Determination of the $g_{\rho \sigma \gamma }$ coupling constant through the process $\gamma +N\to N+V$ with circularly polarized photons

We suggest a method to determine the product of the coupling constants $g_{\rho \sigma \gamma }{g}_{\sigma NN}$, in absolute value and relative sign, through the $t$-dependence of the two possible T-even asymmetries for the photoproduction of vector mesons, $\gamma +p\to p+V^0$, $V^0=\rho$ or $\omega$, in the collision of circularly polarized photons with a polarized proton target. In the framework of a $\pi +\sigma$-model, these asymmetries are very sensitive to the relative role of $\pi$- and $\sigma$-exchanges, in the near threshold region.