The nucleon resonances in the $J/\psi \to p\bar{p}{\eta }^{\prime }$ decay

Abstract

We are aiming to study the $J/\psi \to p\bar{p}{\eta }^{\prime }$ decay in an isobar model and the effective Lagrangian approach. After a careful exploration of the contributions of the $S_{11}(1535)$, $P_{11}(1710)$, $P_{13}(1900)$, $S_{11}(2090)$ and $P_{11}(2100)$ resonances, we conclude that either a subthreshold resonance or a broad $P$-wave state in the near threshold range seems to be indispensable to describe present data of the $\pi N\to {\eta }^{\prime }N$. Furthermore, at least one broad resonance above ${\eta }^{\prime }N$ threshold is preferred. With this detailed analysis, we could give the invariant mass spectrum and Dalitz plot of the $J/\psi \to p\bar{p}{\eta }^{\prime }$ decay for the purpose of assisting the future detailed partial wave analysis. It is found that the $J/\psi \to p\bar{p}{\eta }^{\prime }$ data are useful for disentangling the above or below threshold resonant contribution, though it still further needs the differential cross section data of $\pi N\to {\eta }^{\prime }N$ to realize some of the resonant and the non-resonant contribution. Our results are enlightening for the ${\eta }^{\prime }N$ production mechanism and the properties of the nucleon resonances with the mass around 2.0~GeV.

Comments: 10 pages