Multiple Gluon Exchange Webs

Abstract

Webs are weighted sets of Feynman diagrams which build up the logarithms of correlators of Wilson lines, and provide the ingredients for the computation of the soft anomalous dimension. We present a general analysis of multiple gluon exchange webs (MGEWs) in correlators of semi-infinite non-lightlike Wilson lines, as functions of the exponentials of the Minkowski cusp angles, ${\alpha }_{ij}$, formed between lines $i$ and $j$. We compute a range of webs in this class, connecting up to five Wilson lines through four loops, we give an all-loop result for a special class of diagrams, and we discover a new kind of relation between webs connecting different numbers of Wilson lines, based on taking collinear limits. Our results support recent conjectures, stating that the contribution of any MGEW to the soft anomalous dimension is a sum of products of polylogarithms, each depending on a single cusp angle, and such that their symbol alphabet is restricted to ${\alpha }_{ij}$ and $1-{\alpha }_{ij}^2$. Finally, we construct a simple basis of functions, defined through a one-dimensional integral representation in terms of powers of logarithms, which has all the expected analytic properties. This basis allows us to compactly express the results of all MGEWs computed so far, and we conjecture that it is sufficient for expressing all MGEWs at any loop order.

64 pages, 13 figures; minor changes throughout

References in corpus (10)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
• Webs in multiparton scattering using the replica trick
• General properties of multiparton webs: proofs from combinatorics
• Cusped light-like Wilson loops in gauge theories
• Infrared Singularities and Soft Gluon Resummation with Massive Partons

Cited by in corpus (4)

• Bootstrapping the QCD soft anomalous dimension
• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• Ultraviolet divergences and factorization for coordinate-space amplitudes
• Path description of coordinate-space amplitudes