Signal/noise optimization strategies for stochastically estimated correlation functions

TL;DR

This paper explores strategies to optimize the signal-to-noise ratio in stochastically estimated correlation functions in quantum field theories, improving the extraction of physical information from noisy data.

Contribution

It introduces methods for optimizing correlators via source and sink operators, demonstrating significant noise reduction in toy models and QCD hadron correlators.

Findings

Signal/noise can be significantly improved through operator optimization.

Optimization strategies are effective in both toy models and real QCD data.

Large potential for enhancing numerical studies of quantum field theories.

Abstract

Numerical studies of quantum field theories usually rely upon an accurate determination of stochastically estimated correlation functions in order to extract information about the spectrum of the theory and matrix elements of operators. The reliable determination of such correlators is often hampered by an exponential degradation of signal/noise at late time separations. We demonstrate that it is sometimes possible to achieve significant enhancements of signal/noise by appropriately optimizing correlators with respect to the source and sink interpolating operators, and highlight the large range of possibilities that are available for this task. The ideas are discussed for both a toy model, and single hadron correlators in the context of quantum chromodynamics.