Role of $4S$-$3D$ mixing in explaining the $ω$-like $Y(2119)$ observed in $e^+e^-\toρπ$ and $ρ(1450)π$

Abstract

The BESIII Collaboration has recently reported a new resonance structure in the cross-section analyses of the $e^+e^- \to ρπ$ and $e^+e^- \to ρ(1450)π$ processes, displaying characteristics akin to an $ω$-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 $ω$ 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 $ω_{4S\text{-}3D}^\prime$ 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, $Γ_{e^+e^-}^{\mathcal{R}}\times\mathcal{B}_{\mathcal{R}\toρπ}$ and $Γ_{e^+e^-}^{\mathcal{R}}\times\mathcal{B}_{\mathcal{R}\toρ(1450)π\toπ^+π^-π^0}$. The determined mixing angle, $θ= -\left(31.1^{+2.1}_{-3.1}\right)\degree$, strongly supports the interpretation of this structure as the $ω_{4S\text{-}3D}^\prime$ state. Furthermore, we predict dominant decay channels for $ω_{4S\text{-}3D}^\prime$ and its partner state $ω_{4S\text{-}3D}^{\prime\prime}$. 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.