Exploring the role of higher $ω$ meson states in the $e^+ e^-\rightarrow b_1(1235) π$ process

TL;DR

This work addresses the unclear structure of light vector mesons around $2$ GeV by integrating BESIII cross-section data for $e^+ e^- \rightarrow b_1(1235) \pi$ with the predicted $ω$ spectrum from the Modified Godfrey–Isgur model and decay widths from the Quark Pair Creation model, and then fits a two-resonance interference model. The authors show that the enhancement near $M \sim 2.2$ GeV arises from interference between the $ω(4S)$ and $ω(3D)$ states, rather than a single resonance, with both contributing comparably. The fitted phases and couplings reproduce the cross-section shape and resolve prior parameter inconsistencies. This framework advances the mapping of the light-hadron spectrum by providing a robust method to identify higher radial and orbital ω excitations.

Abstract

The properties of light vector mesons near 2.2 GeV remain poorly understood, impeding progress in mapping the higher-lying hadronic spectrum. Utilizing the newly released BESIII data on the Born cross sections for the process of $e^+ e^- \rightarrow b_1(1235) π$, we conduct a combined analysis incorporating theoretical predictions for the mass spectrum and decay properties of $ω$-meson family. Our fit demonstrates that the enhancement structure near 2.2 GeV originates not from a single resonance, but from the significant interference between the $ω(4S)$ and $ω(3D)$ states, which have comparable contributions. This interpretation resolves the apparent discrepancy in the resonance parameters and yields values consistent with theoretical expectations. Our work provides a key interpretation of the vector enhancement structure and establishes a vital framework for identifying higher radial and orbital excitations in the $ω$ meson family, thereby advancing the mapping of the light-hadron spectrum.

Figures (5)

• Figure 1: A comparison of resonance parameters of these reported $\omega$ states with masses around 2.2 GeV Anisovich:2002xooBugg:2004rjhepdata.33892BESIII:2018ldc
• Figure 2: The decay diagrams of $A \to B+C$ mediated by QPC, there are two possible forms. Generally, only one of them contributes to the amplitude.
• Figure 3: The mass, total width, and the branching ratios of the OZI-allowed strong decays of the $\omega(4S)$ and $\omega(3D)$ states.
• Figure 4: The schematic diagrams depicting the reaction $e^+ e^- \rightarrow b_1(1235) \pi$ . Here, diagram (a) is the virtual photon directly coupling with final states, while diagram (b) is due to the intermediate state $\omega^*$ contribution, where $\omega^*$ denotes the $\omega(4S) /\omega(3D)$.
• Figure 5: The fitted result of the experimental data of the Born cross sections of $e^+ e^- \rightarrow b_1(1235) \pi$ (a), and the calculated cross sections of $e^+ e^- \rightarrow \omega(4S)/\omega(3D) \rightarrow b_1(1235) \pi$ (b).