Integral Coefficients for One-Loop Amplitudes

TL;DR

This paper introduces algebraic functions derived from unitarity cuts to efficiently evaluate coefficients of scalar integral bases in general one-loop amplitudes, streamlining calculations in quantum field theory.

Contribution

It provides a complete, general algebraic framework for calculating one-loop amplitude coefficients directly from tree-level inputs without repeated cut procedures.

Findings

Functions enable black-box calculation of one-loop amplitudes

Framework applicable to general one-loop amplitude evaluations

Reduces computational effort in amplitude calculations

Abstract

We present a set of algebraic functions for evaluating the coefficients of the scalar integral basis of a general one-loop amplitude. The functions are derived from unitarity cuts, but the complete cut-integral procedure has been carried out in generality so that it never needs to be repeated. Where the master integrals are known explicitly, the results here can be used as a black box with tree-level amplitudes as input and one-loop amplitudes as output.