Controlling excited-state contamination in nucleon matrix elements

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 32³×64 generated using the rational hybrid Monte Carlo algorithm at a=0.081 fm and with M_π=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 2-state fit to data at multiple values of the source-sink separation tₛₑₚ. 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 tₛₑₚ needed to demonstrate convergence of the isovector charges of the nucleon to the tₛₑₚ→∞ estimates is presented.