  The $\sigma$-exchange and $f_2$-exchange mechanisms for $\rho$ meson
photoproduction are re-examined. Then the commonly employed $\sigma$-exchange
amplitude is revised by using the recent information from the analyses on the
$\rho \to \pi^0\pi^0\gamma$ decay and the $\sigma NN$ coupling constant from
Bonn potential. Instead of relying on the Pomeron-$f$ proportionality
assumption, the $f_2$ meson exchange amplitude is established from an effective
Lagrangian which is constructed from the tensor structure of the $f_2$ meson.
Phenomenological information together with tensor meson dominance and vector
meson dominance assumptions are used to estimate the $f_2$ coupling constants.
As a first step to improve the current theoretical models, we have also
explored the effects due to the un-correlated $2\pi$ exchange amplitude with
$\pi N$ intermediate state. This leading-order $2\pi$ exchange amplitude can be
calculated using the coupling constants determined from the study of pion
photoproduction and the empirical width of $\rho \to \pi\pi$ decay. In
comparing with the existing differential cross section data, we find that a
model with the constructed $2\pi$, $\sigma$, and $f_2$ exchanges is comparable
to the commonly used $\sigma$ exchange model in which the $\sigma$ coupling
parameters are simply adjusted to fit the experimental data. We suggest that
experimental verifications of the predicted single and double spin asymmetries
in the small $|t|$ ($ < 2$ GeV$^2$) region will be useful for distinguishing
the two models and improving our understanding of the non-resonant amplitude of
$\rho$ photoproduction. Possible further improvements of the model are
discussed.
