Narrow Nucleon-$\psi (2S)$ Bound State and LHCb Pentaquarks

We interpret the newly discovered pentaquark $P_c(4450)$ as a bound state of charmonium $\psi (2S)$ and the nucleon. The binding potential is due to charmonium-nucleon interaction that in the heavy quark approximation is proportional to the product of the charmonium chromoelectric polarizability and the nucleon energy-momentum distribution. We use the large $N_c$ expansion to estimate the quarkonium polarizability and calculate the nucleon properties in the framework of the mean-field picture of light baryons. Two almost degenerate states $J^P=(1\mathrm{/}2{)}^{-}$ and $J^P=(3\mathrm{/}2{)}^{-}$ are predicted at the position of the $P_c(4450)$ pentaquark. We find that the nucleon-$\psi (2S)$ bound state has a naturally narrow width in the range of tens of MeV. The unitary multiplet partners of the $P_c(4450)$ pentaquark and the generalization to $b \bar b$-nucleon pentaquark bound states are discussed.