Massive amplitudes on the Coulomb branch of N=4 SYM

TL;DR

This paper systematically studies massive amplitudes on the Coulomb branch of N=4 SYM, providing new explicit formulas, structural insights, and dual conformal properties, with implications for both theory and phenomenology.

Contribution

It introduces a method using soft-scalar limits to determine Coulomb-branch amplitudes and derives explicit compact expressions for various massive superamplitudes.

Findings

Explicit formulas for two massive W-boson amplitudes with positive helicity gluons.

Structure of superamplitudes with Grassmann polynomials of mixed degree.

Construction and analysis of dual conformal generators for massive amplitudes.

Abstract

We initiate a systematic study of amplitudes with massive external particles on the Coulomb-branch of N=4 super Yang Mills theory: 1) We propose that (multi-)soft-scalar limits of massless amplitudes at the origin of moduli space can be used to determine Coulomb-branch amplitudes to leading order in the mass. This is demonstrated in numerous examples. 2) We find compact explicit expressions for several towers of tree-level amplitudes, including scattering of two massive W-bosons with any number of positive helicity gluons, valid for all values of the mass. 3) We present the general structure of superamplitudes on the Coulomb branch. For example, the n-point "MHV-band" superamplitude is proportional to a Grassmann polynomial of mixed degree 4 to 12, which is uniquely determined by supersymmetry. We find explicit tree-level superamplitudes for this MHV band and for other simple sectors of the theory. 4) Dual conformal generators are constructed, and we explore the dual conformal properties of the simplest massive amplitudes. Our compact expressions for amplitudes and superamplitudes should be of both theoretical and phenomenological interest; in particular the tree-level results carry over to truncations of the theory with less supersymmetry.