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

TL;DR

This paper proposes an $S$-$D$ mixing scheme for $ ho$ mesons to explain the $Y(2044)$ structure observed in $e^+e^- o a_2(1320)\pi$ and other reactions, resolving discrepancies between theory and experiment.

Contribution

It introduces an $S$-$D$ mixing framework for $ ho$ mesons that unifies the explanation of multiple $ ho$-like structures near 2 GeV in $e^+e^-$ annihilation data.

Findings

Reproduces the $Y(2044)$ structure with four $ ho$ meson states.

Resolves the branching ratio discrepancy for $ ho(2D)$.

Successfully fits multiple $e^+e^-$ reaction channels.

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.