Universal Decomposition of Phase-Space Integrands

TL;DR

This paper introduces a universal, process-independent basis for phase-space integrands at NLO, utilizing algebraic geometry techniques to facilitate their decomposition into master integrals.

Contribution

It extends the concept of a universal basis from one-loop integrands to phase-space integrals at NLO, employing computational algebraic geometry methods.

Findings

Demonstrates the existence of a basis for phase-space integrands at NLO.

Uses algebraic geometry to systematically decompose integrands.

Lays groundwork for expressing phase-space integrals in terms of master integrals.

Abstract

One-loop integrands can be written in terms of a simple, process-independent basis. We show that a similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. Our demonstration deploys techniques from computational algebraic geometry to partial-fraction integrands in a systematic way. This takes the first step towards a decomposition of phase-space integrals in terms of a basis of master integrals.