Lattice quantum chromodynamics (QCD) studies on decuplet baryons as meson–baryon bound states in the HAL QCD method

Abstract

Abstract We study decuplet baryons from meson–baryon interactions in lattice quantum chromodynamics (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 $m_{N}+m_{\pi }-m_{\Delta }\lt m_{\Xi }+m_{\bar{K}}-m_{\Omega }$ 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 three quarks. Results of binding energies agree with those obtained from temporal two-point functions within large systematic errors, which arise dominantly from the lattice artifact at short distances.