Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes

Abstract

We study the factorization of soft and collinear singularities in dimensionally-regularized fixed-angle scattering amplitudes in massless gauge theories. Our factorization is based on replacing the hard massless partons by light-like Wilson lines, and defining gauge-invariant jet and soft functions in dimensional regularization. In this scheme the factorized amplitude admits a powerful symmetry: it is invariant under rescaling of individual Wilson-line velocities. This symmetry is broken by cusp singularities in both the soft and the eikonal jet functions. We show that the cancellation of these cusp anomalies in any multi-leg amplitude imposes all-order constraints on the kinematic dependence of the corresponding soft anomalous dimension, relating it to the cusp anomalous dimension. For amplitudes with two or three hard partons the solution is unique: the constraints fully determine the kinematic dependence of the soft function. For amplitudes with four or more hard partons we present a minimal solution where the soft anomalous dimension is a sum over colour dipoles, multiplied by the cusp anomalous dimension. In this case additional contributions to the soft anomalous dimension at three loops or beyond are not excluded, but they are constrained to be functions of conformal cross ratios of kinematic variables.

v1: 35 pages, v2: minor changes - some clarifying remarks and references added. Journal version (to appear in JHEP)

References in corpus (37)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• The four-loop beta-function in Quantum Chromodynamics
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• The Dipole Formalism for the Calculation of QCD Jet Cross Sections at Next-to-Leading Order
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• On planar gluon amplitudes/Wilson loops duality
• Multi-loop Amplitudes and Resummation
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Resummation for QCD Hard Scattering
• Evolution of Color Exchange in QCD Hard Scattering
• Sudakov Factorization and Resummation
• Comments on operators with large spin
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• Universal structure of subleading infrared poles in gauge theory amplitudes
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Threshold resummation for electroweak annihilation from DIS data
• High energy scattering in QCD and cross singularities of Wilson loops
• On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections
• Soft gluons at large angles in hadron collisions
• Exponentiation of the Drell-Yan cross section near partonic threshold in the DIS and MSbar schemes
• Analytic resummation for the quark form factor in QCD
• Iterated amplitudes in the high-energy limit
• On the quark distribution in an on-shell heavy quark and its all-order relations with the perturbative fragmentation function
• The colour evolution of the process q q -> q q g
• Color evolution of 2 -> 3 processes
• Subleading-color contributions to gluon-gluon scattering in N=4 SYM theory and relations to N=8 supergravity
• Symmetry of anomalous dimension matrices explained
• A dispersive approach to Sudakov resummation
• Symmetry of Anomalous Dimension Matrices for Colour Evolution of Hard Scattering Processes

Cited by in corpus (244)

• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Calculation of the quark and gluon form factors to three loops in QCD
• Next-to-next-to-leading soft-gluon corrections for the top quark cross section and transverse momentum distribution
• Infrared singularities of QCD amplitudes with massive partons
• Soft radiation in heavy-particle pair production: all-order colour structure and two-loop anomalous dimension
• Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Two-Loop QCD Corrections to the Helicity Amplitudes for $H\to$ 3 partons
• Factorization Properties of Soft Graviton Amplitudes
• Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
• Soft-/rapidity- anomalous dimensions correspondence
• Two-loop divergences of scattering amplitudes with massive partons
• Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach
• Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• Analytic two-loop form factors in N=4 SYM
• Direct photon production with effective field theory
• The two-loop helicity amplitudes for $q{\bar{q}}^{\prime }\to V_1{V}_2\to 4\mathrm{leptons}$
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• Threshold resummation at N${}^3$LL accuracy and soft-virtual cross sections at N${}^3$LO
• On soft singularities at three loops and beyond
• BCJ duality and the double copy in the soft limit
• The two-loop soft current in dimensional regularization
• Drell-Yan Production at Threshold to Third Order in QCD
• Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC
• A first look at two-loop five-gluon scattering in QCD
• Webs in multiparton scattering using the replica trick
• The gluon jet function at two-loop order
• Bootstrapping the QCD soft anomalous dimension
• The infrared structure of gauge theory amplitudes in the high-energy limit
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Factorization and Resummation for Dijet Invariant Mass Spectra
• Soft-virtual corrections to Higgs production at N${}^3$LO
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
• Non-Global Logarithms, Factorization, and the Soft Substructure of Jets
• The Massive Soft Anomalous Dimension Matrix at Two Loops
• Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
• On the breaking of collinear factorization in QCD
• Eikonal methods applied to gravitational scattering amplitudes
• Numerical NLO QCD calculations
• Hadronization effects in event shape moments
• Leading-color fully differential two-loop soft corrections to QCD dipole showers
• First Subleading Power Resummation for Event Shapes
• The singular behavior of one-loop massive QCD amplitudes with one external soft gluon
• Local Analytic Sector Subtraction at NNLO
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO
• The Non-Abelian Exponentiation theorem for multiple Wilson lines
• Leading-Color Two-Loop Amplitudes for Four Partons and a W Boson in QCD
• Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders
• The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals
• Antenna subtraction for the production of heavy particles at hadron colliders
• Wilson line approach to gravity in the high energy limit
• Two-parton scattering in the high-energy limit
• Diagrammatic Exponentiation for Products of Wilson Lines
• An infrared approach to Reggeization
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• Infrared Singularities of Scattering Amplitudes and N${}^3$LL Resummation for $n$-Jet Processes
• The infrared structure of e+ e- --> 3 jets at NNLO reloaded
• On the renormalization of multiparton webs
• Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations
• General properties of multiparton webs: proofs from combinatorics
• The QCD form factor of heavy quarks at NNLO
• An $S$-Matrix for Massless Particles
• Four-loop quark form factor with quartic fundamental colour factor
• All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes
• Three-loop gluon scattering in QCD and the gluon Regge trajectory
• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• On the Computation of Form Factors in Massless QCD with Finite Master Integrals
• High-energy QCD amplitudes at two loops and beyond
• Sequential Discontinuities of Feynman Integrals and the Monodromy Group
• Isolated photon production in association with a jet pair through next-to-next-to-leading order in QCD
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Effective Field Theory after a New-Physics Discovery
• Computation of the Soft Anomalous Dimension Matrix in Coordinate Space
• The $Hb\bar{b}$ form factor to three loops in QCD
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• 1-loop matching and NNLL resummation for all partonic 2 to 2 processes in QCD
• A prescription for projectors to compute helicity amplitudes in D dimensions
• Structure of Infrared Singularities of Gauge-Theory Amplitudes at Three and Four Loops
• The Heavy Quark Form Factors at Two Loops
• Triple (and quadruple) soft-gluon radiation in QCD hard scattering
• The Soft Quark Sudakov
• Transverse momentum dependent operator expansion at next-to-leading power
• Feynman Polytopes and the Tropical Geometry of UV and IR Divergences
• Factorization and Resummation for Generic Hierarchies between Jets
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Threshold expansion at order alpha_s^4 for the t-tbar invariant mass distribution at hadron colliders
• Pseudo-scalar Form Factors at Three Loops in QCD
• Master integrals for the four-loop Sudakov form factor
• Collinear factorization violation and effective field theory
• Higgs boson production through $b\bar{b}$ annihilation at threshold in N${}^3$LO QCD
• Small-mass effects in heavy-to-light form factors
• Double collinear splitting amplitudes at next-to-leading order
• Factorisation and Subtraction beyond NLO
• Color structure for soft gluon resummation - a general recipe
• Tree-level splitting amplitudes for a quark into four collinear partons
• Computing one-loop corrections to effective vertices with two scales in the EFT for Multi-Regge processes in QCD
• Two-Loop Virtual Corrections to Drell-Yan Production at order alpha_s alpha^3
• Soft gluon emission at two loops in full color
• From Webs to Polylogarithms
• SCET approach to regularization-scheme dependence of QCD amplitudes
• On next to soft corrections to Drell-Yan and Higgs Boson productions
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• Non-abelian infrared divergences on the celestial sphere
• Combined threshold and transverse momentum resummation for inclusive observables
• A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes
• N${}^3$LO+N${}^3$LL QCD improved Higgs pair cross sections
• Ultraviolet divergences and factorization for coordinate-space amplitudes
• Electroweak Sudakov effects in W, Z and gamma production at large transverse momentum
• NNLO soft function for electroweak boson production at large transverse momentum
• Soft anomalous dimensions for single-top production at three loops
• The NNLO soft function for the pair invariant mass distribution of boosted top quarks
• Mixed EW-QCD two-loop amplitudes for $q\bar{q}\to {\ell }^{+}{\ell }^{-}$ and ${\gamma }_5$ scheme independence of multi-loop corrections
• Employing Helicity Amplitudes for Resummation
• An on-shell approach to factorization
• Tree-level splitting amplitudes for a gluon into four collinear partons
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Three-loop helicity amplitudes for quark-gluon scattering in QCD
• Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel
• Threshold Resummation for Di-hadron Production in Hadronic Collisions
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Webs and Posets
• Loop-level gluon OPEs in celestial holography
• Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders
• Two-loop massless QCD corrections to the $g+g\to H+H$ four-point amplitude
• Multiple Gluon Exchange Webs
• Higgs Rapidity Distribution in $b\bar{b}$ Annihilation at Threshold in N${}^3$LO QCD
• Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Two-Loop QCD Corrections to Higgs $\to b+\bar{b}+g$ Amplitude
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• Two-loop anomalous dimension for the resummation of non-global observables
• Polarised Amplitudes and Soft-Virtual Cross Sections for $b\bar{b}\to ZH$ at NNLO in QCD
• On next to soft threshold corrections to DIS and SIA processes
• Full-color three-loop three-point form factors in N=4 SYM
• NNLO subtraction for any massless final state: a complete analytic expression
• Next-to SV resummed Drell-Yan cross section beyond leading-logarithm
• The structure of IR divergences in celestial gluon amplitudes
• Multiparton webs beyond three loops
• Building Bases of Loop Integrands
• Factorization of Non-Global LHC Observables and Resummation of Super-Leading Logarithms
• Relating amplitude and PDF factorisation through Wilson-line geometries
• Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM
• The Four Dimensional Helicity Scheme Beyond One Loop
• Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism
• The asymptotic behavior of the heavy quark form factors at higher order
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• Multiple soft radiation at one-loop order and the emission of a soft quark-antiquark pair
• Climbing three-Reggeon ladders: four-loop amplitudes in the high-energy limit in full colour
• Analytic integration of soft and collinear radiation in factorised QCD cross sections at NNLO
• Generating function for web diagrams
• Two-loop helicity amplitudes for $H+$jet production to higher orders in the dimensional regulator
• Cwebs beyond three loops in multiparton amplitudes
• Full-colour double-virtual amplitudes for associated production of a Higgs boson with a bottom-quark pair at the LHC
• Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator
• Cross-Order Integral Relations from Maximal Cuts
• Higher-order QCD corrections for the W-boson transverse momentum distribution
• Rapidity distribution at soft-virtual and beyond for n-colorless particles to N${}^4$LO in QCD
• The colourful antenna subtraction method
• IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM Theory
• Numerical evaluation of two-loop QCD helicity amplitudes for $gg\to t\bar{t}g$ at leading colour
• Higgs pair production from bottom quark annihilation to NNLO in QCD
• Quark and gluon spin-2 form factors to two-loops in QCD
• Computation of $H\to gg$ in FDH and DRED: renormalization, operator mixing, and explicit two-loop results
• The gravitational cusp anomalous dimension from AdS space
• Two-Loop QCD Helicity Amplitudes for (2+1)-Jet Production in Deep Inelastic Scattering
• Regularization-scheme dependence of QCD amplitudes in the massive case
• Two loop QCD corrections for the process Pseudo-scalar Higgs $\to 3$ partons
• Resummed Higgs boson cross section at next-to SV to $\mathrm{NNLO}+\overline{\mathrm{NNLL}}$
• The parton-level structure of $e^{+}{e}^{-}$ to 2 jets at N${}^3$LO
• Three-loop cusp anomalous dimension and a conjecture for $n$ loops
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Toward NNLL Threshold Resummation for Hadron Pair Production in Hadronic Collisions
• Polarized $q\bar{q}\to Z+$Higgs amplitudes at two loops in QCD: the interplay between vector and axial vector form factors and a pitfall in applying a non-anticommuting ${\gamma }_5$
• Identifying regions in wide-angle scattering via graph-theoretical approaches
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• Soft Theorem to Three Loops in QCD and $\mathcal{N}=4$ Super Yang-Mills Theory
• Does one need the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes in an NNLO calculation ?
• Factorization of Boosted Multijet Processes for Threshold Resummation
• Going beyond Soft plus Virtual
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• Near-to-planar three-jet events at NNLL accuracy
• Three loop form factors of a massive spin-2 particle with nonuniversal coupling
• Resummation prediction on the jet mass spectrum in one-jet inclusive production at the LHC
• Form factors with two operator insertions and the principle of maximal transcendentality
• Two-Loop QCD Correction to massive spin-2 resonance $\to$ 3 gluons
• Two loop QCD amplitudes for di-pseudo scalar production in gluon fusion
• Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes
• The next-to-next-to-leading order soft function for top quark pair production
• Rings and strings: a basis for understanding subleading colour and QCD coherence beyond the two-jet limit
• Infrared Singularities and Soft Gluon Resummation with Massive Partons
• The transverse-momentum spectrum of Higgs bosons near threshold at NNLO
• Soft anomalous dimensions and resummation in QCD
• Building blocks of Cwebs in multiparton scattering amplitudes
• Iterating QCD scattering amplitudes in the high-energy limit
• Position-space cuts for Wilson line correlators
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• Three-loop helicity amplitudes for photon+jet production
• Analytic two-loop amplitudes for $tW$ production: leading color and light fermion-loop contributions
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Deciphering Colour Building Blocks of Massive Multiparton Amplitudes at 4-loops and beyond
• Spin-2 Form Factors at Three Loop in QCD
• Jet veto resummation for STXS $H+$1-jet bins at aNNLL${}^{\prime }$+NNLO
• Two-loop Doubly Massive Four-Point Amplitude Involving a half-BPS and Konishi Operator
• Removing phase-space restrictions in factorized cross sections
• Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory
• Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
• Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
• The two-loop Higgs impact factor
• Dimensional schemes for cross sections at NNLO
• Two-Loop Four-Fermion Scattering Amplitude in QED
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• Two-loop QCD Correction to Massive Spin-2 Resonance $\to q\bar{q}g$
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair
• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory
• Two-loop scattering amplitude for heavy-quark pair production through light-quark annihilation in QCD
• Infrared Anomalous Dimensions at Three-Loop in the SM from Conserved Currents
• Top-Yukawa contributions to $pp\to b\bar{b}H$: two-loop leading-colour amplitudes
• Jet Physics from Static Charges in AdS
• A tale of two Regge limits
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• Non-abelian soft radiation data for a celestial theory
• One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}({\epsilon }^2)$
• Two-loop mixed QCD-EW corrections to neutral current Drell-Yan
• Boomerang webs up to three-loop order
• The analytic two-loop soft function for leading-jet $p_T$
• The integrand form of infrared singularities of two-loop QCD scattering amplitudes
• Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit