A study of the excited radial vector meson $\rho$

We study the strong and radiative decays of the radial excitation of the $\rho$ meson, with quantum numbers $n$ ${}^{2S+1}{L}_J=2$ ${}^3{S}_1,$ $I=1$, and denoted as ${\rho }_E$, by making use of an effective model. We test different masses: $1.45$ GeV, corresponding to well known assignment ${\rho }_E\equiv \rho (1450)$ state; $1.25$ GeV for the assignment $\rho _{E}\equiv\rho(1250)$ (a resonance whose existence has not yet been confirmed), and $1.35$ GeV, which lies just in the middle between them in order to study the dependence of the results on the mass. The decay widths for different decay processes and two branching ratios of the radially excited meson ${\rho }_E$ were determined and compared to the experimental data reported in the Particle Data Group.