  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.
