Decoding the role of $\rho$ mesonic states for elucidating the $e^{+}{e}^{-}\to a_2(1320)\pi$ data and other reactions

Abstract

Recently, the BESIII Collaboration observed a $\rho$-like structure $Y(2044)$ in $e^{+}{e}^{-}\to a_2(1320)\pi$, suggesting that $Y(2044)$ may be a candidate of vector meson $\rho (2D)$ by comparing resonance parameters. However, the theoretical prediction for the combined branching ratio ${\Gamma }_{e^{+}{e}^{-}}{\mathcal{B}}_{a_2(1320)\pi }$ for the pure $\rho (2D)$ state is about two orders of magnitude smaller than the experimental value. To resolve this discrepancy and decipher the nature of $Y(2044)$, this work propose an $S$-$D$ mixing scheme to reanalyze the cross section of $e^{+}{e}^{-}\to a_2(1320)\pi$, and find that the aforementioned branching ratio discrepancy can be resolved. Our results show that the $Y(2044)$ structure can be reproduced by introducing four theoretically predicted $S$-$D$ mixing $\rho$ meson states ${\rho }_{3S-2D}^{\prime }$, ${\rho }_{3S-2D}^{\prime \prime }$, ${\rho }_{4S-3D}^{\prime }$, and ${\rho }_{4S-3D}^{\prime \prime }$ as intermediate resonances, in which dominant contribution arises from ${\rho }_{3S-2D}^{\prime \prime }$ and their inference effect is also significant. Furthermore, we reanalyzed five additional isospin vector processes $e^{+}{e}^{-}\to \omega {\pi }^0$, $e^{+}{e}^{-}\to f_1(1285){\pi }^{+}{\pi }^{-}$, $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$, $e^{+}{e}^{-}\to \rho \eta$, and $e^{+}{e}^{-}\to {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ based on the same $S$-$D$ mixing framework, and simultaneously reproduced their experimental cross section data. This work provides a unified framework to elucidate all observed $\rho$-like structures near 2 GeV in the $e^{+}{e}^{-}$ annihilation processes, and suggests that the $S$-$D$ mixing effect may be crucial for understanding the mass spectrum and decay behaviors of the higher $\rho$ meson states.

11 pages, 5 figures

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