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

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 dependencemore » 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.« less
Authors:
 [1] ;  [2]
  1. Stanford Univ., Stanford, CA (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
  2. Stanford Univ., Stanford, CA (United States)
Publication Date:
Report Number(s):
SLAC-PUB-16467
Journal ID: ISSN 1029-8479; PII: 4373; TRN: US1601633
Grant/Contract Number:
AC02-76SF00515
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Phenomenology-HEP; Theory-HEP; HEPPH; HEPTH; 1/N expansion scattering amplitudes; supersymmetric gauge theory
OSTI Identifier:
1237021

Dixon, Lance J., and Esterlis, Ilya. All orders results for self-crossing Wilson loops mimicking double parton scattering. United States: N. p., Web. doi:10.1007/JHEP07(2016)116.
Dixon, Lance J., & Esterlis, Ilya. All orders results for self-crossing Wilson loops mimicking double parton scattering. United States. doi:10.1007/JHEP07(2016)116.
Dixon, Lance J., and Esterlis, Ilya. 2016. "All orders results for self-crossing Wilson loops mimicking double parton scattering". United States. doi:10.1007/JHEP07(2016)116. https://www.osti.gov/servlets/purl/1237021.
@article{osti_1237021,
title = {All orders results for self-crossing Wilson loops mimicking double parton scattering},
author = {Dixon, Lance J. and Esterlis, Ilya},
abstractNote = {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.},
doi = {10.1007/JHEP07(2016)116},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2016,
place = {United States},
year = {2016},
month = {7}
}