The double-soft integral for an arbitrary angle between hard radiators

TL;DR

This paper analytically computes the double-soft limit integrals in QCD for arbitrary angles between hard radiators, aiding the development of precise subtraction schemes for higher-order calculations.

Contribution

It provides the first analytical integration of double-soft eikonal functions at arbitrary angles, filling a key gap in soft-collinear subtraction methods.

Findings

Analytical expressions for double-soft integrals at arbitrary angles.

Facilitates more accurate and complete subtraction schemes in QCD calculations.

Supports higher-order perturbative QCD computations.

Abstract

We consider the double-soft limit of a generic QCD process involving massless partons and integrate analytically the double-soft eikonal functions over the phase-space of soft partons (gluons or quarks) allowing for an arbitrary relative angle between the three-momenta of two hard massless radiators. This result provides one of the missing ingredients for a fully analytic formulation of the nested soft-collinear subtraction scheme recently proposed by some of us.