Role of $4S$-$3D$ mixing in explaining the $\omega$-like $Y(2119)$ observed in $e^{+}{e}^{-}\to \rho \pi$ and $\rho (1450)\pi$

Abstract

The BESIII Collaboration has recently reported a new resonance structure in the cross-section analyses of the $e^{+}{e}^{-}\to \rho \pi$ and $e^{+}{e}^{-}\to \rho (1450)\pi$ processes, displaying characteristics akin to an $\omega$-meson. However, its measured mass, $M=2119\pm 11\pm 15\text{MeV}$, significantly deviates from the predictions of the unquenched relativized potential model for conventional $\omega$ vector meson spectroscopy. To address this discrepancy, we propose a $4S$-$3D$ mixing scheme and investigate the corresponding decay properties within this framework. Our analysis demonstrates that the mixed state ${\omega }_{4S\text{-}3D}^{\prime }$ exhibits excellent agreement with the observed resonance, not only in mass and width but also in the products of its dielectron width and branching ratios, ${\Gamma }_{e^{+}{e}^{-}}^{\mathcal{R}}\times {\mathcal{B}}_{\mathcal{R}\to \rho \pi }$ and ${\Gamma }_{e^{+}{e}^{-}}^{\mathcal{R}}\times {\mathcal{B}}_{\mathcal{R}\to \rho (1450)\pi \to {\pi }^{+}{\pi }^{-}{\pi }^0}$. The determined mixing angle, $\theta =-\left(31.1_{-3.1}^{+2.1}\right)°$, strongly supports the interpretation of this structure as the ${\omega }_{4S\text{-}3D}^{\prime }$ state. Furthermore, we predict dominant decay channels for ${\omega }_{4S\text{-}3D}^{\prime }$ and its partner state ${\omega }_{4S\text{-}3D}^{\prime \prime }$. These predictions, together with the proposed mixing mechanism, provide crucial guidance for future experimental studies aimed at probing this structure and rigorously testing the $4S$-$3D$ mixing hypothesis.

6 pages, 1 figure and 4 tables. Accepted by Phys. Rev. D

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• Prospects for observing the missing $2D$ and $1F$ charmonium states around 4 GeV
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