Progress on soft gluon exponentiation and long-distance singularities

Abstract

I review the recent progress in studying long-distance singularities in gauge-theory scattering amplitudes in terms of Wilson lines. The non-Abelian exponentiation theorem, which has been recently generalised to the case of multi-leg amplitudes, states that diagrams exponentiate such that the colour factors in the exponent are fully connected. After a brief review of the diagrammatic approach to soft gluon exponentiation, I sketch the method we used to prove the theorem and illustrate how connected colour factors emerge in the exponent in webs that are formed by sets of multiple-gluon-exchange diagrams. In the second part of the talk I report on recent progress in evaluating the corresponding integrals, where a major simplification is achieved upon formulating the calculation in terms of subtracted webs. I argue that the contributions of all multiple-gluon-exchange diagrams to the soft anomalous dimension take the form of products of specific polylogarithmic functions, each depending on a single cusp angle.

22 pages, 13 figures; presented at the 11th International Symposium on Radiative Corrections, RADCOR 2013, 22-27 September 2013, Lumley Castle, UK

References in corpus (17)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• 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 Massive Soft Anomalous Dimension Matrix at Two Loops
• Diagrammatic Exponentiation for Products of Wilson Lines
• General properties of multiparton webs: proofs from combinatorics
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Computation of the Soft Anomalous Dimension Matrix in Coordinate Space
• From Webs to Polylogarithms
• Webs and Posets
• When does the gluon reggeize?
• Infrared Singularities and Soft Gluon Resummation with Massive Partons
• Web worlds, web-colouring matrices, and web-mixing matrices
• Analytic results for multiloop scattering amplitudes