BCJ Relations for One-Loop QCD Integral Coefficients

TL;DR

This paper derives relations among one-loop QCD integral coefficients using tree-level BCJ relations, simplifying calculations of one-loop amplitudes by reducing independent coefficients.

Contribution

It introduces a novel set of coefficient relations in QCD based on BCJ amplitude relations, enhancing computational efficiency.

Findings

Reduces the number of independent one-loop coefficients needed

Provides explicit examples for box, triangle, and bubble coefficients

Demonstrates the utility of tree-level relations in loop calculations

Abstract

We present a set of one-loop integral coefficient relations in QCD. The unitarity method is useful for exposing one-loop amplitudes in terms of tree amplitudes. The coefficient relations are induced by tree-level BCJ amplitude relations. We provide examples for box, triangle, and bubble coefficients. These relations reduce the total number of independent coefficients needed to calculate one-loop QCD amplitudes.