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

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 $\frac{3}{2}$ bound states of $\Psi (2S)$ and $\Delta$ with masses around $4.5\mathrm{GeV}$ and widths around $70\mathrm{MeV}$. The approach also predicts broader resonances in the $\Psi (2S)$-$\Delta$ channel at $4.9\mathrm{GeV}$ with widths of the order of $150\mathrm{MeV}$. We discuss in which reactions these new isospin $\frac{3}{2}$ pentaquarks with hidden charm can be observed.

arXiv comment19 pages, 2 figures, added comments on how to observe the new Delta-charmonium bound states, accepted version

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