Factorization and Resummation for Generic Hierarchies between Jets

Abstract

Jets are an important probe to identify the hard interaction of interest at the LHC. They are routinely used in Standard Model precision measurements as well as in searches for new heavy particles, including jet substructure methods. In processes with several jets, one typically encounters hierarchies in the jet transverse momenta and/or dijet invariant masses. Large logarithms of the ratios of these kinematic jet scales in the cross section are at present primarily described by parton showers. We present a general factorization framework called SCET${}_{+}$, which is an extension of Soft-Collinear Effective Theory (SCET) and allows for a systematic higher-order resummation of such kinematic logarithms for generic jet hierarchies. In SCET${}_{+}$ additional intermediate soft/collinear modes are used to resolve jets arising from additional soft and/or collinear QCD emissions. The resulting factorized cross sections utilize collinear splitting amplitudes and soft gluon currents and fully capture spin and color correlations. We discuss how to systematically combine the different kinematic regimes to obtain a complete description of the jet phase space. To present its application in a simple context, we use the case of $e^{+}{e}^{-}\to$3 jets. We then discuss in detail the application to N-jet processes at hadron colliders, considering representative classes of hierarchies from which the general case can be built. This includes in particular multiple hierarchies that are either strongly ordered in angle or energy or not.

63 pages, 6 figures, v2: minor typos fixed, Ref. added, v3: journal version

References in corpus (89)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Identifying Boosted Objects with N-subjettiness
• Invariant Operators in Collinear Effective Theory
• Multi-Parton Amplitudes in Gauge Theories
• Hard Scattering Factorization from Effective Field Theory
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• Higher Order Corrections to Jet Cross Sections in Hadron Colliders
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• N-Jettiness: An Inclusive Event Shape to Veto Jets
• Maximizing Boosted Top Identification by Minimizing N-subjettiness
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Calculating Scattering Amplitudes Efficiently
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• MINLO: Multi-scale improved NLO
• The Rapidity Renormalization Group
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• Jet Shapes and Jet Algorithms in SCET
• Factorization at the LHC: From PDFs to Initial State Jets
• One-Loop Splitting Amplitudes in Gauge Theory
• Merging H/W/Z + 0 and 1 jet at NLO with no merging scale: a path to parton shower + NNLO matching
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• The soft-gluon current at one-loop order
• Jets from Massive Unstable Particles: Top-Mass Determination
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• Double Unresolved Approximations to Multiparton Scattering Amplitudes
• Treating the b quark distribution function with reliable uncertainties
• Power Counting to Better Jet Observables
• Higgs Production with a Central Jet Veto at NNLL+NNLO
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• Jet Shapes with the Broadening Axis
• Deep inelastic scattering as x -> 1 using soft-collinear effective theory
• Collinear Factorization and Splitting Functions for Next-to-next-to-leading Order QCD Calculations
• All-Order Collinear Behavior in Gauge Theories
• Reparameterization Invariance for Collinear Operators
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• Toward a NNLO calculation of the B-->X_s+gamma decay rate with a cut on photon energy: II. Two-loop result for the jet function
• Factorization of e+e- Event Shape Distributions with Hadronic Final States in Soft Collinear Effective Theory
• The Quark Beam Function at NNLL
• Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production
• Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in GENEVA
• Drell-Yan Production at NNLL'+NNLO Matched to Parton Showers
• Shape function effects in B -> X_s gamma and B -> X_u l nu decays
• Jet Shapes in Hadron Collisions: Higher Orders, Resummation and Hadronization
• An Effective Field Theory for Jet Processes
• Direct photon production with effective field theory
• Threshold Resummation for Higgs Production in Effective Field Theory
• Toward a NNLO calculation of the B-->X_s gamma decay rate with a cut on photon energy: I. Two-loop result for the soft function
• The N-jettiness soft function at next-to-next-to-leading order
• The two-loop soft current in dimensional regularization
• Two-loop splitting functions in QCD
• Matching of Singly- and Doubly-Unresolved Limits of Tree-level QCD Squared Matrix Elements
• The gluon jet function at two-loop order
• Enhanced Nonperturbative Effects in Z Decays to Hadrons
• Constructing All-Order Corrections to Multi-Jet Rates
• Single soft gluon emission at two loops
• Matching Fully Differential NNLO Calculations and Parton Showers
• Factorization and Resummation for Dijet Invariant Mass Spectra
• Non-global logarithms and jet algorithms in high-pT jet shapes
• Antenna Factorization in Strongly-Ordered Limits
• Jet Mass Spectra in Higgs + One Jet at NNLL
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
• Non-Global Logarithms, Factorization, and the Soft Substructure of Jets
• Resumming the color-octet contribution to e+ e- -> J/psi + X
• Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions
• Glauber Gluons and Multiple Parton Interactions
• Electroweak Corrections using Effective Field Theory: Applications to the LHC
• Building Blocks for Subleading Helicity Operators
• XCone: N-jettiness as an Exclusive Cone Jet Algorithm
• A Soft-Collinear Mode for Jet Cross Sections in Soft Collinear Effective Theory
• Event Generation from Effective Field Theory
• Abelian Non-Global Logarithms from Soft Gluon Clustering
• Drell-Yan process with jet vetoes: breaking of generalized factorization
• Constraint equations for heavy-to-light currents in SCET
• Double collinear splitting amplitudes at next-to-leading order
• Phase Space and Jet Definitions in SCET
• Employing Helicity Amplitudes for Resummation
• The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory
• Extending the MINLO method
• Resolving Boosted Jets with XCone
• The Edge of Jets and Subleading Non-Global Logs
• The Singular Behavior of Jet Substructure Observables
• Systematic Improvement of Parton Showers with Effective Theory
• Combining Fixed-Order Helicity Amplitudes With Resummation Using SCET

Cited by in corpus (34)

• Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning
• 50 Years of Quantum Chromodynamics
• New Angles on Energy Correlation Functions
• A Complete Basis of Helicity Operators for Subleading Factorization
• Connecting Different TMD Factorization Formalisms in QCD
• Higgsstrahlung at NNLL${}^{\prime }+$NNLO Matched to Parton Showers in GENEVA
• Jet axes and universal transverse-momentum-dependent fragmentation
• Subleading Power Factorization with Radiative Functions
• Precision Photon Spectra for Wino Annihilation
• Resummed Photon Spectra for WIMP Annihilation
• Transverse Momentum Dependent Fragmenting Jet Functions with Applications to Quarkonium Production
• Factorization and Resummation for Massive Quark Effects in Exclusive Drell-Yan
• Nonperturbative Corrections to Soft Drop Jet Mass
• Joint Two-Dimensional Resummation in $q_T$ and $0$-Jettiness at NNLL
• Electroweak Logarithms in Inclusive Cross Sections
• Convolved Substructure: Analytically Decorrelating Jet Substructure Observables
• Probing Transverse-Momentum Dependent Evolution With Groomed Jets
• Hunting for Heavy Winos in the Galactic Center
• Factorization for Jet Radius Logarithms in Jet Mass Spectra at the LHC
• Joint resummation of two angularities at next-to-next-to-leading logarithmic order
• Factorization and Resummation for Groomed Multi-Prong Jet Shapes
• Predictions for energy correlators probing substructure of groomed heavy quark jets
• Underlying event sensitive observables in Drell-Yan production using GENEVA
• Collinear expansion for color singlet cross sections
• Collinear Drop
• Power Counting and Modes in SCET
• Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders
• Quark jet rates and quark/gluon discrimination in multi-jet final states
• Analytic Boosted Boson Discrimination
• New Insights on an Old Problem: Resummation of the D-parameter
• How much joint resummation do we need?
• Employing Helicity Amplitudes for Resummation in SCET
• Soft evolution after a hard scattering process
• QCD Beyond Leading Power