A phenomenological note on the missing $\rho_2$ meson

Abstract

The $\rho_2$ meson is the missing isovector member of the meson nonet with the quantum numbers $J^{PC}=2^{--}$. It belongs to the class of $\rho$-mesons such as the vector meson $\rho(770)$, the excited vector $\rho(1700)$ and the tensor $\rho_3(1690)$. Yet, despite the rich experimental and theoretical studies for other $\rho$-meson states, no resonance that could be assigned to the $\rho_2$ meson has been measured. In this note, we present the results for the mass and dominant decay channels of the $\rho_2$ meson within the extended Linear Sigma Model.