Perturbative Renormalization of Wilson line operators

TL;DR

This paper calculates the one-loop renormalization of gauge-invariant nonlocal fermion operators with Wilson lines in lattice QCD, addressing divergences and proposing nonperturbative methods for divergence removal.

Contribution

It provides the first detailed one-loop perturbative renormalization results for Wilson line operators with various fermion and gluon actions, including nonperturbative prescriptions for divergences.

Findings

Renormalization includes linear and logarithmic divergences.

Nonperturbative methods proposed for divergence subtraction.

Results applicable to Wilson and clover fermions with Symanzik improved gluons.

Abstract

We present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions. The extended nature of such `long-link' operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors. We present nonperturbative prescriptions to extract the linearly divergent contributions.