Role of the $\rho(1450)$ in low-energy observables from an analysis in the meson dominance approach

Abstract

The $\rho(1450)$ vector meson ($\rho^\prime$) is becoming increasingly important to properly describe precision observables. We analyse a set of decay modes and cross sections, in the low-energy regime, to determine the role played by this meson. This is done through the extraction of the parameters for its description, in the context of the vector meson dominance model and its effective hadronic interactions, involving the low mass lying hadrons ($\rho$, $\omega$ and $\pi$). In a first step, we determine the parameters of the model from ten decay modes which are insensitive to the $\rho^\prime$. Then, we consider the $\omega \rightarrow 3\pi$ decay and exhibit the need to extend the description, by incorporating the $\rho^\prime$ and a contact term as prescribed by the Wess-Zumino-Witten anomaly. In a second step, we incorporate the data from the $e^+e^- \rightarrow 3\pi$ cross section (as measured by SND, CMD2, BABAR and BESIII) and then the $e^+e^- \rightarrow \pi^0 \pi^0 \gamma$ data (as measured by SND and CDM2) to further restrict the $\rho^\prime$ parameters validity region. As an application of the results, we compute the $e^+e^- \rightarrow 4\pi$ cross section for the so-called omega channel, measured by BABAR, and find a good description of the data considering the parameters found. As a byproduct, the coupling between $\rho$, $\omega$ and $\pi$ ($g_{\rho\omega\pi}= 11.314 \pm 0.383$ GeV$^{-1}$) is found to be consistent with all the relevant observables, upon the inclusion of the $\rho^\prime$ and the contact term.