Confirming the existence of a new higher charmonium <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4500</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> by the newly released data of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi></mml:mrow></mml:math>
Jun-Zhang Wang, Xiang Liu
Abstract
Recently, the BESIII Collaboration published the Born cross section of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}J/\ensuremath{\psi}$, in which a new vector enhancement structure $Y(4500)$ was observed for the first time. The mass of the $Y(4500)$ resonance structure is in good agreement with our previous prediction for a $5S\text{\ensuremath{-}}4D$ mixing charmonium candidate $\ensuremath{\psi}(4500)$, while the measured width is $2\ensuremath{\sigma}$ larger than the theoretical estimate. In this work, we reanalyzed the cross section of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}J/\ensuremath{\psi}$ by introducing two theoretically predicted charmonium states $\ensuremath{\psi}(4220)$ and $\ensuremath{\psi}(4500)$ as intermediate resonances, and found that this width deviation problem can be resolved. Meanwhile, we found that the inclusion of two established charmonium states $\ensuremath{\psi}(4160)$ and $\ensuremath{\psi}(4415)$ can further improve the fit quality, with four sets of widely different solutions to ${\mathrm{\ensuremath{\Gamma}}}_{{e}^{+}{e}^{\ensuremath{-}}}\mathcal{B}(\ensuremath{\psi}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}J/\ensuremath{\psi})$. In order to better identify the properties of the $Y(4500)$, we calculated the charmonium hadronic transition to final states ${K}^{+}{K}^{\ensuremath{-}}J/\ensuremath{\psi}$ within the charmed meson loop mechanism, where the fitted branching ratio of $\ensuremath{\psi}(4500)\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}J/\ensuremath{\psi}$ can be well explained by the theoretical calculation, further supporting the new enhancement structure around 4.5 GeV as a higher charmonium $\ensuremath{\psi}(4500)$ that we predicted. Finally, we also discussed the possible signal of another predicted charmonium candidate $\ensuremath{\psi}(4380)$ in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}J/\ensuremath{\psi}$. These research results should be an important step in constructing the charmonium family and thoroughly solving the charmoniumlike $Y$ problem.