Identifying the contribution of higher $\rho$ mesons around 2 GeV in the $e^+ e^- \to \omega\pi^0$ and $e^+ e^- \to \rho \eta^{\prime}$ processes

TL;DR

This study analyzes recent BESIII data on $e^+ e^- o ext{vector meson}$ processes around 2 GeV, identifying contributions from multiple $ ho$ meson resonances and highlighting the importance of these channels for future meson spectroscopy.

Contribution

It provides a combined analysis of experimental data and theoretical models to identify specific $ ho$ meson states contributing to observed enhancements near 2 GeV.

Findings

Enhancement near 2034 MeV is from $ ho(1900)$ and $ ho(2150)$ interference.

Enhancement at 2111 MeV is from $ ho(2000)$ and $ ho(2150)$ contributions.

$e^+ e^- o ext{vector meson}$ processes are promising for studying $ ho(1900)$ and $ ho(2000)$, especially the $D$-wave $ ho(2000)$.

Abstract

The properties of the light vector meson states around 2.0 GeV have been poorly understood for a long time, which has become a barrier to the expansion to higher light vector meson spectrum. Recently, the BESIII collaboration released the measurements of the $e^+ e^- \to \omega\pi^0$ and $e^+ e^- \to \rho\eta^{\prime}$ reactions above 2.0 GeV, both of which are ideal processes to study the isovector $\rho$ meson family. In this work, through carrying out a combined analysis of the Born cross section data for the above two processes with the theoretical support on mass spectrum, and production and strong decay behaviors of the $\rho$ meson family around 2.0 GeV, we identify the enhancement structure near 2034 MeV observed in $e^+e^-\to\omega\pi^0$ to be the interference contribution from two resonances $\rho(1900)$ and $\rho(2150)$, and another enhancement structure at 2111 MeV reported in $e^+e^-\to\rho\eta^{\prime}$ to be the contributions from $\rho(2000)$ and $\rho(2150)$. This conclusion means that the $e^+e^-\to\omega\pi^0$ and $e^+e^-\to\rho \eta^{\prime}$ are the excellent golden channels to establish $\rho(1900)$ and $\rho(2000)$, especially for a $D$-wave state $\rho(2000)$, whose experimental search in the $e^+e^-$ collision should be quite challenging. The relevant cross section measurements with higher precision are expected in the future BESIII and Belle II experiments.