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

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.

Comments: 8 pages, 4 figures and 3 tables