Perturbative renormalization of moments of quark momentum, helicity and transversity distributions with overlap and Wilson fermions

TL;DR

This paper calculates one-loop renormalization factors for various quark distribution operators using overlap and Wilson fermions, highlighting the advantages of chiral symmetry in avoiding operator mixing issues.

Contribution

It provides new one-loop renormalization factors for moments of quark distributions with overlap fermions and improves existing results for Wilson fermions, emphasizing chiral symmetry benefits.

Findings

Overlap fermions maintain chiral symmetry, avoiding power-divergent operator mixing.

Many Wilson fermion results are new or confirmed with high accuracy.

Gauge invariance of the renormalization factors is verified using FORM.

Abstract

Using overlap as well as Wilson fermions, we have computed the one-loop renormalization factors of ten non-singlet operators which measure the third moment of quark momentum and helicity distributions (the lowest two having been computed in a previous paper), as well as the lowest three moments of the $g_2$ structure function and the lowest two non-trivial moments of the $h_1$ transversity structure function (plus the tensor charge). These factors are needed to extract physical observables from Monte Carlo simulations of the corresponding matrix elements. An exact chiral symmetry is maintained in our calculations with overlap fermions, and its most important consequence here is that the operators measuring $g_2$ do not show any of the power-divergent mixings with operators of lower dimension which are present in the Wilson case. Many of our results for Wilson fermions are also new; for the remaining ones, we agree with the literature except in one case. The computations have been carried out using the symbolic language FORM, in a general covariant gauge, which turns out also to be useful in checking the gauge-invariance of the final results.