$\Lambda$(1405) in the flavor SU(3) limit using a separable potential in the HAL QCD method

TL;DR

This study uses the HAL QCD method with a separable potential to analyze meson-baryon interactions in the flavor SU(3) limit, providing insights into the nature of the $ ext{Lambda}(1405)$ resonance.

Contribution

It introduces a separable potential approach within the HAL QCD framework to avoid singularities in the analysis of $ ext{Lambda}(1405)$ in the flavor SU(3) limit.

Findings

Attractive interactions found in both singlet and octet channels.

Stronger attraction in the singlet channel compared to the octet.

Binding energies align with chiral unitary model predictions.

Abstract

Using the HAL QCD method, we investigate S-wave meson-baryon interactions in singlet and two octet channels in the flavor SU(3) limit, where the chiral unitary model predicts that a combination of bound-state poles in these channels corresponds to $\Lambda(1405)$. To avoid the singular behavior of the leading-order potentials of these channels in the derivative expansion, we instead employ a separable potential in the time-dependent HAL QCD method. To calculate all-to-all propagators in the three-point correlation functions including $\Lambda$-baryon source operators with zero momentum, we employ the conventional stochastic estimation combined with the covariant approximation averaging. Separable potentials both in the singlet and octet channels show attraction without singular behavior. Our results of the corresponding phase shifts indicate that the attractive interaction in the singlet channel is stronger than that in the octet. Binding energies are consistent with the estimates from the two-point correlation function within one (two) sigma for the singlet (octet) channel, and this ordering of binding energies is consistent with the mass hierarchy suggested by the chiral unitary model.