2009/10/31 by Lance J. Dixon, Einan Gardi, Lorenzo Magnea · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Factorization #Gravitational singularity #Massless particle #Mathematical analysis #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Parton #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Resummation #Scattering #Scattering amplitude #Singularity #hep-ph #hep-th
paper · pdf · doi:10.1007/jhep02(2010)081
published as JHEP 1002:081,2010 · v2: revised version published in JHEP (minor corrections in Sec. 4; added discussion in Sec. 5.3; refs. added); v3: minor corrections (eqs. 5.11, 5.12 and 5.29); 38 pages, 3 figures
openalex publication_date 2010/02/01 · arxiv created 2011/08/16 · arxiv updated 2011/08/17 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We report on further progress in understanding soft singularities of massless gauge theory scattering amplitudes. Recently, a set of equations was derived based on Sudakov factorization, constraining the soft anomalous dimension matrix of multi-leg scattering amplitudes to any loop order, and relating it to the cusp anomalous dimension. The minimal solution to these equations was shown to be a sum over color dipoles. Here we explore potential contributions to the soft anomalous dimension that go beyond the sum-over-dipoles formula. Such contributions are constrained by factorization and invariance under rescaling of parton momenta to be functions of conformally invariant cross ratios. Therefore, they must correlate the color and kinematic degrees of freedom of at least four hard partons, corresponding to gluon webs that connect four eikonal lines, which first appear at three loops. We analyze potential contributions, combining all available constraints, including Bose symmetry, the expected degree of transcendentality, and the singularity structure in the limit where two hard partons become collinear. We find that if the kinematic dependence is solely through products of logarithms of cross ratios, then at three loops there is a unique function that is consistent with all available constraints. If polylogarithms are allowed to appear as well, then at least two additional structures are consistent with the available constraints.