Bootstrapping the QCD soft anomalous dimension

Abstract

The soft anomalous dimension governs the infrared singularities of scattering amplitudes to all orders in perturbative quantum field theory, and is a crucial ingredient in both formal and phenomenological applications of non-abelian gauge theories. It has recently been computed at three-loop order for massless partons by explicit evaluation of all relevant Feynman diagrams. In this paper, we show how the same result can be obtained, up to an overall numerical factor, using a bootstrap procedure. We first give a geometrical argument for the fact that the result can be expressed in terms of single-valued harmonic polylogarithms. We then use symmetry considerations as well as known properties of scattering amplitudes in collinear and high-energy (Regge) limits to constrain an ansatz of basis functions. This is a highly non-trivial cross-check of the result, and our methods pave the way for greatly simplified higher-order calculations.

37 pages, 1 figure

References in corpus (91)

• A General Algorithm for Calculating Jet Cross Sections in NLO QCD
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• New Relations for Gauge-Theory Amplitudes
• Harmonic Polylogarithms
• 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
• Classical Polylogarithms for Amplitudes and Wilson Loops
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Local Integrals for Planar Scattering Amplitudes
• Multi-loop Amplitudes and Resummation
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Evolution of Color Exchange in QCD Hard Scattering
• Calculation of the quark and gluon form factors to three loops in QCD
• From polygons and symbols to polylogarithmic functions
• Bootstrapping the three-loop hexagon
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• The soft-gluon current at one-loop order
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• Three-Loop Results for Quark and Gluon Form Factors
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Infrared singularities of QCD amplitudes with massive partons
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Universal structure of subleading infrared poles in gauge theory amplitudes
• Two-loop QCD corrections to gluon-gluon scattering
• Bootstrapping an NMHV amplitude through three loops
• All-Order Collinear Behavior in Gauge Theories
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Heptagons from the Steinmann Cluster Bootstrap
• Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
• Hexagon functions and the three-loop remainder function
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Two-loop QCD corrections to the scattering of massless distinct quarks
• Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
• Two-loop QCD corrections to massless quark-gluon scattering
• Leading singularities and off-shell conformal integrals
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Pulling the straps of polygons
• Sudakov resummation of multiparton QCD cross sections
• On soft singularities at three loops and beyond
• High energy scattering in QCD and cross singularities of Wilson loops
• The two-loop soft current in dimensional regularization
• Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC
• Webs in multiparton scattering using the replica trick
• Two-loop QCD corrections to massless identical quark scattering
• The three-loop cusp anomalous dimension in QCD
• Single soft gluon emission at two loops
• Three-mass triangle integrals and single-valued polylogarithms
• The infrared structure of gauge theory amplitudes in the high-energy limit
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• Evidence for a Nonplanar Amplituhedron
• The Massive Soft Anomalous Dimension Matrix at Two Loops
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Evolution equation for gluon Regge trajectory
• Four-gluon scattering at three loops, infrared structure and Regge limit
• On the breaking of collinear factorization in QCD
• On near forward high energy scattering in QCD
• Soft gluons at large angles in hadron collisions
• The triple collinear limit of one-loop QCD amplitudes
• The Non-Abelian Exponentiation theorem for multiple Wilson lines
• Two-parton scattering in the high-energy limit
• An infrared approach to Reggeization
• On the renormalization of multiparton webs
• General properties of multiparton webs: proofs from combinatorics
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes
• High-energy QCD amplitudes at two loops and beyond
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Computation of the Soft Anomalous Dimension Matrix in Coordinate Space
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Structure of Infrared Singularities of Gauge-Theory Amplitudes at Three and Four Loops
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• From Webs to Polylogarithms
• Ultraviolet divergences and factorization for coordinate-space amplitudes
• Subleading-color contributions to gluon-gluon scattering in N=4 SYM theory and relations to N=8 supergravity
• Webs and Posets
• Multiple Gluon Exchange Webs
• The BFKL equation, Mueller-Navelet jets and single-valued harmonic polylogarithms
• Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics
• IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM Theory

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