Two-loop four-point amplitudes on the Coulomb branch of ${\mathcal{N}}=4$ super Yang-Mills

TL;DR

This paper investigates two-loop four-point scattering amplitudes on the Coulomb branch of ${\mathcal{N}}=4$ super Yang-Mills, extending the Amplituhedron framework to include massive particles and analyzing their behavior in the Regge limit.

Contribution

It introduces a new scalar vacuum expectation value pattern, extending the Amplituhedron to massive particles, and performs detailed two-loop amplitude computations with consistency checks.

Findings

Infrared-finite four-particle amplitudes with massive particles

Exponentiation of subleading power terms in the Regge limit

Matching of exponent with the anomalous dimension of a cusped Wilson line

Abstract

We explore scattering amplitudes on the Coulomb branch of maximally supersymmetric Yang-Mills theory. We introduce a particular pattern of scalar vacuum expectation values that allow us to define amplitudes with a different mass pattern compared to what was studied previously. This is motivated by an extension of the Amplituhedron that leads to infrared-finite four-particle amplitudes involving massive particles. We work out the Feynman rules on the Coulomb branch and use them, together with generalized unitarity techniques, to perform consistency checks on the Amplituhedron expectations for the one- and two-loop integrands for the four-particle amplitude. We present details of the computation of the required two-loop four-point integrals via a four-dimensional version of the differential equations method. Finally, we study the Regge limit of the four-point amplitude, including the first power suppressed terms. We find that when organized in terms of a suitable expansion parameter, the subleading power term exponentiates, with the exponent matching the anomalous dimension of a cusped Wilson line with a local operator insertion. The latter is known from integrability, which leads to a prediction at higher loop orders in the Regge limit.