Exploiting stochastic locality in lattice QCD: hadronic observables and their uncertainties

TL;DR

This paper develops new techniques to analyze hadronic observables in lattice QCD by leveraging stochastic locality, enabling more efficient variance estimation and comparison of position-space correlators with traditional methods.

Contribution

It introduces methods for studying hadronic observables using localized position-space correlators and adapts variance estimation techniques for correlated spatial samples.

Findings

Position-space correlators provide a localized approach to hadronic observables.

New variance estimation methods account for autocorrelations in spatially-separated samples.

Comparison shows advantages of position-space methods over time-momentum representation.

Abstract

Because of the mass gap, lattice QCD simulations exhibit stochastic locality: distant regions of the lattice fluctuate independently. There is a long history of exploiting this to increase statistics by obtaining multiple spatially-separated samples from each gauge field; in the extreme case, we arrive at the master-field approach in which a single gauge field is used. Here we develop techniques for studying hadronic observables using position-space correlators, which are more localized, and compare with the standard time-momentum representation. We also adapt methods for estimating the variance of an observable from autocorrelated Monte Carlo samples to the case of correlated spatially-separated samples.