111 4.3 Invariant mass distribution of the two b jets for a ZH event with multiple inter- pretations using the telescoping jet algorithms. ........... 112 4.4 Signal and background mjj distributions reconstructed using the anti-kT algo- rithm with R=0.7,