One-loop corrections to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD

TL;DR

This paper analytically computes the one-loop correction to the double-real emission part of the zero-jettiness soft function at N3LO in QCD, addressing complex phase-space integrals with advanced reduction techniques.

Contribution

It provides the first detailed analytic calculation of this correction at N3LO, including gluon-gluon and quark-antiquark contributions, with a comprehensive methodology.

Findings

Analytic expressions for one-loop double-real corrections at N3LO.

Methodology for phase-space integral reduction with Heaviside functions.

Framework applicable to other soft function calculations in QCD.

Abstract

We present an analytic calculation of the one-loop correction to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD, accounting for both gluon-gluon and quark-antiquark soft final-state partons. We explain all the relevant steps of the computation including the reduction of phase-space integrals to master integrals in the presence of Heaviside functions, and the methods we employed to compute them.