One-loop amplitudes in Einstein-Yang-Mills from forward limits

TL;DR

This paper introduces a method to compute one-loop Einstein-Yang-Mills amplitudes using a double-copy structure and forward limits, providing explicit results and relations to simplify calculations across different supersymmetries.

Contribution

It develops a novel approach to derive one-loop Einstein-Yang-Mills integrands from forward limits of tree-level inputs, applicable to any number of external particles and supersymmetries.

Findings

Derived explicit four-point amplitudes for maximal and half-maximal supersymmetry.

Established relations reducing Einstein-Yang-Mills integrands to pure gauge theories.

Identified six-dimensional anomalies in half-maximal supersymmetric cases.

Abstract

We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as (super-)Yang-Mills with the so-called YM+$\phi^3$ theory -- pure Yang-Mills coupled to bi-adjoint scalars -- which we implement via one-loop Cachazo-He-Yuan formulae. The YM+$\phi^3$ building blocks are obtained from forward limits of tree-level input in external gluons and scalars, and we give the composition rules for any number of traces and orders in the couplings $g$ and $\kappa$. On the one hand, we spell out supersymmetry- and dimension-agnostic relations that reduce loop integrands of Einstein-Yang-Mills to those of pure gauge theories. On the other hand, we present four-point results for maximal and half-maximal supersymmetry where all supersymmetry cancellations are exposed. In the half-maximal case, we determine six-dimensional anomalies due to chiral hypermultiplets in the loop.