Model independent determination of the spins of the $P_c$(4440) and $P_c$(4457) from the spectroscopy of the triply charmed dibaryons

Abstract

The LHCb collaboration has recently observed three narrow pentaquark states --- the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ ---that are located close to the $\bar{D}{\Sigma }_c$ and ${\bar{D}}^{\ast }{\Sigma }_c$ thresholds. Among the so-far proposed theoretical interpretations for these pentaquarks, the molecular hypothesis seems to be the preferred one. Nevertheless, in the molecular picture the spins of the $P_c(4440)$ and $P_c(4457)$ have not been unambiguously determined yet. In this letter we point out that heavy antiquark-diquark symmetry induces a model-independent relation between the spin-splitting in the masses of the $P_c(4440)$ and $P_c(4457)$ ${\bar{D}}^{\ast }{\Sigma }_c$ pentaquarks and the corresponding splitting for the $0^{+}$ and $1^{+}$ ${\Xi }_{cc}{\Sigma }_c$ triply charmed dibaryons. This is particularly relevant owing to a recent lattice QCD prediction of the $1^{+}$ triply charmed dibaryon, which suggests that a calculation of the mass of its $0^{+}$ partner might be within reach. This in turn would reveal the spins of the $P_c(4440)$ and $P_c(4457)$ pentaquarks, providing a highly nontrivial test of heavy-quark symmetry and the molecular nature of the pentaquarks. Furthermore, the molecular interpretation of the hidden-charm pentaquarks implies the existence of a total of ten triply charmed dibaryons as ${\Xi }_{cc}^{(\ast )}{\Sigma }_c^{(\ast )}$ molecules, which, if confirmed in the lattice, will largely expand our understanding of the non-perturbative strong interaction in the heavy-quark sector.

Comments: 6 pages, 1 figure, 3 tables