Multiple parton scattering in nuclei: gauge invariance

TL;DR

This paper establishes gauge invariance in the calculation of twist-4 contributions to deep inelastic scattering off nuclei, demonstrating equivalence of different gauge choices and providing a unified framework for multiple parton scattering analysis.

Contribution

It proves the gauge invariance of twist-4 contributions in nuclear DIS and shows the equivalence of hard parts in light-cone and covariant gauges.

Findings

Hard parts correspond to transverse gluon interactions in light-cone gauge.

Hard parts relate to second derivatives of cross sections with longitudinal gluons in covariant gauge.

Demonstrates gauge invariance at both lowest and next-to-leading order calculations.

Abstract

Within the framework of a generalized collinear factorization for multiple parton scattering in nuclear medium, twist-4 contributions to DIS off a large nucleus can be factorized as a convolution of hard parts and two-parton correlation functions. The hard parts for the quark scattering in the light-cone gauge correspond to interaction with a transverse (physical) gluon in the target, while they are given by the second derivative of the cross section with a longitudinal gluon in the covariant gauge. We provide a general proof of the equivalence of the hard parts in the light-cone and covariant gauge. We further demonstrate the equivalence in calculations of twist-4 contributions to semi-inclusive cross section of DIS in both lowest order and next leading order. Calculations of the nuclear transverse momentum broadening of the struck quark in the light-cone and covariant gauge are also discussed.