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

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.