Flavor-spin symmetry of the PNψ/H_ΩcccN and P^Λψ s/HΛ_Ωcccs 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 PψN, Pψ s^Λ (with quark components [nc̄][$nnc$], [sc̄][$nnc$], or [nc̄][$nsc$]) systems and di-baryon H_ΩcccN, HΛ_Ωcccs (with quark components [$nnc$][$ncc$], [$nnc$][$scc$] or [$nsc$][$ncc$]) systems ($n=u$, d). The light quark components of the PψN (Pψ s^Λ) and H_ΩcccN (H_Ωcccs^Λ) systems have identical flavors, the interactions generated from the exchanges of light mesons in the PψN (P^Λψ s) systems should be very similar to that of the H_ΩcccN (HΛ_Ωcccs) systems. We perform the single-channel and multi-channel calculations on the PψN/P^Λψ s/H_ΩcccN/HΛ_Ωcccs systems and introduce the SU(3) breaking effect to identify the different mass spectra among the PψN (H_ΩcccN) and P^Λψ s (HΛ_Ωcccs) systems. We suggest two kinds of evidences for the existence of the flavor-spin symmetry among the heavy flavor PψN/H_ΩcccN/P^Λψ s/HΛ_Ωcccs molecule community, i.e., the mass arrangements of the PψN/H_ΩcccN/P^Λψ s/HΛ_Ωcccs mass spectra and the binding energies of the heavy flavor meson-baryon (di-baryon) systems attributed to the same contact potentials.