Systematics of the heavy flavor hadronic molecules

Abstract

With a quark level interaction, we give a unified description of the loosely bound molecular systems composed of the heavy flavor hadrons $(\bar{D},{\bar{D}}^{\ast })$, $({\Lambda }_c,{\Sigma }_c,{\Sigma }_c^{\ast })$, and $({\Xi }_c,{\Xi }_c^{\prime },{\Xi }_c^{\ast })$. 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 $[D^{\ast }{D}^{\ast }{]}_{J=1}^{I=0}$. 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 $[{\Sigma }_c{\bar{D}}^{\ast }{]}_{J=1/2}^{I=1/2}$ and $[{\Sigma }_c{\bar{D}}^{\ast }{]}_{J=3/2}^{I=1/2}$ 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.

Comments: 7 pages, 5 tables, 1 figure