Perturbative renormalization of the first moment of structure functions for domain-wall QCD

TL;DR

This paper calculates one-loop renormalization factors for certain operators in domain-wall QCD, aiding the extraction of physical parton distribution data from lattice simulations.

Contribution

It provides automated perturbative calculations of renormalization factors for structure function operators in domain-wall QCD, showing many are close to unrenormalized.

Findings

Renormalization factors are often close to one.

Operators are practically unrenormalized for specific parameters.

Automated FORM codes facilitate these calculations.

Abstract

Using the domain-wall formulation of lattice fermions, we have computed the one-loop renormalization factors of one-link operators which measure the first nontrivial moment of the unpolarized, polarized and transversity structure functions, in the flavor nonsinglet sector. The knowledge of these factors is necessary in order to extract physical numbers from domain-wall Monte Carlo simulations of parton distributions. We have automated the perturbative calculations by developing suitable FORM codes. The results show that in many instances the total renormalization factors are almost equal to one, and that hence the corresponding operators are, for the appropriate values of the Dirac mass $M$ and the coupling $g_0$, practically unrenormalized.