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 $\Xi \bar{K}$ interactions, respectively. Interaction potentials are calculated in the HAL QCD method using 3-quark-type source operators at mπ ≈ 410 MeV and mK ≈ 635 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 $\Xi \bar{K}$ 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 $m_{N}+m_{\pi }-m_{\Delta }<m_{\Xi }+m_{\bar{K}}-m_{\Omega }$ comes mainly from a smaller spatial size of a $\Xi \bar{K}$ 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.

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We study decuplet baryons from meson-baryon interactions in lattice QCD, in particular, ∆ and Ω baryons from P-wave I = 3/2 N π and I = 0 Ξ K interactions, respectively. Interaction potentials are calculated in the HAL QCD method using 3-quark-type source operators at m π ≈ 410 MeV and m K ≈ 635 MeV, where ∆ 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 K system has a weaker attraction than the N π system while the binding energy from the threshold is larger for Ω than ∆. This suggests that an inequalitymainly from a smaller spatial size of a Ξ 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 ∆ 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.

In this paper, employing an all-to-all quark propagator technique, we investigate the kaon-nucleon interactions in lattice QCD. We calculate the S-wave kaon-nucleon potentials at the leading order in the derivative expansion in the time-dependent HAL QCD method, using (2+1)-flavor gauge configurations at the lattice spacing a ≈ 0.09 fm on 323 × 64 lattices and the pion mass mπ ≈ 570 MeV. We take the one-end trick for all-to-all propagators, which allows us to put the zero momentum hadron operators at both source and sink and to smear quark operators at the source. We find the stronger repulsive interaction in the I = 1 channel than in the I =0 . The phase shifts obtained by solving the Schrödinger equations with the potentials qualitatively reproduce the energy dependence of the experimental phase shifts, and have the similar behavior to the previous results from lattice QCD without all-to-all propagators. Our study demonstrates that the all-to-all quark propagator technique with the one-end trick is useful to study interactions for meson-baryon systems in the HAL QCD method, so that we will apply it to meson-baryon systems which contain quark-antiquark creation/annihilation processes in our future studies.