Life Outside the Golden Window: Statistical Angles on the Signal-to-Noise Problem

TL;DR

This paper explores the signal-to-noise problem in lattice QCD simulations of multi-baryon systems, revealing a connection to the sign problem and proposing phase-based estimators to mitigate the exponential noise growth.

Contribution

It introduces a novel phase-based estimator approach that circumvents the traditional signal-to-noise issue in lattice QCD calculations of baryonic observables.

Findings

Phase of baryon correlation functions relates to sign problem.

Phase difference estimators avoid exponential noise growth.

Hadronic observables can be extracted from large-time correlations.

Abstract

Lattice QCD simulations of multi-baryon correlation functions can predict the structure and reactions of nuclei without encountering the baryon chemical potential sign problem. However, they suffer from a signal-to-noise problem where Monte Carlo estimates of observables have quantum fluctuations that are exponentially larger than their average values. Recent lattice QCD results demonstrate that the complex phase of baryon correlations functions relates the baryon signal-to-noise problem to a sign problem and exhibits unexpected statistical behavior resembling a heavy-tailed random walk on the unit circle. Estimators based on differences of correlation function phases evaluated at different Euclidean times are discussed that avoid the usual signal-to-noise problem, instead facing a signal-to-noise problem as the time interval associated with the phase difference is increased, and allow hadronic observables to be determined from arbitrarily large-time correlation functions.