New results on gauge-invariant TMD PDFs in QCD

TL;DR

This paper investigates the gauge-invariant formulation of transverse-momentum dependent parton distribution functions in QCD, calculating their anomalous dimensions and proposing a generalized, renormalized definition.

Contribution

It introduces a new gauge-invariant definition of TMD PDFs using a renormalization approach for Wilson lines with obstructions, addressing singularities and their impact.

Findings

Calculated the UV anomalous dimension at one-loop in light-cone gauge.

Proposed a generalized, renormalized definition of TMD PDFs.

Discussed the reduction to integrated PDFs and their probabilistic interpretation.

Abstract

The renormalization properties of unintegrated (transverse-momentum dependent) parton distribution functions (TMD PDF's) are used for analyzing their completely gauge-invariant definition. To this end, the UV anomalous dimension is calculated at the one-loop order in the light-cone gauge and a consistent treatment of the extra singularities, which produce undesirable contributions in the anomalous dimensions, is given. The generalized definition of a TMD PDF, based on the renormalization procedure for the Wilson exponentials with obstructions, is proposed. The reduction of the re-defined TMD PDF to the integrated PDF's, as well as their probabilistic interpretation, are discussed.