Systematics of the heavy flavor hadronic molecules

With a quark level interaction, we give a unified description of the loosely bound molecular systems composed of the heavy flavor hadrons $(\bar{D},\bar{D}^*)$, $(Λ_c, Σ_c, Σ_c^*)$, and $(Ξ_c, Ξ_c^\prime,Ξ_c^*)$. Using the $P_c$ states as inputs to fix the interaction strength of light quark-quark pairs, we reproduce the observed $P_{cs}$ and $T_{cc}^+$ states and predict another narrow $T_{cc}^{\prime+}$ state with quantum numbers $[D^*D^*]_{J=1}^{I=0}$. If we require a satisfactory description of the $T_{cc}^+$ and $P_c$ states simultaneously, our framework prefers the assignments of the $P_{c}(4440)$ and $P_{c}(4457)$ as the $[Σ_c\bar{D}^*]_{J=1/2}^{I=1/2}$ and $[Σ_c\bar{D}^*]_{J=3/2}^{I=1/2}$ states, respectively. We propose the isospin criterion to explain naturally why the experimentally observed $T_{cc}$, $P_c$, and $P_{cs}$ molecular candidates prefer the lowest isospin numbers. We also predict the loosely bound states for the bottom di-hadrons.

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