Exponentiation of soft quark effects from the replica trick

TL;DR

This paper demonstrates that multiple soft quark and gluon emissions in QCD exponentiate at the amplitude or cross-section level, generalizing Wilson lines and using the replica trick for proof, applicable to various scattering processes.

Contribution

It introduces new soft emission operators for quarks and gluons and proves their exponentiation using the replica trick, extending soft-gluon exponentiation to soft quark effects in QCD.

Findings

Soft quark and gluon emissions exponentiate at amplitude and cross-section levels.

New soft emission operators generalize Wilson lines for soft quark effects.

Exponentiation proven using the replica trick, applicable to various processes.

Abstract

In this paper, we show that multiple maximally soft (anti-)quark and gluon emissions exponentiate at the level of either the amplitude or cross-section. We first show that such emissions can be captured by introducing new soft emission operators, which serve to generalise the well-known Wilson lines describing emissions of maximally soft gluons. Next, we prove that vacuum expectation values of these operators exponentiate using the replica trick, a statistical-physics argument that has previously been used to demonstrate soft-gluon exponentiation properties in QCD. The obtained results are general, i.e. not tied to a particular scattering process. We illustrate our arguments by demonstrating the exponentiation of certain real and virtual corrections affecting subleading partonic channels in deep-inelastic scattering.