Deep Inelastic Scattering in Improved Lattice QCD. I. The first moment of structure functions

TL;DR

This paper provides a detailed 1-loop perturbative calculation of renormalization constants for operators related to the first moment of deep inelastic scattering structure functions using improved lattice QCD, aiding more accurate lattice simulations.

Contribution

It introduces a comprehensive perturbative computation of renormalization factors employing an improved lattice action, with automated algebraic verification, enhancing precision in lattice QCD analyses.

Findings

Discrepancies found with some published results

Agreement with known energy-momentum tensor results

Development of automated lattice algebraic computation code

Abstract

We present the complete 1-loop perturbative computation of the renormalization constants and mixing coefficients of the operators that measure the first moment of deep inelastic scattering structure functions, employing the nearest neighbor improved lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order $a$ ($a$ being the lattice spacing) have been proven to be absent from on-shell hadronic lattice matrix elements. Because of the complexity of the calculations, we have checked the analytical expression of all Feynman diagrams using Schoonschip. To this end we have developed a suitable code designed to automatically carry out all the necessary lattice algebraic manipulations, starting from the elementary building blocks of each diagram. We have found discrepancies with some of the published numbers, but we are in agreement with the known results on the energy-momentum tensor.