The six-point remainder function to all loop orders in the multi-Regge limit

A bstract We present an all-orders formula for the six-point amplitude of planar maximally supersymmetric Yang-Mills theory in the leading-logarithmic approximation of multi-Regge kinematics. In the MHV helicity configuration, our results agree with an integral formula of Lipatov and Prygarin throug...

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Bibliographic Details
Published in:The journal of high energy physics Vol. 2013; no. 1; pp. 1 - 24
Main Author: Pennington, Jeffrey
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.01.2013
Springer Nature B.V
Subjects:
Approximation
Classical and Quantum Gravitation
Complex variables
Conjugates
Differential equations
Elementary Particles
Helicity
High energy physics
Kinematics
Mathematical analysis
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
Scattering Amplitudes
Extended Supersymmetry
Supersymmetric gauge theory
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract We present an all-orders formula for the six-point amplitude of planar maximally supersymmetric Yang-Mills theory in the leading-logarithmic approximation of multi-Regge kinematics. In the MHV helicity configuration, our results agree with an integral formula of Lipatov and Prygarin through at least 14 loops. A differential equation linking the MHV and NMHV helicity configurations has a natural action in the space of functions relevant to this problem — the single-valued harmonic polylogarithms introduced by Brown. These functions depend on a single complex variable and its conjugate, w and w * , which are quadratically related to the original kinematic variables. We investigate the all-orders formula in the near-collinear limit, which is approached as |w| → 0. Up to power-suppressed terms, the resulting expansion may be organized by powers of log |w| . The leading term of this expansion agrees with the all-orders double-leading-logarithmic approximation of Bartels, Lipatov, and Prygarin. The explicit form for the sub-leading powers of log |w| is given in terms of modified Bessel functions.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2013)059