$1/N_c$ approximation and universality of vector mesons

Abstract

In this work, we argue that the observed differences in the value of the vector coupling constant extracted from the decays $\rho \to \pi \pi$ ($g_{\rho }=6.0$), $\rho \to l^{+}{l}^{-}$ ($g_{\rho }=5.0$) and $\omega \to l^{+}{l}^{-}$ ($g_{\rho }=5.7$), where $l=e,\mu$, are an indication of the important role played by the $1/N_c$ corrections in the description of these processes. We show that an emission of a photon by charged meson loops in the ${\rho }^0,\omega ,\varphi \to \gamma$ transitions is a key process that allows to describe above vector meson decays into two leptons with a single value $g_{\rho }=6.0$. Our result supports the idea of universality of neutral vector mesons and clarifies the role of accounting of $1/N_c$ corrections to its fulfilment.

Comments: 9 pages, 2 figuras, the version accepted for publication in Physical Review D