Proper definition and evolution of generalized transverse momentum distributions

TL;DR

This paper redefines generalized transverse momentum distributions (GTMDs) to include soft gluon dependence, enabling proper evolution equations and resummation of large logarithms, advancing their theoretical understanding.

Contribution

It introduces a new definition of GTMDs that incorporates soft gluon radiation, ensuring correct evolution properties and enabling high-precision resummation.

Findings

Derived the evolution kernel for all quark and gluon GTMDs

Found the evolution kernel to be spin independent

Achieved resummation of large logarithms up to NNLL accuracy

Abstract

We consider one of the most fundamental sets of hadronic matrix elements, namely the generalized transverse momentum distributions (GTMDs), and argue that their existing definitions lack proper evolution properties. By exploiting the similarity of GTMDs with the much better understood transverse momentum distributions, we argue that the existing definitions of GTMDs have to include an additional dependence on soft gluon radiation in order to render them properly defined. With this, we manage to obtain the evolution kernel of all (un)polarized quark and gluon GTMDs, which turns out to be spin independent. As a byproduct, all large logarithms can be resummed up to next-to-next-to-leading-logarithmic accuracy with the currently known perturbative ingredients.