Are the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Y</mml:mi></mml:math> states around 4.6 GeV from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> annihilation higher charmonia?
Jun-Zhang Wang, Ri-Qing Qian, Xiang Liu, Takayuki Matsuki
Abstract
In this work, we present the mass spectrum of higher charmonia around and above 4.6 GeV by adopting the unquenched potential model. We perform a combined fit to the updated experimental data of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\psi}(2S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{\mathrm{\ensuremath{\Lambda}}}}_{c}$. To understand the ``platform'' structure observed in the range of 4.57--4.60 GeV existing in the ${\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{\mathrm{\ensuremath{\Lambda}}}}_{c}$ invariant mass spectrum of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{\mathrm{\ensuremath{\Lambda}}}}_{c}$ of BESIII, we introduce two resonances in this combined fit to ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\psi}(2S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{\mathrm{\ensuremath{\Lambda}}}}_{c}$, which have resonance parameters, ${m}_{{Y}_{1}}=4585\ifmmode\pm\else\textpm\fi{}2\text{ }\text{ }\mathrm{MeV}$, ${\mathrm{\ensuremath{\Gamma}}}_{{Y}_{1}}=29.8\ifmmode\pm\else\textpm\fi{}8.0\text{ }\text{ }\mathrm{MeV}$, ${m}_{{Y}_{2}}=4676\ifmmode\pm\else\textpm\fi{}7\text{ }\text{ }\mathrm{MeV}$, and ${\mathrm{\ensuremath{\Gamma}}}_{{Y}_{2}}=85.7\ifmmode\pm\else\textpm\fi{}15.0\text{ }\text{ }\mathrm{MeV}$. Furthermore, combining with our theoretical results, we indicate that the two charmoniumlike $Y$ states can be due to two higher charmonia, which are mixtures of $6S$ and $5D$ $c\overline{c}$ states. Their two-body open-charm decay behaviors are given. Under the same framework, our analysis of the data of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}_{s}^{+}{D}_{s1}(2536{)}^{\ensuremath{-}}$ recently released by Belle supports the introduction of these two higher charmonia around 4.6 GeV. Additionally, we predict the masses and two-body open-charm decays of six higher charmonia $\ensuremath{\psi}(nS)$ and $\ensuremath{\psi}(mD)$ with $n=7$, 8, 9 and $m=6$, 7, 8 above 4.6 GeV. The 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.