Improved quasi parton distribution through Wilson line renormalization

TL;DR

This paper introduces a renormalization method for quasi parton distributions involving Wilson lines, effectively removing power divergences and improving their theoretical properties for lattice QCD calculations.

Contribution

It demonstrates that a mass counterterm can eliminate UV power divergences in quasi distributions to all orders, enhancing their usability in extracting parton distributions.

Findings

Power divergence removed by counterterm to all orders

Quasi distributions contain at most logarithmic divergences after renormalization

One-loop matching kernel derived for lattice and continuum schemes

Abstract

Recent developments showed that hadron light-cone parton distributions could be directly extracted from spacelike correlators, known as quasi parton distributions, in the large hadron momentum limit. Unlike the normal light-cone parton distribution, a quasi parton distribution contains ultraviolet (UV) power divergence associated with the Wilson line self energy. We show that to all orders in the coupling expansion, the power divergence can be removed by a "mass" counterterm in the auxiliary $z$-field formalism, in the same way as the renormalization of power divergence for an open Wilson line. After adding this counterterm, the quasi quark distribution is improved such that it contains at most logarithmic divergences. Based on a simple version of discretized gauge action, we present the one-loop matching kernel between the improved non-singlet quasi quark distribution with a lattice regulator and the corresponding quark distribution in dimensional regularization.