Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD

TL;DR

This paper highlights the risk of fake plateaus in temporal correlation functions in lattice QCD, which can mislead the extraction of baryon interactions, especially in multi-baryon systems, emphasizing caution in interpreting these signals.

Contribution

It explicitly demonstrates the danger of fake plateaus in lattice QCD baryon correlation functions for multi-baryon systems using numerical simulations.

Findings

Fake plateaus can occur in two, three, and four baryon systems.

Caution is needed when interpreting correlation functions for bound state analysis.

Simulations were performed on multiple lattice volumes at a pion mass of 0.51 GeV.

Abstract

Single state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for the system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons ($\Xi\Xi$ and $NN$), and three and four baryons ($^3{\rm He}$ and $^4{\rm He})$ as well, employing (2+1)-flavor lattice QCD at $m_{\pi}=0.51$ GeV on four lattice volumes with $L=$ 2.9, 3.6, 4.3 and 5.8 fm. Caution is given for drawing conclusion on the bound $NN$, $3N$ and $4N$ systems only based on the temporal correlation functions.