Role of the ω(4S) and ω(3D) states in mediating the e+e−→ωη and ωπ0π0 processes

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Abstract

The ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\eta}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ processes are ideal platforms to search for higher $\ensuremath{\omega}$ states. Focusing on the observations of two enhancement structures around 2.2 GeV existing in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\eta}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ at BESIII, we analyze how the $\ensuremath{\omega}(4S)$ and $\ensuremath{\omega}(3D)$ states play the role in the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\eta}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ processes. The present study is supported by theoretical $\ensuremath{\omega}$ mesonic spectroscopy. For reproducing the data of the cross sections of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\eta}$ and $\ensuremath{\omega}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, the intermediate $\ensuremath{\omega}(4S)$ and $\ensuremath{\omega}(3D)$ should be introduced, which indicates that the enhancement structures around 2.2 GeV existing in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\eta}$ and $\ensuremath{\omega}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ contain the $\ensuremath{\omega}(4S)$ and $\ensuremath{\omega}(3D)$ signals. Nonetheless, in the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\eta}$, the $\ensuremath{\omega}(4S)$ plays a dominant role, while the $\ensuremath{\omega}(4S)$ and $\ensuremath{\omega}(3D)$ have similar sizable contributions in the process of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, which leads to a difference in the line shape of enhancement structure in the cross sections under the interference effect. Thus, we find a solution to alleviate the puzzling difference of resonance parameter of two reported enhancement structures around 2.2 GeV existing in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\eta}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ at BESIII. The present study provides valuable information to construct $\ensuremath{\omega}$ meson family, which can be accessible at future experiment like BESIII.

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