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

TL;DR

The study addresses the puzzle of a ρ-like structure, Y(2044), observed in $e^+e^- o a_2(1320)π$, which cannot be accommodated by a pure $ρ(2D)$ interpretation due to a large mismatch in the di-leptonic width–branching product. It introduces an $S$-$D$ mixing framework among nearby ρ states and determines two mixing angles from clean channels, leading to four mixed states $ρ_{3S-2D}^{′}$, $ρ_{3S-2D}^{′′}$, $ρ_{4S-3D}^{′}$, and $ρ_{4S-3D}^{′′}$ with masses and widths calculated via QPC and related methods. The analysis shows that the enhanced Y(2044) signal is predominantly from $ρ_{3S-2D}^{′′}$, while a global fit to six isospin-vector $e^+e^-$ processes using Scheme 2 yields good agreement, supporting a unified description of ρ-like structures near 2 GeV. This work demonstrates that $S$-$D$ mixing and interference are crucial for understanding the higher-lying ρ spectrum and provides guidance for identifying golden channels to test the four mixed states in future experiments."

Abstract

Recently, the BESIII Collaboration observed a $ρ$-like structure $Y(2044)$ in $e^+e^-\to a_2(1320)π$, suggesting that $Y(2044)$ may be a candidate of vector meson $ρ(2D)$ by comparing resonance parameters. However, the theoretical prediction for the combined branching ratio $Γ_{e^+e^-}\mathcal{B}_{a_2(1320)π}$ for the pure $ρ(2D)$ 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 $e^+e^-\to a_2(1320)π$, 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 $ρ$ meson states $ρ_{3S-2D}^{\prime}$, $ρ_{3S-2D}^{\prime\prime}$, $ρ_{4S-3D}^{\prime}$, and $ρ_{4S-3D}^{\prime\prime}$ as intermediate resonances, in which dominant contribution arises from $ρ_{3S-2D}^{\prime\prime}$ and their inference effect is also significant. Furthermore, we reanalyzed five additional isospin vector processes $e^+e^-\to ωπ^0$, $e^+e^-\to f_1(1285)π^+π^-$, $e^+e^-\to π^+π^-$, $e^+e^-\to ρη$, and $e^+e^-\to η^{\prime} π^+π^-$ 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 $ρ$-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 $ρ$ meson states.

Figures (5)

• Figure 1: Fit to the cross section of the process $e^+e^-\to a_2(1320)\pi$ measured by the BESIII Collaboration BESIII:2023sbq.
• Figure 2: The dependence of masses of mixed states on mixing angele $\theta$. The sub-figure (a) shows the masses of mixed states $\rho_{3S-2D}^{\prime}$ and $\rho_{3S-2D}^{\prime\prime}$ as a function of the mixing angle, while sub-figure (b) shows the masses of mixed states $\rho_{4S-3D}^{\prime}$ and $\rho_{4S-3D}^{\prime\prime}$ as a function of the mixing angle.
• Figure 3: The decay behavior of $\rho_{3S-2D}^{\prime}$, $\rho_{3S-2D}^{\prime\prime}$, $\rho_{4S-3D}^{\prime}$, and $\rho_{4S-3D}^{\prime\prime}$ as functions of the mixing angle $\theta$.
• Figure 4: Fit to the cross sections of the processes $e^+e^-\to a_2(1320)\pi$BESIII:2023sbq, $e^+e^-\to \omega\pi^0$BESIII:2020xmwAchasov:2016zvn, $e^+e^-\to f_1(1285)\pi^+\pi^-$BaBar:2007qjuBaBar:2022ahi, $e^+e^-\to \pi^+\pi^-$BaBar:2019kds, $e^+e^-\to \rho \eta$BESIII:2023sbq, and $e^+e^-\to \eta^{\prime} \pi^+\pi^-$BESIII:2020kpr within the scheme 1.
• Figure 5: Fit to the cross sections of the processes $e^+e^-\to a_2(1320)\pi$BESIII:2023sbq, $e^+e^-\to \omega\pi^0$BESIII:2020xmwAchasov:2016zvn, $e^+e^-\to f_1(1285)\pi^+\pi^-$BaBar:2007qjuBaBar:2022ahi, $e^+e^-\to \pi^+\pi^-$BaBar:2019kds, $e^+e^-\to \rho \eta$BESIII:2023sbq, and $e^+e^-\to \eta^{\prime} \pi^+\pi^-$BESIII:2020kpr within the scheme 2.