# Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes

## TL;DR

This paper develops a framework for calculating superamplitudes involving massive BPS states in 4d $
N=4$ super-Yang-Mills on the Coulomb branch, using super-BCFW recursion and on-shell superspace, revealing new structural insights.

## Contribution

It introduces a super-BCFW recursion method for massive amplitudes and explicitly computes multi-particle superamplitudes with all massive external states.

## Key findings

- Validated super-BCFW recursion for Coulomb branch superamplitudes
- Derived exact three-particle superamplitudes for massive states
- Computed four- and five-particle superamplitudes with all massive external states

## Abstract

We study scattering amplitudes of massive BPS states on the Coulomb branch of $4d$ $\mathcal{N}=4$ super-Yang-Mills, utilising a little group covariant on-shell superspace for massive particles. Super-BCFW recursion for massive amplitudes is constructed and its validity is proven for all Coulomb branch superamplitudes. We then determine the exact three-particle superamplitudes for massive states. These ingredients allow us to explicitly compute the four- and five-particle superamplitudes, which is the first non-trivial usage of BCFW recursion for amplitudes with entirely massive external states. The manifest little group covariance helps clarify both the role of special kinematic properties of BPS states and the organizational structures of the superamplitudes.