Calm Multi-Baryon Operators

TL;DR

This paper introduces a new, less computationally intensive method using the Matrix Prony technique to create 'calm baryon' operators that reduce excited state contamination in lattice QCD two-baryon calculations, improving early-time signal extraction.

Contribution

The paper presents a novel approach combining the Matrix Prony method with baryon operators to efficiently suppress excited state contamination in two-baryon lattice QCD studies.

Findings

Calm baryon operators effectively remove excited state contamination early in Euclidean time.

The method improves the extraction of two-nucleon correlation functions on specific gauge configurations.

Significant excited state contamination remains in local two-nucleon correlators despite the new approach.

Abstract

Outstanding problems in nuclear physics require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolators. Very early in Euclidean time this linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions. To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with m{\pi} $\sim$ 800 MeV --- the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.