Are the $Y$ states around 4.6 GeV from $e^{+}{e}^{-}$ annihilation higher charmonia?

Abstract

In this work, we present the mass spectrum of higher charomona around and above 4.6 GeV by adopting the unquenched potential model. We perform a combined fit to the updated experimental data of $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$ and $e^{+}{e}^{-}\to {\Lambda }_c{\bar{\Lambda }}_c$. To understand the "platform" structure observed in the range of $4.57\sim 4.60$ GeV existing in the ${\Lambda }_c{\bar{\Lambda }}_c$ invariant mass spectrum of $e^{+}{e}^{-}\to {\Lambda }_c{\bar{\Lambda }}_c$ of BESIII, we introduce two resonances in this combined fit to the $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$ and $e^{+}{e}^{-}\to {\Lambda }_c{\bar{\Lambda }}_c$, which have resonance parameters, $m_{Y_1}=4585\pm 2$ MeV, ${\Gamma }_{Y_1}=29.8\pm 8.0$ MeV, $m_{Y_2}=4676\pm 7$ MeV, and ${\Gamma }_{Y_2}=85.7\pm 15.0$ MeV. Furthermore, combining with our theoretical results, we indicate that the two charmonium-like $Y$ states can be due to two higher charmonia, which are mixtures of $6S$ and $5D$ $c\bar{c}$ states. Their two-body open-charm decay behaviors are given. Under the same framework, our analysis of the data of $e^{+}{e}^{-}\to D_s^{+}{D}_{s1}(2536{)}^{-}$ recently released by Belle supports to introduce these two higher charmonia around 4.6 GeV. Additionally, we predict the masses and two-body open-charm decays of six higher charmonia $\psi (nS)$ and $\psi (mD)$ with $n=7,8,9$ and $m=6,7,8$ above 4.6 GeV. Search for these higher charmonia will be an interesting issue for the running BESIII and BelleII, and even the possible Super Tau-Charm Factory discussed in China.

arXiv comment11 pages, 4 tables and 8 figures. More discussions and references added. Accepted by Phys. Rev. D

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