Signal/noise enhancement strategies for stochastically estimated correlation functions

We develop strategies for enhancing the signal/noise ratio for stochastically sampled correlation functions. The techniques are general and offer a wide range of applicability. We demonstrate the potential of the approach with a generic two-state system and then explore the practical applicability of the method for single hadron correlators in lattice quantum chromodynamics. In the latter case, we determine the ground state energies of the pion, proton, and delta baryon, as well as the ground and first excited state energy of the rho meson using matrices of correlators computed on an exemplary ensemble of anisotropic gauge configurations. In the majority of cases, we find a modest reduction in the statistical uncertainties on extracted energies compared to conventional variational techniques. However, in the case of the delta baryon, we achieve a factor of 3 reduction in statistical uncertainties. The variety of outcomes achieved for single hadron correlators illustrates an inherent dependence of the method on the properties of the system under consideration and the operator basis from which the correlators are constructed.United States. Dept. of Energy (Cooperative Research Agreement DE-FG02-94ER40818)United States. Dept. of Energy (Early Career Research Award DE-SC0010495)Solomon Buchsbaum AT&T Research Fun