Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits

TL;DR

This paper calculates the three-loop four-gluon amplitude in N=4 SYM using Higgs IR regularization, confirming the exponential ansatz and analyzing Regge limits across different IR schemes, revealing insights into amplitude behavior and gluon Regge trajectories.

Contribution

It provides the first three-loop computation of the four-gluon amplitude with Higgs regularization and tests the exponential ansatz at this order, also exploring Regge limits with various IR regulators.

Findings

The exponential ansatz is validated at three loops.

Leading logarithmic behavior matches ladder approximation in Higgs and cutoff schemes.

Dimensional regularization does not isolate a dominant diagram set in LL approximation.

Abstract

We compute the three-loop contribution to the N=4 supersymmetric Yang-Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and Schuster. In particular, we test the proposed exponential ansatz for the four-gluon amplitude that is the analog of the BDS ansatz in dimensional regularization. By evaluating our results at a number of kinematic points, and also in several kinematic limits, we establish the validity of this ansatz at the three-loop level. We also examine the Regge limit of the planar four-gluon amplitude using several different IR regulators: dimensional regularization, Higgs regularization, and a cutoff regularization. In the latter two schemes, it is shown that the leading logarithmic (LL) behavior of the amplitudes, and therefore the lowest-order approximation to the gluon Regge trajectory, can be correctly obtained from the ladder approximation of the sum of diagrams. In dimensional regularization, on the other hand, there is no single dominant set of diagrams in the LL approximation. We also compute the NLL and NNLL behavior of the L-loop ladder diagram using Higgs regularization.