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

TL;DR

This paper models the $P_c(4450)$ pentaquark as a bound state of $ ext{psi}(2S)$ and a nucleon, predicting nearly degenerate states and a narrow width, and extends the analysis to bottomonium-nucleon systems.

Contribution

It introduces a novel interpretation of the pentaquark as a nucleon-$ ext{psi}(2S)$ bound state using heavy quark and large $N_c$ approximations, predicting new states and properties.

Findings

Predicted two nearly degenerate states at the pentaquark's mass.

Estimated the narrow width of the bound state to be tens of MeV.

Discussed the extension to bottomonium-nucleon pentaquark states.

Abstract

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 $J^P=(1/2)^-$ and $J^P=(3/2)^-$ 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.