From Webs to Polylogarithms

Abstract

We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of ${\alpha }_{ij}$, the exponential of the Minkowski cusp angle formed between the lines $i$ and $j$. We show that beyond the obvious inversion symmetry ${\alpha }_{ij}\to 1/{\alpha }_{ij}$, at the level of the symbol the result also admits a crossing symmetry ${\alpha }_{ij}\to -{\alpha }_{ij}$, relating spacelike and timelike kinematics, and hence argue that in this class of webs the symbol alphabet is restricted to ${\alpha }_{ij}$ and $1-{\alpha }_{ij}^2$. We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.

64 pages, 8 figures

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Cited by in corpus (24)

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• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• High-energy QCD amplitudes at two loops and beyond
• Factorisation and Subtraction beyond NLO
• Webs and Posets
• Multiple Gluon Exchange Webs
• Multiparton webs beyond three loops
• An Introduction to Webs
• Cwebs beyond three loops in multiparton amplitudes
• Three-loop cusp anomalous dimension and a conjecture for $n$ loops
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• Imaginary parts and discontinuities of Wilson line correlators
• A factorization approach to next-to-leading-power threshold logarithms
• Building blocks of Cwebs in multiparton scattering amplitudes
• Position-space cuts for Wilson line correlators
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair
• The Standard Model from the LHC to future colliders: a contribution to the Workshop "What Next" of INFN
• Progress on soft gluon exponentiation and long-distance singularities
• Boomerang webs up to three-loop order
• Progress on the infrared structure of multi-particle gauge theory amplitudes