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

Michael Wagman,M Della Morte,C Pena Ruano,P Fritzsch,E Gámiz Sánchez

doi:10.1051/epjconf/201817505003

Michael Wagman, M Della Morte + Show 3 more

Open Access

https://doi.org/10.1051/epjconf/201817505003

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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.

Highlights

Properties of large nuclei, nuclear matter, and colliding neutron stars could be predicted from first principles if lattice quantum chromodynamics (LQCD) calculations could be performed with nonzero baryon chemical potentials
Nuclei can be studied in LQCD by calculating multi-baryon correlation functions averaged over zero-density importance sampled gluon field configurations
M − MR − Mθ is consistent with zero at large t. These results suggest the Parisi-Lepage StN problem can be identified with the StN problem arising from reweighting the complex correlation function sign problem associated with eiθi

Summary

Introduction

Properties of large nuclei, nuclear matter, and colliding neutron stars could be predicted from first principles if lattice quantum chromodynamics (LQCD) calculations could be performed with nonzero baryon chemical potentials. Nuclei can be studied in LQCD by calculating multi-baryon correlation functions averaged over zero-density importance sampled gluon field configurations. N where t denotes the Euclidean time separation of the correlation function source and sink, Uμ(x) ∈ S U(3) denotes the gluon field, S (U) denotes the gluon action after quarks have been integrated out, C(t; U) denotes nucleon correlation functions computed in gluon field configuration U, n labels QCD. The path integral over gluon field configurations can be numerically approximated using a MC ensemble of i = 1, · · · , N correlation functions Ci(t) = C(t, Ui) computed in zero-density importance sampled gluon field configurations, N. i=1 where equality holds in the limit N → ∞. The lowest-energy state with nucleon-antinucleon quantum numbers and no valence quark annihilation is composed of three pions, and so the signal-to-noise (StN) ratio of nucleon correlation functions decays exponentially as. The golden window shrinks with increasing baryon number, and , different analysis strategies may be required when studying large nuclei whose correlation functions have no apparent golden window

Complex Correlation Function Statistics

Phase Reweighting

Conclusion