Sudakov Factorization and Resummation

Abstract

We present a unified derivation of the resummation of Sudakov logarithms, directly from the factorization properties of cross sections in which they occur. We rederive in this manner the well-known exponentiation of leading and nonleading logarithmic enhancements near the edge of phase space for cross sections such as deeply inelastic scattering, which are induced by an electroweak hard scattering. For QCD hard-scattering processes, such as heavy-quark production, we show that the resummation of nonleading logarithms requires in general mixing in the space of the color tensors of the hard scattering. The exponentiation of Sudakov logarithms implies that many weighted cross sections obey particular evolution equations in momentum transfer, which streamline the computation of their Sudakov exponents. We illustrate this method with the resummation of soft-gluon enhancements of the inclusive Drell-Yan cross section, in both DIS and $\overline{\mathrm{MS}}$ factorization schemes.

32 pages, phyzzx.tex macropackage, 1 figure

References in corpus (20)

• Calculation of Power Corrections to Hadronic Event Shapes
• Nonperturbative Corrections in Resummed Cross Sections
• Power corrections and renormalons in Drell-Yan production
• Top Quark Production Cross Section
• Infrared factorization in inclusive B meson decays
• Estimation of Power Corrections to Hadronic Event Shapes
• The Top Cross Section in Hadronic Collisions
• High energy scattering in QCD and cross singularities of Wilson loops
• The Perturbative Resummed Series for Top Quark Production in Hadron Reactions
• On the Universality of the Leading, $1/Q$ Power Corrections in QCD
• Principal Value Resummation
• Power Suppressed Corrections to Hadronic Event Shape Variables
• Perturbative Gluon Resummation of the Top Quark Production Cross Section
• On near forward high energy scattering in QCD
• Infrared Renormalons and Power Suppressed Effects in $e^{+}{e}^{-}$ Jet Events
• Color Exchange in Near-forward Hard Elastic Ecattering
• Proton-Proton Near-Forward Hard Elastic Scattering
• Top quark inclusive differential distributions
• Non-leading Logarithms in Principal Value Resummation
• The Dilepton-Production Cross Section in Principal Value Resummation

Cited by in corpus (197)

• Two-loop soft anomalous dimensions for single top quark associated production with a W- or H-
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• Next-to-next-to-leading-order collinear and soft gluon corrections for t-channel single top quark production
• NNLL resummation for s-channel single top quark production
• Soft Gluon Radiation in Higgs Boson Production at the LHC
• Higgs boson production in bottom quark fusion at next-to-next-to-leading order
• Multi-loop Amplitudes and Resummation
• Soft-gluon resummation for squark and gluino hadroproduction
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Theoretical status and prospects for top-quark pair production at hadron colliders
• Resummation for QCD Hard Scattering
• Evolution of Color Exchange in QCD Hard Scattering
• Calculation of the quark and gluon form factors to three loops in QCD
• Jet Shapes and Jet Algorithms in SCET
• Power corrections to event shapes and factorization
• Three-Loop Results for Quark and Gluon Form Factors
• Event Shape/Energy Flow Correlations
• The Quark Form Factor at Higher Orders
• Higher-Order threshold effects to inclusive processes in QCD
• Resummation of Threshold Corrections for Single-Particle Inclusive Cross Sections
• Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory
• Threshold Resummation for Dijet Cross Sections
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories
• Single-Transverse Spin Asymmetries: From DIS to Hadronic Collisions
• Factorization of e+e- Event Shape Distributions with Hadronic Final States in Soft Collinear Effective Theory
• Higgs production in gluon fusion beyond NNLO
• Soft-/rapidity- anomalous dimensions correspondence
• Two-loop divergences of scattering amplitudes with massive partons
• Super-leading logarithms in non-global observables in QCD?
• Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach
• The singular behavior of massive QCD amplitudes
• Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log
• NNLL-fast: predictions for coloured supersymmetric particle production at the LHC with threshold and Coulomb resummation
• Threshold resummation for electroweak annihilation from DIS data
• Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production
• Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell-Yan process
• The method of regions and next-to-soft corrections in Drell-Yan production
• Sudakov resummation of multiparton QCD cross sections
• Threshold resummation for pair production of coloured heavy (s)particles at hadron colliders
• On soft singularities at three loops and beyond
• Recoil and Threshold Corrections in Short-distance Cross Sections
• Comparing and Counting Logs in Direct and Effective Methods of Resummation
• Sudakov Resummation and Finite Order Expansions of Heavy Quark Hadroproduction Cross Sections
• On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections
• Top-quark pair production near threshold at LHC
• The Theory of Deeply Inelastic Scattering
• Non-global logarithms in inter-jet energy flow with kt clustering requirement
• Non-abelian factorisation for next-to-leading-power threshold logarithms
• Resummed Higgs cross section at N${}^3$LL
• Next-to-Next-to-Leading Logarithms in Four-Fermion Electroweak Processes at High Energy
• NNLL resummation for squark and gluino production at the LHC
• Non-global Structure of the O(α_s^2) Dijet Soft Function
• NNLL resummation for squark-antisquark pair production at the LHC
• Heavy Neutrinos with Dynamic Jet Vetoes: Multilepton Searches at $\sqrt{s}=14,27,$ and $100$ TeV
• Renormalization group approach to soft gluon resummation
• On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x
• NNLL resummation for stop pair-production at the LHC
• Towards NNLL resummation: hard matching coefficients for squark and gluino hadroproduction
• Renormalon resummation and exponentiation of soft and collinear gluon radiation in the thrust distribution
• On non-singlet physical evolution kernels and large-x coefficient functions in perturbative QCD
• High-order corrections and subleading logarithms for top quark production
• Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions
• QCD resummation for hadronic final states
• Precision predictions for scalar leptoquark pair-production at hadron colliders
• Exponentiation of the Drell-Yan cross section near partonic threshold in the DIS and MSbar schemes
• The Effective Vector Boson Approximation in High-Energy Muon Collisions
• On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering
• QCD threshold corrections to di-lepton and Higgs rapidity distributions beyond N${}^2$LO
• Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions
• Soft Gluon Resummation for Heavy Quark Electroproduction
• Soft gluon resummation of Drell-Yan rapidity distributions: theory and phenomenology
• On the renormalization of multiparton webs
• Diagrammatic resummation of leading-logarithmic threshold effects at next-to-leading power
• Top Quark Pair Production beyond NNLO
• Automated Predictions from Polarized Matrix Elements
• Analytic resummation for the quark form factor in QCD
• Threshold Resummation for Drell-Yan Process in Soft-Collinear Effective Theory
• Higher-order soft corrections to squark hadro-production
• Soft-gluon resummation and NNLO corrections for direct photon production
• Soft corrections to inclusive deep-inelastic scattering at four loops and beyond
• Next-to-next-to-next-to-leading-order soft-gluon corrections in hard-scattering processes near threshold
• Threshold Resummation of the Total Cross Section for Heavy Quark Production in Hadronic Collisions
• Abelian Non-Global Logarithms from Soft Gluon Clustering
• NLO+NLL squark and gluino production cross-sections with threshold-improved parton distributions
• Origin and Resummation of Threshold Logarithms in the Lattice QCD Calculations of PDFs
• Threshold resummation in SCET vs. perturbative QCD: an analytic comparison
• On the Cutoff Dependence of the Quark Mass Parameter in Angular Ordered Parton Showers
• Dressed gluon exponentiation
• The interplay between Sudakov resummation, renormalons and higher twist in deep inelastic scattering
• Resummation prescriptions and ambiguities in SCET vs. direct QCD: Higgs production as a case study
• Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering
• The resummation of inter-jet energy flow for gaps-between-jets processes at HERA
• Color structure for soft gluon resummation - a general recipe
• The colour evolution of the process q q -> q q g
• Conceptual design of the Spin Physics Detector
• Resummation for heavy quark and jet cross sections
• From Webs to Polylogarithms
• Color evolution of 2 -> 3 processes
• Pseudo-scalar Higgs boson production at N${}^3$LO${}_{\text{A}}$+N${}^3$LL${}^{\prime }$
• On next-to-leading power threshold corrections in Drell-Yan production at N${}^3$LO
• Quantifying Comparisons of Threshold Resummations
• A unified approach to NNLO soft and virtual corrections in electroweak, Higgs, QCD, and SUSY processes
• Next-to-leading power threshold effects for inclusive and exclusive processes with final state jets
• What is a parton shower?
• Towards all-order factorization of QED amplitudes at next-to-leading power
• Associated $t\bar{t}H$ production at the LHC: theoretical predictions at NLO+NNLL accuracy
• Combined threshold and transverse momentum resummation for inclusive observables
• Top-quark production and QCD
• Soft Photon Theorem for High Energy Amplitudes in Yukawa and Scalar Theories
• QCD Factorization for Deep-Inelastic Scattering At Large Bjorken $x_B\sim 1-\mathcal{O}({\Lambda }_{\mathrm{QCD}}/Q$
• Vector Boson Scattering Processes: Status and Prospects
• Double Non-Global Logarithms In-N-Out of Jets
• QCD threshold corrections for gluino pair production at hadron colliders
• Pseudo-scalar Higgs Boson Production at Threshold N${}^3$LO and N${}^3$LL QCD
• The three loop soft function for N${}^3$LL${}^{\prime }$ gluon fusion Higgs production in SCET
• Electroweak-boson hadroproduction at large transverse momentum: factorization, resummation, and NNLO corrections
• Higher order QCD corrections to charged-lepton deep-inelastic scattering and global fits of parton distributions
• Soft Resummation of Quark Anomalous Dimensions and Coefficient Functions in MS-bar Factorization
• Heavy neutrinos from gluon fusion
• An operator expansion for the elastic limit
• Higher-order threshold resummation for semi-inclusive e^+e^- annihilation
• Next-to-leading power threshold effects for resummed prompt photon production
• Threshold Resummation at NNLL for Single-particle Production in Hadronic Collisions
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• Next-to-leading power threshold corrections for finite order and resummed colour-singlet cross sections
• Interjet Energy Flow/Event Shape Correlations
• Phenomenology of threshold corrections for inclusive jet production at hadron colliders
• High energy behaviour of form factors
• Relating amplitude and PDF factorisation through Wilson-line geometries
• Resummed heavy quark production cross sections to next-to-leading logarithm
• On the Perturbative Stability of the QCD Predictions for the Ratio $R=F_L/F_T$ in Heavy-Quark Leptoproduction
• Jets and threshold summation in Deductor
• An Introduction to Webs
• Summing threshold logs in a parton shower
• Probing the Gauge Content of Heavy Resonances with Soft Radiation
• Symmetry of anomalous dimension matrices explained
• Resummation for $2\to n$ processes in single-particle-inclusive kinematics
• Soft-gluon corrections in top-quark production
• Renormalization group approach to Sudakov resummation in prompt photon production
• Perturbative Stability of the QCD Predictions for Single Spin Asymmetry in Heavy Quark Photoproduction
• Radiative and semi-leptonic B-meson decay spectra: Sudakov resummation beyond logarithmic accuracy and the pole mass
• Scalar leptoquark pair production at the LHC: precision predictions in the era of flavour anomalies
• Higher-order QCD corrections for the W-boson transverse momentum distribution
• Threshold Improved QCD Corrections for Stop-Antistop production at Hadron colliders
• Azimuthal Asymmetries in DIS as a Probe of Intrinsic Charm Content of the Proton
• Azimuthal Dependence of the Heavy Quark Initiated Contributions to DIS
• Evolution of parton showers and parton distribution functions
• Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation
• Measurement of $J/\psi$ production cross-sections in $pp$ collisions at $\sqrt{s}=5$ TeV
• The scale of soft resummation in SCET vs perturbative QCD
• Integrated and Differential Accuracy in Resummed Cross Sections
• Threshold resummation of transverse momentum distributions beyond next-to-leading log
• Soft-gluon corrections for the associated production of a single top quark and a Higgs boson
• Soft-gluon resummation for heavy quark production in hadronic collisions
• Photoproduction of events with rapidity gaps between jets at HERA
• Threshold Resummation Effects in the Associated Production of Chargino and Neutralino at Hadron Colliders
• Soft Gluon Resummation for Polarized Deep-inelastic Production of Heavy Quarks
• Threshold enhanced cross sections for colorless productions
• A factorization approach to next-to-leading-power threshold logarithms
• Azimuthal Asymmetries in Heavy Quark Leptoproduction as a Test of pQCD
• Factorization of low-energy gluons in exclusive processes
• On the approaches to threshold resummation of rapidity distributions for the Drell-Yan process
• Soft anomalous dimensions and resummation in QCD
• Resummation of double logarithms in loop-induced processes with effective field theory
• Resummation of next-to-leading logarithms in top quark production
• Nuclear $p_{\perp }$-broadening of an energetic parton pair
• Notes on QED Corrections in Weak Decays
• Large x Resummation in Q^2 Evolution
• Thrust distribution in Higgs decays up to the fifth logarithmic order
• Studies of high-transverse momentum jet substructure and top quarks produced in 1.96 TeV proton-antiproton collisions
• NNLL-fast 2.0: Coloured Sparticle Production at the LHC Run 3 with $\sqrt{S}$ = 13.6 TeV
• Spin analyzing power for polarized top decays with jets
• Phenomenology of QCD threshold resummation for gluino pair production at NNLL
• N${}^3$LO soft-gluon corrections in single-particle-inclusive kinematics and $H^{+}{H}^{-}$ production
• Coherent gluon radiation: beyond leading-log accuracy
• Sudakov Logarithms in Four-Fermion Electroweak Processes at High Energy
• Progress in computing inclusive B decay spectra
• Explicit computation of jet functions in coordinate space
• The Standard Model from the LHC to future colliders: a contribution to the Workshop "What Next" of INFN
• All-order results for soft and collinear gluons
• Sudakov Resummations at Higher Orders
• Factorisation schemes for proton PDFs
• Squark production with R-symmetry beyond NLO at the LHC
• Towards Colour Flow Evolution at Two Loops
• Probing the Structure of Jets: Factorized and Resummed Angularity Distributions in SCET
• Drell-Yan process in soft-collinear effective theory near end-point
• Scalar-pseudoscalar pair production at the Large Hadron Collider at NLO+NLL accuracy in QCD
• Spin Effects in Quantum Chromodynamics and Recurrence Lattices with Multi-Site Exchanges
• Higher-order soft and virtual corrections in $pp\to \gamma W$ production at the LHC
• Perturbative stability of the QCD predictions for the ratio $R=F_L/F_T$ and azimuthal asymmetry in heavy-quark leptoproduction
• Heavy Flavours at Colliders
• Weak bosons as partons below 10 TeV partonic center-of-momentum
• Some Basic Concepts of Perturbative QCD
• Leading and Non-leading Singularities in Gauge Theory Hard Scattering
• NNLL resummation for squark-antisquark production