Renormalization-group properties of transverse-momentum dependent parton distribution functions in the light-cone gauge with the Mandelstam-Leibbrandt prescription

TL;DR

This paper investigates the renormalization-group behavior of transverse-momentum dependent parton distribution functions in the light-cone gauge using the Mandelstam-Leibbrandt prescription, revealing gauge-invariant anomalous dimensions without extra divergences.

Contribution

It provides a new expression for the gauge field at light-cone infinity and calculates the leading-order anomalous dimension in this specific gauge with the Mandelstam-Leibbrandt prescription.

Findings

Anomalous dimension is gauge-invariant with no extra rapidity divergences.

Derived the transverse component of the gauge field at light-cone infinity.

Established the relation between results in different gauges.

Abstract

The renormalization-group properties of transverse-momentum dependent parton distribution functions in the light-cone gauge with the Mandelstam-Leibbrandt prescription for the gluon propagator are addressed. An expression for the transverse component of the gauge field at light-cone infinity, which plays a crucial role in the description of the final-/initial-state interactions in the light-cone axial gauge, is obtained. The leading-order anomalous dimension is calculated in this gauge and the relation to the results obtained in other gauges is worked out. It is shown that, using the Mandelstam-Leibbrandt prescription, the ensuing anomalous dimension does not receive contributions from extra rapidity divergences related to a cusped junction point of the Wilson lines.