Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach

TL;DR

This paper develops a diagrammatic approach to compute next-to-eikonal corrections in soft gluon radiation, proving exponentiation at the amplitude level and analyzing sub-eikonal effects on cross sections, advancing threshold resummation techniques.

Contribution

It introduces effective Feynman rules for next-to-eikonal emissions and extends soft gluon resummation to next-to-leading power in the threshold expansion.

Findings

Exponentiation of factorizable contributions at next-to-eikonal order

Effective Feynman rules for direct computation of emissions

Analysis of sub-eikonal phase space corrections in Drell-Yan

Abstract

We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-to-eikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using path-integral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple soft-gluon emissions, which contribute to next-to-eikonal logarithms. To clarify the discussion, we examine a class of log(1 - x) terms in the Drell-Yan cross-section up to two loops. Our results are the first steps towards a systematic generalization of threshold resummations to next-to-leading power in the threshold expansion.