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

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.