BFKL approach and 2 → 5 maximally helicity violating amplitude in N = 4 super-Yang-Mills theory

166

332

Abstract:We extend the hexagon function bootstrap to the next-to-maximally-helicityviolating (NMHV) configuration for six-point scattering in planar N = 4 super-Yang-Mills theory at three loops. Constraints from theQ differential equation, from the operator product expansion (OPE) for Wilson loops with operator insertions, and from multi-Regge factorization, lead to a unique answer for the three-loop ratio function. The three-loop result also predicts additional terms in the OPE expansion, as well as the behavior of NMHV amplitudes in the multi-Regge limit at one higher logarithmic accuracy (NNLL) than was used as input. Both predictions are in agreement with recent results from the flux-tube approach. We also study the multi-particle factorization of multi-loop amplitudes for the first time. We find that the function controlling this factorization is purely logarithmic through three loops. We show that a function U , which is closely related to the parity-even part of the ratio function V , is remarkably simple; only five of the nine possible final entries in its symbol are non-vanishing. We study the analytic and numerical behavior of both the parity-even and parity-odd parts of the ratio function on simple lines traversing the space of cross ratios (u, v, w), as well as on a few two-dimensional planes. Finally, we present an empirical formula for V in terms of elements of the coproduct of the six-gluon MHV remainder function R 6 at one higher loop, which works through three loops for V (four loops for R 6 ).

“…This proposal is based on an analytic continuation from the near-collinear limit, which is similar in spirit to earlier work [52,60], but now provides much more detailed information.…”

Section: Jhep10(2014)065mentioning

confidence: 96%

Section: Jhep10(2014)065mentioning

confidence: 99%

See 1 more Smart Citation

Bootstrapping an NMHV amplitude through three loops

Dixon

Hippel²

2014

166

332

“…In Fourier-Mellin space, they factorize into universal building blocks known as the adjoint BFKL eigenvalue and impact factor, which may be determined perturbatively from first principles, or extracted [31][32][33] from fixed-order expressions for the amplitude that have been obtained by other means [34][35][36]. A leading-order strong-coupling analysis is also possible [37,38], but even more remarkably, the building blocks in question can also be obtained to all loops [39] by means of analytic continuation from a collinear limit where the dynamics is governed by an integrable flux tube [40][41][42][43][44][45][46][47][48][49][50][51], see also [52][53][54]. These developments render the MRK as one of the best sources of 'boundary data' [54][55][56][57] for determining the six-gluon amplitude in general kinematics through five loops, by exploiting its analytic structure with the help of the bootstrap method [30,[58][59][60][61][62].…”

Section: Jhep06(2018)116mentioning

confidence: 99%

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

Duca

Druc

Drummond

et al. 2018

Abstract:We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2 → 5 amplitude in planar N = 4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N -particle MHV amplitude in this region to a function, we specialize to N = 7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the wellstudied six-gluon case. As an application of our results, we explicitly compute the sevengluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.

“…A second limit we study is the limit of multi-Regge kinematics (MRK), which has provided another important guide to the perturbative structure of the six-point remainder function [33,[45][46][47][48][49][50][51], as well as higher-point remainder functions [52,53] and NMHV amplitudes [54]. The six-point remainder function and, more generally, the hexagon functions that we define shortly have simple behavior in the multi-Regge limit.…”

Section: Jhep12(2013)049mentioning

confidence: 99%

Hexagon functions and the three-loop remainder function

Dixon

Drummond

Hippel

et al. 2013

165

398

We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar N = 4 superYang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematic limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multiRegge factorization directly at the function level, and thereby to fix uniquely a set of Riemann ζ valued constants that could not be fixed at the level of the symbol. The nearcollinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to −7.