On LHCb pentaquarks as a baryon-psi(2S) bound state -- prediction of isospin 3/2 pentaquarks with hidden charm

TL;DR

This paper predicts the existence of isospin 3/2 pentaquarks with hidden charm as bound states of $ ext{Psi}(2S)$ and baryons, confirming previous interpretations of LHCb pentaquarks through a model-independent approach.

Contribution

It provides a model-independent demonstration that $ ext{Psi}(2S)$ can form bound states with nucleons and $ ext{Delta}$ baryons, and predicts new isospin 3/2 pentaquark states with specific masses and widths.

Findings

Confirmation of $ ext{Psi}(2S)$-nucleon bound states.

Prediction of isospin 3/2 pentaquarks around 4.5 GeV.

Estimation of widths around 70 MeV for these states.

Abstract

The pentaquark $P_c^+(4450)$ recently discovered by LHCb has been interpreted as a bound state of $\Psi(2S)$ and nucleon. The charmonium-nucleon interaction which provides the binding mechanism is given, in the heavy quark limit, in terms of charmonium chromoelectric polarizabilities and densities of the nucleon energy-momentum tensor (EMT). In this work we show in model-independent way, by exploring general properties of the effective interaction, that $\Psi(2S)$ can form bound states with nucleon and $\Delta$. Using the Skyrme model to evaluate the effective interaction in the large-$N_c$ limit and estimate $1/N_c$ corrections, we confirm the results from prior work which were based on a different effective model (chiral quark soliton model). This shows that the interpretation of $P_c^+(4450)$ is remarkably robust and weakly dependent on the details of the effective theories for the nucleon EMT. We explore the formalism further and present robust predictions of isospin $\frac32$ bound states of $\Psi(2S)$ and $\Delta$ with masses around $4.5\,{\rm GeV}$ and widths around $70\,{\rm MeV}$. The approach also predicts broader resonances in the $\Psi(2S)$-$\Delta$ channel at $4.9\,{\rm GeV}$ with widths of the order of $150\,{\rm MeV}$. We discuss in which reactions these new isospin $\frac 32$ pentaquarks with hidden charm can be observed.