Flavor-spin symmetry of the $P^N_{\psi}/H_{\Omega_{ccc}}^N$ and $P^\Lambda_{\psi s}/H^{\Lambda}_{\Omega_{ccc}s}$ molecular states

Based on a contact lagrangian that incorporates the SU(3) flavor and SU(2) spin symmetries, we discuss the symmetry properties of the interactions among the heavy flavor meson-baryon $P_{\psi}^N$, $P_{\psi s}^\Lambda$ (with quark components [$n\bar{c}$][$nnc$], [$s\bar{c}$][$nnc$], or [$n\bar{c}$][$nsc$]) systems and di-baryon $H_{\Omega_{ccc}}^N$, $H^{\Lambda}_{\Omega_{ccc}s}$ (with quark components [$nnc$][$ncc$], [$nnc$][$scc$] or [$nsc$][$ncc$]) systems ($n=u$, $d$). The light quark components of the $P_{\psi}^N$ ($P_{\psi s}^\Lambda$) and $H_{\Omega_{ccc}}^N$ ($H_{\Omega_{ccc}s}^\Lambda$) systems have identical flavors, the interactions generated from the exchanges of light mesons in the $P_{\psi}^N$ ($P^\Lambda_{\psi s}$) systems should be very similar to that of the $H_{\Omega_{ccc}}^N$ ($H^{\Lambda}_{\Omega_{ccc}s}$) systems. We perform the single-channel and multi-channel calculations on the $P_{\psi}^N/P^\Lambda_{\psi s}/H_{\Omega_{ccc}}^N/H^{\Lambda}_{\Omega_{ccc}s}$ systems and introduce the SU(3) breaking effect to identify the different mass spectra among the $P_{\psi}^N$ ($H_{\Omega_{ccc}}^N$) and $P^\Lambda_{\psi s}$ ($H^{\Lambda}_{\Omega_{ccc}s}$) systems. We suggest two kinds of evidences for the existence of the flavor-spin symmetry among the heavy flavor $P_{\psi}^N/H_{\Omega_{ccc}}^N/P^\Lambda_{\psi s}/H^{\Lambda}_{\Omega_{ccc}s}$ molecule community, i.e., the mass arrangements of the $P_{\psi}^N/H_{\Omega_{ccc}}^N/P^\Lambda_{\psi s}/H^{\Lambda}_{\Omega_{ccc}s}$ mass spectra and the binding energies of the heavy flavor meson-baryon (di-baryon) systems attributed to the same contact potentials.