Five-flavor pentaquarks and other light- and heavy-flavor symmetry partners of the LHCb hidden-charm pentaquark

The discovery of three pentaquark peaks – the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ – by the LHCb collaboration has a series of interesting consequences for hadron spectroscopy. If these hidden-charm objects are indeed hadronic molecules, as suspected, they will be constrained by heavy-flavor and SU(3)-flavor symmetries. The combination of these two symmetries will imply the existence of a series of five-flavor pentaquarks with quark content $\bar{b} c s d u$and$b \bar{c} s d u$, that is, pentaquarks that contain each of the five quark flavors that hadronize. In addition, from SU(3)-flavor symmetry alone we expect the existence of light-flavor partners of the three $P_c$ pentaquarks with strangeness $S=-1$ and $S=-2$. The resulting structure for the molecular pentaquarks is analogous to the light-baryon octet – we can label the pentaquarks as $P_{Q^{\mathrm{\prime }}\bar{Q}}^N$, $P_{Q^{\mathrm{\prime }}\bar{Q}}^{\mathrm{\Lambda }}$, $P_{Q’ \bar{Q}}^{\Sigma}$,$P_{Q’ \bar{Q}}^{\Xi}$ depending on their heavy- and light-quark content (with $N$, $\mathrm{\Lambda }$, $\mathrm{\Sigma }$, $\mathrm{\Xi }$ the member of the light-baryon octet to which the light-quark structure resembles and $Q^{\mathrm{\prime }}$, $\bar Q$theheavyquark-antiquarkpair)\mathrm{.}Intotalwepredict$45$ new pentaquarks from heavy- and light-flavor symmetries alone, which extend up to $109$ undiscovered states if we also consider heavy-quark spin symmetry. If an isoquartet ($I=3\mathrm{/}2$) hidden-charm pentaquark is ever observed, this will in turn imply a second multiplet structure resembling the light-baryon decuplet: $P_{Q^{\mathrm{\prime }}\bar{Q}}^{\mathrm{\Delta }}$, $P_{Q^{\mathrm{\prime }}\bar{Q}}^{{\mathrm{\Sigma }}^{\ast }}$, $P_{Q’ \bar{Q}}^{\Xi^*}$,$P_{Q’ \bar{Q}}^{\Omega}$.