# Subleading Poles in the Numerical Unitarity Method at Two Loops

## TL;DR

This paper introduces a universal algorithm to compute subleading pole contributions in two-loop scattering amplitudes, enhancing the numerical unitarity method by enabling direct calculation of complex integral coefficients.

## Contribution

The authors develop a novel algorithm to extract subleading pole terms at two loops, addressing a gap in the numerical unitarity approach for scattering amplitudes.

## Key findings

- Successfully computed two-loop four-gluon integral coefficients numerically.
- Demonstrated the effectiveness of the new algorithm in handling subleading poles.
- Enhanced the numerical unitarity method for two-loop amplitude calculations.

## Abstract

We describe the unitarity approach for the numerical computation of two-loop integral coefficients of scattering amplitudes. It is well known that the leading propagator singularities of an amplitude's integrand are related to products of tree amplitudes. At two loops, Feynman diagrams with doubled propagators appear naturally, which lead to subleading pole contributions. In general, it is not known how these contributions can be directly expressed in terms of a product of on-shell tree amplitudes. We present a universal algorithm to extract these subleading pole terms by releasing some of the on-shell conditions. We demonstrate the new approach by numerically computing two-loop four-gluon integral coefficients.