Single-valued harmonic polylogarithms and the multi-Regge limit

A bstract We argue that the natural functions for describing the multi-Regge limit of six-gluon scattering in planar super Yang-Mills theory are the single-valued harmonic polylogarithmic functions introduced by Brown. These functions depend on a single complex variable and its conjugate, ( w , w ∗...

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Bibliographic Details
Published in:The journal of high energy physics Vol. 2012; no. 10
Main Authors: Dixon, Lance J., Duhr, Claude, Pennington, Jeffrey
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.10.2012
Springer Nature B.V
Subjects:
Approximation
Classical and Quantum Gravitation
Complex variables
Constants
Eigenvalues
Elementary Particles
Gluons
Harmonic functions
High energy physics
Kinematics
Mathematical analysis
Mellin transforms
Phenomenology-HEP, Theory-HEP,HEPTH
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
Yang-Mills 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 argue that the natural functions for describing the multi-Regge limit of six-gluon scattering in planar super Yang-Mills theory are the single-valued harmonic polylogarithmic functions introduced by Brown. These functions depend on a single complex variable and its conjugate, ( w , w ∗ ). Using these functions, and formulas due to Fadin, Lipatov and Prygarin, we determine the six-gluon MHV remainder function in the leading-logarithmic approximation (LLA) in this limit through ten loops, and the next-to-LLA (NLLA) terms through nine loops. In separate work, we have determined the symbol of the four-loop remainder function for general kinematics, up to 113 constants. Taking its multi-Regge limit and matching to our four-loop LLA and NLLA results, we fix all but one of the constants that survive in this limit. The multi-Regge limit factorizes in the variables ( ν , n ) which are related to ( w , w ∗ ) by a Fourier-Mellin transform. We can transform the single-valued harmonic polylogarithms to functions of (ν, n ) that incorporate harmonic sums, systematically through transcendental weight six. Combining this information with the four-loop results, we determine the eigenvalues of the BFKL kernel in the adjoint representation to NNLLA accuracy, and the MHV product of impact factors to N 3 LLA accuracy, up to constants representing beyond-the-symbol terms and the one symbol-level constant. Remarkably, only derivatives of the polygamma function enter these results. Finally, the LLA approximation to the six-gluon NMHV amplitude is evaluated through ten loops.
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USDOE Office of Science (SC)
AC02-76SF00515
High Energy Physics (HEP)
SLAC-PUB-15132
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2012)074