On Soft Sngularities at Three Loops and Beyond

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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. ... continued below

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36 pages

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Dixon, Lance J.; /SLAC; Gardi, Einan; U., /Edinburgh; Magnea, Lorenzo & /Turin U. /INFN, Turin December 11, 2009.

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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.

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36 pages

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  • Journal Name: Submitted to Journal of High Energy Physics (JHEP)

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  • Report No.: SLAC-PUB-13816
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 969253
  • Archival Resource Key: ark:/67531/metadc927014

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  • December 11, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 15, 2016, 3:40 p.m.

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Dixon, Lance J.; /SLAC; Gardi, Einan; U., /Edinburgh; Magnea, Lorenzo & /Turin U. /INFN, Turin. On Soft Sngularities at Three Loops and Beyond, article, December 11, 2009; United States. (digital.library.unt.edu/ark:/67531/metadc927014/: accessed August 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.