More loops and legs in Higgs-regulated N=4 SYM amplitudes

TL;DR

This paper extends the analysis of Higgs-regulated planar amplitudes in N=4 SYM to higher loops and legs, confirming an all-loop ansatz and exploring Regge limits with different regulator schemes.

Contribution

It provides four-loop four-gluon and two-loop five-gluon amplitude calculations in Higgs regularization, supporting an all-loop ansatz and analyzing Regge limits with scheme-dependent results.

Findings

Consistent with all-loop ansatz for planar MHV amplitudes.

IR-finite parts depend similarly on kinematic variables as in dimensional regularization.

Regge limit dominated by ladder diagrams and H-shaped insertions.

Abstract

We extend the analysis of Higgs-regulated planar amplitudes of N=4 supersymmetric Yang-Mills theory to four loops for the four-gluon amplitude and to two loops for the five-gluon amplitude. Our calculations are consistent with a proposed all-loop ansatz for planar MHV n-gluon amplitudes that is the analog of the BDS ansatz in dimensional regularization. In all cases considered, we have verified that the IR-finite parts of the logarithm of the amplitudes have the same dependence on kinematic variables as the corresponding functions in dimensionally-regulated amplitudes (up to overall additive constants, which we determine). We also study various Regge limits of N=4 SYM planar n-gluon amplitudes. Euclidean Regge limits of Higgs-regulated n \geq 4 amplitudes yield results similar in form to those found using dimensional regularization, but with different expressions for the gluon trajectory and Regge vertices resulting from the different regulator scheme. We also show that the Regge limit of the four-gluon amplitude is dominated at next-to-leading-log order by vertical ladder diagrams together with the class of vertical ladder diagrams with a single H-shaped insertion.