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 $a=0.081\mathrm{fm}$ and with $M_{\pi }=312\mathrm{MeV}$. 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 2-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.

• Received 29 March 2016

DOI:https://doi.org/10.1103/PhysRevD.93.114506