Heavy-Quark Symmetry Partners of the Pc(4450) Pentaquark

The spectrum of heavy-hadron molecules is constrained by heavy-quark symmetry in its different manifestations. Heavy-quark spin symmetry for instance connects the properties of the ground and excited states of heavy hadrons, while heavy-antiquark-diquark symmetry connects the properties of heavy antimesons ($\bar{D}$, $\bar{D}^*$) and doubly heavy baryons ($\Xi_{cc}$, $\Xi_{cc}^*$). A prediction of these symmetries is that if the $P_c(4450)$ is indeed a $\bar{D}^* \Sigma_c$ bound state, then there should be a series of $\bar{D}^* \Sigma_c^*$, $\Xi_{cc} \Sigma_c$, $\Xi_{cc}^* \Sigma_c$, $\Xi_{cc} \Sigma_c^*$ and $\Xi_{cc}^* \Sigma_c^*$ partners. The concrete application of heavy-quark spin symmetry indicates that, if the $P_c(4450)$ is a $\frac{3}{2}^{-}$ $\bar{D}^* \Sigma_c$ molecule, the existence of a $\frac{5}{2}^{-}$ $\bar{D}^* \Sigma_c^*$ partner with similar binding energy --- which we call $P_c(4515)$, given its expected mass --- is likely. Conversely, the application of heavy-antiquark-diquark symmetry indicates that the $0^+$ $\Xi_{cc} \Sigma_c$, $1^+$ $\Xi_{cc} \Sigma_c^*$, $2^+$ $\Xi_{cc}^* \Sigma_c$ and $3^+$ $\Xi_{cc}^* \Sigma_c^*$ molecules are likely to bind too, with binding energies in the $20-30\,{\rm MeV}$ range.