Theory Seminar: Valerio Bertone

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Speaker: Valerio Bertone (University of Paris-Saclay)

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

Abstract: In this seminar I will present the computation of the one-loop corrections to the unpolarised off-forward matching functions.These functions allow one to obtain generalised transverse-momentum-dependent (GTMD) distributions in terms of generalised parton distributions (GPDs).

The computation proceeds through the appropriate definition of GTMDs as a combination of GTMD correlators and soft function that guarantees the cancellation of rapidity divergences.Using the principal-value regulator, I will show the explicit cancellation of the rapidity divergences at one-loop accuracy. GTMDs remain however affected by ultraviolet (UV) divergences that will be renormalised by means of suitable renormalisation constants. Renormalised GTMDs acquire a dependence of two additional (semi)arbitrary scales, the renormalisation scale and the so-called rapidity scale, whose dependence is governed by appropriate evolution equations. I will show how to extract the anomalous dimensions of these evolution equations at one-loop accuracy from the knowledge of the renormalisation constants. Unsurprisingly, the results will reproduce known results obtained in the forward case (i.e. in the case of transverse-momentum-dependent (TMD) distributions).

After having presented the details of the analytic calculation of the matching functions, I will move to present numerical results. Specifically, by convoluting these matching functions with a phenomenological model for GPDs, I will reconstruct a specific family of GTMDs in the perturbative regime. Transverse non-perturbative corrections can finally be incorporated using recent determinations of TMD distributions. Since evolution effects for GTMDs closely follow those for TMDs, they can also be easily accounted for up to next-to-next-to-leading logarithmic accuracy. This numerical analysis highlights some salient features that open the floor to further investigations.