Closed-Form Decomposition of One-Loop Massive Amplitudes

TL;DR

This paper derives explicit formulas for calculating coefficients of master integrals in one-loop massive amplitudes using unitarity cuts, applicable for both analytical and numerical evaluations.

Contribution

It introduces a new set of formulas for master integral coefficients in one-loop massive amplitudes derived from unitarity cuts in D dimensions, applicable to various processes.

Findings

Formulas validated on gg -> gg helicity amplitudes.

Applicable to processes with arbitrary masses in loops.

Suitable for both analytical and numerical computations.

Abstract

We present formulas for the coefficients of 2-, 3-, 4- and 5-point master integrals for one-loop massive amplitudes. The coefficients are derived from unitarity cuts in D dimensions. The input parameters can be read off from any unitarity-cut integrand, as assembled from tree-level expressions, after simple algebraic manipulations. The formulas presented here are suitable for analytical as well as numerical evaluation. Their validity is confirmed in two known cases of helicity amplitudes contributing to gg -> gg and gg -> gH, where the masses of the Higgs and the fermion circulating in the loop are kept as free parameters.