Gluon quasidistribution function at one loop

TL;DR

This paper investigates the one-loop unpolarized gluon quasidistribution function within the large momentum effective theory, revealing ultraviolet divergence structures and deriving matching and evolution equations aligned with DGLAP kernels.

Contribution

It provides the first detailed analysis of linear ultraviolet divergences in gluon quasidistributions and derives complete one-loop matching factors and P^z evolution equations.

Findings

Linear UV divergences exist in real diagrams without Wilson lines.

Complete one-loop matching factors between quasi and light cone PDFs are derived.

P^z evolution kernels match DGLAP evolution kernels.

Abstract

We study the unpolarized gluon quasidistribution function in the nucleon at one loop level in the large momentum effective theory. For the quark quasidistribution, power law ultraviolet divergences arise in the cut-off scheme and an important observation is that they all are subjected to Wilson lines. However for the gluon quasidistribution function, we first point out that the linear ultraviolet divergences also exist in the real diagram which is not connected to any Wilson line. We then study the one loop corrections to parton distribution functions in both cut-off scheme and dimensional regularization to deal with the ultraviolet divergences. In addition to the ordinary quark and gluon distributions, we also include the quark to gluon and gluon to quark splitting diagrams. The complete one-loop matching factors between the quasi and light cone parton distribution functions are presented in the cut-off scheme. We derive the $P^z$ evolution equation for quasi parton distribution functions, and find that the $P^z$ evolution kernels are identical to the DGLAP evolution kernels.