Matching generalised transverse-momentum-dependent distributions onto generalised parton distributions at one loop

TL;DR

This paper computes the one-loop corrections to the matching functions between GTMDs and GPDs, enabling perturbative calculations of GTMDs and providing insights into their evolution and anomalous dimensions.

Contribution

It provides the first full one-loop correction calculations for off-forward matching functions connecting GTMDs and GPDs, including derivation of anomalous dimensions.

Findings

One-loop corrections to matching functions are computed.

Evolution of GTMDs follows TMDs up to NNLL accuracy.

Numerical results illustrate key features of specific GTMDs.

Abstract

The operator definition of generalised transverse-momentum-dependent (GTMD) distributions is exploited to compute for the first time the full set of one-loop corrections to the off-forward matching functions. These functions allow one to obtain GTMDs in the perturbative regime in terms of generalised parton distributions (GPDs). In the unpolarised case, non-perturbative corrections can be incorporated using recent determinations of transverse-momentum-dependent (TMD) distributions. Evolution effects for GTMDs closely follow those for TMDs and can thus be easily accounted for up to next-to-next-to-leading logarithmic accuracy. As a by-product, the relevant one-loop anomalous dimensions are derived, confirming previous results. As a practical application, numerical results for a specific kind of GTMDs are presented, highlighting some salient features.