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Decoding the role of $ρ$ mesonic states for elucidating the $e^{+} e^{-} \to a_{2} (1320) π$ data and other reactions

Qin-Song Zhou^1,2,3,*, Zi-Yue Bai ^4,5,6,†, Jun-Zhang Wang ^7,‡, Hao Xu ^8,§, and Xiang Liu ^4,5,6,9,∥

¹School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China
²Research Center for Quantum Physics and Technologies, Inner Mongolia University, Hohhot 010021, China
³Inner Mongolia Key Laboratory of Microscale Physics and Atomic Manufacturing, Hohhot 010021, China
⁴School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
⁵Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
⁶Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China
⁷Department of Physics, Chongqing University, Chongqing 401331, China
⁸Institute of Theoretical Physics, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
⁹MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China

^*Contact author: zhouqs@imu.edu.cn
^†Contact author: baizy15@lzu.edu.cn
^‡Contact author: wangjzh@cqu.edu.cn
^§Contact author: xuh2020@nwnu.edu.cn
^∥Contact author: xiangliu@lzu.edu.cn

Phys. Rev. D 112, 074021 – Published 17 October, 2025

DOI: https://doi.org/10.1103/pdfh-mk79

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 $ρ (2 D)$ by comparing resonance parameters. However, the theoretical prediction for the combined branching ratio $Γ_{e^{+} e^{-}} B_{a_{2} (1320) π}$ for the pure $ρ (2 D)$ state is about 2 orders of magnitude smaller than the experimental value. To resolve this discrepancy and decipher the nature of $Y (2044)$ , this work proposes an $S − D$ mixing scheme to reanalyze the cross section of $e^{+} e^{-} \to a_{2} (1320) π$ , and finds 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 $ρ_{3 S - 2 D}^{'}$ , $ρ_{3 S - 2 D}^{''}$ , $ρ_{4 S - 3 D}^{'}$ , and $ρ_{4 S - 3 D}^{''}$ as intermediate resonances, in which dominant contribution arises from $ρ_{3 S - 2 D}^{''}$ and their inference effect is also significant. Furthermore, we reanalyzed five additional isospin vector processes $e^{+} e^{-} \to ω π^{0}$ , $e^{+} e^{-} \to f_{1} (1285) π^{+} π^{-}$ , $e^{+} e^{-} \to π^{+} π^{-}$ , $e^{+} e^{-} \to ρ η$ , and $e^{+} e^{-} \to η^{'} π^{+} π^{-}$ 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.

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Phys. Rev. D 112, 074021– Published 17 October, 2025

Vol. 112, Iss. 7 — 1 October 2025

Received 31 July 2025
Accepted 15 September 2025

DOI: https://doi.org/10.1103/pdfh-mk79

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Decoding the role of $ρ$ mesonic states for elucidating the $e^{+} e^{-} \to a_{2} (1320) π$ data and other reactions

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Decoding the role of ρ mesonic states for elucidating the e+e−→a2(1320)π data and other reactions

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Decoding the role of $ρ$ mesonic states for elucidating the $e^{+} e^{-} \to a_{2} (1320) π$ data and other reactions