Investigations of decuplet baryons from meson-baryon interactions in the HAL QCD method

TL;DR

This study uses the HAL QCD method to analyze meson-baryon interactions, revealing that $ ext{Delta}$ and $ ext{Omega}$ baryons are bound states with similar potentials, and their mass differences are mainly due to kinematic effects.

Contribution

It demonstrates the application of the HAL QCD method to decuplet baryons, providing insights into their interactions and mass differences in lattice QCD simulations.

Findings

$ ext{Delta}$ and $ ext{Omega}$ are bound states in this setup.

Potentials for $N ext{pi}$ and $ ext{Xi}ar{ ext{K}}$ interactions are similar.

Mass differences mainly stem from kinematic structures.

Abstract

We study decuplet baryons from meson-baryon interactions, in particular, $\Delta$ and $\Omega$ baryons from P-wave $I=3/2$ $N\pi$ and $I=0$ $\Xi\bar{K}$ interactions, respectively. The interaction potentials are calculated in the HAL QCD method using 3-quark-type source operators at $m_{\pi} \approx 410~\textrm{MeV}$. We use the conventional stochastic estimation of all-to-all propagators combined with the all-mode averaging to reduce statistical fluctuations. We have found that two potentials have quite similar behaviors, suggesting that a mass difference between $\Delta$ and $\Omega$ comes mainly from a difference of kinematical structure between $N\pi$ and $\Xi \bar K$, rather than their interactions. The scattering phase shifts calculated from the potentials indicate that $\Delta$ and $\Omega$ baryons exist as bound states in this lattice setup, whose binding energies are consistent with those obtained from 2-point functions.