Controlling Excited-State Contamination in Nucleon Matrix Elements

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 $t_{\mathrm{sep}}$. 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 $t_{\mathrm{sep}}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_{\mathrm{sep}}\to \infty$ estimates is presented.

Comments: Published version