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

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.