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

• Published in: The journal of high energy physics Vol. 2016; no. 7; pp. 1 - 62
• Main Authors: Dixon, Lance J., Esterlis, Ilya
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-07-2016; Springer Nature B.V; Springer Berlin
• Subjects: 1/N expansion scattering amplitudes; Amplitudes; Classical and Quantum Gravitation; Elementary Particles; Formulas (mathematics); Gluons; HEPPH; HEPTH; High energy physics; Mathematical analysis; Partons; Phenomenology-HEP; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering; Scattering amplitude; Singularities; String Theory; supersymmetric gauge theory; Theory-HEP; Scattering Amplitudes; 1/N Expansion; Supersymmetric gauge theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2016)116

A
bstract
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. 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.