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

Abstract

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 ($\bar{D}$, ${\bar{D}}^{\ast }$) and doubly heavy baryons (${\Xi }_{cc}$, ${\Xi }_{cc}^{\ast }$). A prediction of these symmetries is that if the $P_c(4450)$ is indeed a ${\bar{D}}^{\ast }{\Sigma }_c$ bound state, then there should be a series of ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$, ${\Xi }_{cc}{\Sigma }_c$, ${\Xi }_{cc}^{\ast }{\Sigma }_c$, ${\Xi }_{cc}{\Sigma }_c^{\ast }$ and ${\Xi }_{cc}^{\ast }{\Sigma }_c^{\ast }$ partners. The concrete application of heavy-quark spin symmetry indicates that, if the $P_c(4450)$ is a ${\frac{3}{2}}^{-}$ ${\bar{D}}^{\ast }{\Sigma }_c$ molecule, the existence of a ${\frac{5}{2}}^{-}$ ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ 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 $0^{+}$ ${\Xi }_{cc}{\Sigma }_c$, $1^{+}$ ${\Xi }_{cc}{\Sigma }_c^{\ast }$, $2^{+}$ ${\Xi }_{cc}^{\ast }{\Sigma }_c$ and $3^{+}$ ${\Xi }_{cc}^{\ast }{\Sigma }_c^{\ast }$ molecules are likely to bind too, with binding energies in the $20-30\mathrm{MeV}$ range.

Comments: 5 pages; corresponds to published version