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

被引:0
作者
Jeffrey Pennington
机构
[1] Stanford University,SLAC National Accelerator Laboratory
来源
Journal of High Energy Physics | / 2013卷
关键词
Scattering Amplitudes; Extended Supersymmetry; Supersymmetric gauge theory;
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摘要
We present an all-orders formula for the six-point amplitude of planar maximally supersymmetric \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N}=4 $\end{document} 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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[1]  
Bern Z(1994)One loop n point gauge theory amplitudes, unitarity and collinear limits Nucl. Phys. B 425 217-undefined
[2]  
Dixon LJ(1995)Fusing gauge theory tree amplitudes into loop amplitudes Nucl. Phys. B 435 59-undefined
[3]  
Dunbar DC(2005)New recursion relations for tree amplitudes of gluons Nucl. Phys. B 715 499-undefined
[4]  
Kosower DA(2005)Direct proof of tree-level recursion relation in Yang-Mills theory Phys. Rev. Lett. 94 181602-undefined
[5]  
Bern Z(2011)The All-Loop Integrand For Scattering Amplitudes in Planar N = 4 SYM JHEP 01 041-undefined
[6]  
Dixon LJ(2012)Local Integrals for Planar Scattering Amplitudes JHEP 06 125-undefined
[7]  
Dunbar DC(2008)New Relations for Gauge-Theory Amplitudes Phys. Rev. D 78 085011-undefined
[8]  
Kosower DA(2010)Perturbative Quantum Gravity as a Double Copy of Gauge Theory Phys. Rev. Lett. 105 061602-undefined
[9]  
Britto R(1977)Iterated path integrals Bull. Amer. Math. Soc. 83 831-undefined
[10]  
Cachazo F(2010)Classical Polylogarithms for Amplitudes and Wilson Loops Phys. Rev. Lett. 105 151605-undefined