Aspects of Precision Calculations of Nucleon Generalized Form Factors with Domain Wall Fermions on an Asqtad Sea

TL;DR

This paper enhances lattice QCD calculations of nucleon form factors by analyzing statistical methods, volume effects, and mixed action approaches to improve precision in understanding nucleon structure.

Contribution

It introduces optimized statistical techniques and compares different lattice actions to improve the accuracy of nucleon form factor calculations.

Findings

Optimal number of configurations depends on pion mass.

Coherent sink method improves statistical precision.

Volume dependence affects form factor results.

Abstract

In order to advance lattice calculations of moments of unpolarized, helicity, and transversity distributions, electromagnetic form factors, and generalized form factors of the nucleon to a new level of precision, this work investigates several key aspects of precision lattice calculations. We calculate the number of configurations required for constant statistical errors as a function of pion mass, describe the coherent sink method to help achieve these statistics, examine the statistical correlations between separate measurements, study correlations in the behavior of form factors at different momentum transfer, examine volume dependence, and compare mixed action results with those using comparable dynamical domain wall configurations. We also show selected form factor results and comment on the QCD evolution of our calculations of the flavor non-singlet nucleon angular momentum.