Anomalous dimensions of transverse-momentum dependent parton distribution functions

TL;DR

This paper investigates the gauge-invariant anomalous dimensions of transverse-momentum dependent parton distribution functions, revealing gauge-dependent contributions and proposing a modified definition to address cusp-related issues.

Contribution

It computes the leading-order anomalous dimension of TMD PDFs in the light-cone gauge and links it to cusp obstructions, proposing a new definition to improve gauge invariance.

Findings

Anomalous dimension receives a cusp-related contribution in light-cone gauge.

The contribution is absent in covariant gauges.

A modified TMD PDF definition is proposed to address gauge issues.

Abstract

We discuss recent developments in the understanding of gauge-invariant transverse-momentum dependent (TMD) parton-distribution functions (PDF). We compute the leading-order $\overline{\text{MS}\vphantom{^1}}$-scheme anomalous dimension of such a quantity in the light-cone gauge and show that it receives a contribution that can be associated with a cusp obstruction at transverse light-cone infinity. This anomalous dimension is intimately related to expectation values composed of fields and eikonal factors along a cusped contour and is absent in covariant gauges. The implications of these findings are addressed and a modified definition of TMD PDFs is proposed.