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 (25)

• New Relations for Gauge-Theory Amplitudes
• Classical Polylogarithms for Amplitudes and Wilson Loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Bootstrapping an NMHV amplitude through three loops
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
• Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log
• Webs in multiparton scattering using the replica trick
• The three-loop cusp anomalous dimension in QCD
• The Massive Soft Anomalous Dimension Matrix at Two Loops
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Four-gluon scattering at three loops, infrared structure and Regge limit
• General properties of multiparton webs: proofs from combinatorics
• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• 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
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• 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
• Multiple Gluon Exchange Webs