Signal/noise enhancement strategies for stochastically estimated correlation functions

TL;DR

This paper introduces general strategies to improve the signal/noise ratio in stochastically sampled correlation functions, demonstrating their effectiveness in lattice QCD calculations of hadron energies with significant uncertainty reductions.

Contribution

The authors develop and test a versatile approach for enhancing signal quality in stochastic correlation functions, applicable across various systems including lattice QCD.

Findings

Modest reduction in statistical uncertainties for most hadron energies.

Threefold reduction in uncertainty for the delta baryon.

Method's effectiveness varies depending on system properties and operator basis.

Abstract

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 three 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.