One-loop matching for leading-twist generalised transverse-momentum-dependent distributions

TL;DR

This paper derives one-loop matching coefficients to connect leading-twist GTMDs with GPDs, revealing how radiative corrections influence their complex dynamics and mixing behaviors in high-energy QCD processes.

Contribution

It provides the first detailed calculation of one-loop matching functions for all leading-twist GTMDs onto GPDs, including their mixing and evolution effects.

Findings

Time-reversal even and odd GTMDs mix under matching and evolution.

Matching functions are derived for all leading-twist GTMDs.

Numerical results illustrate the behavior of GTMDs under radiative corrections.

Abstract

We present the one-loop matching coefficients necessary to match all of the leading-twist generalised transverse-momentum-dependent distributions (GTMDs) onto generalised parton distributions (GPDs). Matching functions are extracted by computing the first radiative corrections to partonic bilocal correlators with staple-like Wilson lines, as appropriate for high-energy collisions. These correlators are characterised by a transverse displacement and skewed kinematics of external states. Using the proton helicity basis, they are parametrised in terms of GTMDs, which are subsequently related to leading-twist GPDs. Our results provide new insights into the complex dynamics of GTMDs generated by radiative corrections. In particular, we show that time-reversal even and odd contributions to GTMDs in the so-called ERBL region mix both under matching and evolution. Finally, we present a selection of numerical results and comment on the quantitative behaviour of GTMDs.