The baryo-quarkonium picture for hidden-charm and bottom pentaquarks and LHCb $P_{\mathrm{c}}(4380)$ and $P_{\mathrm{c}}(4450)$ states

Abstract

We study baryo-charmonium [${\eta }_{\mathrm{c}}$- and $J/\psi$-$N^{\ast }$, ${\eta }_{\mathrm{c}}(2S)$-, $\psi (2S)$- and ${\chi }_{\mathrm{c}}(1P)$-$N$] and baryo-bottomonium [${\eta }_{\mathrm{b}}(2S)$-, ${\rm Y}(2S)$- and ${\chi }_{\mathrm{b}}(1P)$-$N$] bound states, where $N$ is the nucleon and $N^{\ast }$ a nucleon resonance. In the baryo-quarkonium model, the five $qqqQ\bar{Q}$ quarks are arranged in terms of a heavy quarkonium core, $Q\bar{Q}$, embedded in light baryonic matter, $qqq$, with $q=u$ or $d$. The interaction between the $Q\bar{Q}$ core and the light baryon can be written in terms of the QCD multipole expansion. The spectrum of baryo-charmonium states is calculated and the results compared with the existing experimental data. In particular, we can interpret the recently discovered $P_{\mathrm{c}}(4380)$ and $P_{\mathrm{c}}(4450)$ pentaquarks as $\psi (2S)$-$N$ and ${\chi }_{c2}(1P)$-$N$ bound states, respectively. We observe that in the baryo-bottomonium sector the binding energies are, on average, slightly larger than those of baryo-charmonia. Because of this, the hidden-bottom pentaquarks are more likely to form than their hidden-charm counterparts. We thus suggest the experimentalists to look for five-quark states in the hidden-bottom sector in the $10.4-10.9$ GeV energy region.