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

¹ Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
² Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550, USA
³ Department of Physics, University of Washington, Box 351560, Seattle, WA 98195, USA

^* Speaker, gratefully acknowledges Martin Savage for contributions to the results presented. e-mail: mlwagman@mit.edu

Published online: 26 March 2018

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.