All orders results for self-crossing Wilson loops mimicking double parton scattering

Dixon, Lance J.; Esterlis, Ilya

doi:10.1007/JHEP07(2016)116

Title: All orders results for self-crossing Wilson loops mimicking double parton scattering

Journal Article · Thu Jul 21 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP07(2016)116· OSTI ID:1237021

Dixon, Lance J. ^[1]; Esterlis, Ilya ^[2]

Stanford Univ., Stanford, CA (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
Stanford Univ., Stanford, CA (United States)

Loop-level scattering amplitudes for massless particles have singularities in regions where tree amplitudes are perfectly smooth. For example, a 2 → 4 gluon scattering process has a singularity in which each incoming gluon splits into a pair of gluons, followed by a pair of 2 → 2 collisions between the gluon pairs. This singularity mimics double parton scattering because it occurs when the transverse momentum of a pair of outgoing gluons vanishes. The singularity is logarithmic at fixed order in perturbation theory. We exploit the duality between scattering amplitudes and polygonal Wilson loops to study six-point amplitudes in this limit to high loop order in planar N = 4 super-Yang-Mills theory. The singular configuration corresponds to the limit in which a hexagonal Wilson loop develops a self-crossing. The singular terms are governed by an evolution equation, in which the hexagon mixes into a pair of boxes; the mixing back is suppressed in the planar (large N c) limit. Because the kinematic dependence of the box Wilson loops is dictated by (dual) conformal invariance, the complete kinematic dependence of the singular terms for the self-crossing hexagon on the one nonsingular variable is determined to all loop orders. The complete logarithmic dependence on the singular variable can be obtained through nine loops, up to a couple of constants, using a correspondence with the multi-Regge limit. As a byproduct, we obtain a simple formula for the leading logs to all loop orders. Furthermore, we also show that, although the MHV six-gluon amplitude is singular, remarkably, the transcendental functions entering the non-MHV amplitude are finite in the same limit, at least through four loops.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-76SF00515; SC0011632

OSTI ID:: 1237021

Alternate ID(s):: OSTI ID: 1600531

Report Number(s):: SLAC-PUB-16467; PII: 4373; TRN: US1601633

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 7; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 1 work

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