High Statistics Analysis using Anisotropic Clover Lattices: (III) Baryon-Baryon Interactions

TL;DR

This study uses high-statistics lattice QCD to analyze low-energy baryon-baryon interactions, revealing spin dependencies, attraction in S_1 channels, and small NN scattering lengths at a pion mass of ~390 MeV.

Contribution

It provides the first detailed lattice QCD analysis of multiple baryon-baryon channels at this pion mass with high statistics, using L"uscher's method to extract phase shifts.

Findings

NA extsubscript{3/2} S_1 channel is strongly spin-dependent.

LambdaLambda interaction is attractive.

NN scattering lengths are small, indicating no fine-tuning at this pion mass.

Abstract

Low-energy baryon-baryon interactions are calculated in a high-statistics lattice QCD study on a single ensemble of anisotropic clover gauge-field configurations at a pion mass of m_\pi ~ 390 MeV, a spatial volume of L^3 ~ (2.5 fm)^3, and a spatial lattice spacing of b~0.123 fm. L\"uscher's method is used to extract nucleon-nucleon, hyperon-nucleon and hyperon-hyperon scattering phase shifts at one momentum from the one- and two-baryon ground-state energies in the lattice volume. The isospin-3/2 N\Sigma interactions are found to be highly spin-dependent, and the interaction in the ^3S_1 channel is found to be strong. In contrast, the N\Lambda interactions are found to be spin-independent, within the uncertainties of the calculation, consistent with the absence of one-pion-exchange. The only channel for which a negative energy-shift is found is \Lambda\Lambda, indicating that the \Lambda\Lambda interaction is attractive, as anticipated from model-dependent discussions regarding the H-dibaryon. The NN scattering lengths are found to be small, clearly indicating the absence of any fine-tuning in the NN-sector at this pion mass. This is consistent with our previous Lattice QCD calculation of NN interactions. The behavior of the signal-to-noise ratio in the baryon-baryon correlation functions, and in the ratio of correlation functions that yields the ground-state energy splitting is explored. In particular, focus is placed on the window of time slices for which the signal-to-noise ratio does not degrade exponentially, as this provides the opportunity to extract quantitative information about multi-baryon systems.