Nucleon matrix elements using the variational method in lattice QCD

TL;DR

This paper applies the variational method in lattice QCD to accurately extract nucleon matrix elements, reducing excited state contamination and improving robustness over traditional methods.

Contribution

It introduces the variational method for nucleon matrix element calculations in lattice QCD and compares its effectiveness to existing approaches.

Findings

The variational method provides more efficient extraction of matrix elements.

It reduces systematic errors from excited state contamination.

Results are consistent with or improve upon traditional methods.

Abstract

The extraction of hadron matrix elements in lattice QCD using the standard two- and three-point correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current $g_{A}$, the scalar current $g_{S}$ and the quark momentum fraction $\left<x\right>$ of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.