学术文献库

We study decuplet baryons from meson-baryon interactions in lattice QCD, in particular, $Δ$ and $Ω$ baryons from P-wave $I=3/2$ $Nπ$ and $I=0$ $Ξ\bar{K}$ interactions, respectively. Interaction potentials are calculated in the HAL QCD method using 3-quark-type source operators at $m_π \approx 410~\textrm{MeV}$ and $m_{K} \approx 635~\textrm{MeV}$, where $Δ$ as well as $Ω$ baryons are stable. We use the conventional stochastic estimate of all-to-all propagators combined with the all-mode averaging to reduce statistical fluctuations. We have found that the $Ξ\bar K$ system has a weaker attraction than the $Nπ$ system while the binding energy from the threshold is larger for $Ω$ than $Δ$. This suggests that an inequality $m_{N}+m_π-m_Δ<m_Ξ+m_{\bar K}-m_Ω$ comes mainly from a smaller spatial size of a $Ξ\bar K$ bound state due to a larger reduced mass, rather than its interaction. Root-mean-square distances of bound states in both systems are small, indicating that $Δ$ and $Ω$ are tightly bound states and thus can be regarded qualitatively as composite states of 3 quarks. Results of binding energies agree with those obtained from temporal 2-point functions within large systematic errors, which arise dominantly from the lattice artifact at short distances.