Controlling Excited-State Contamination in Nucleon Matrix Elements

TL;DR

This paper compares methods to reduce excited-state contamination and statistical errors in nucleon matrix element calculations using lattice QCD, demonstrating effective tuning of techniques like variational analysis and two-state fits.

Contribution

It provides a detailed comparison of variational and two-state fit methods for excited-state suppression in nucleon matrix element calculations.

Findings

Both methods effectively reduce excited-state contamination.

Optimal source smearing and source-sink separation are crucial for convergence.

The study offers guidance on cost-effective strategies for lattice QCD calculations.

Abstract

We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1 flavor ensemble with lattices of size $32^3 \times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $M_\pi=312$ MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a two-state fit to data at multiple values of the source-sink separation $t_{\rm sep}$. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost-effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of $t_{\rm sep}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_{\rm sep} \to \infty $ estimates is presented.