  The $\sigma$ meson exchange model for $\rho$ photoproduction at low energies
is re-examined and a new model is developed by considering explicit two-pion
exchange and the $f_2$ tensor meson exchange. The $f_2$ exchange model, which
is motivated by the low energy proton-proton elastic scattering, is constructed
by fully taking into account of the tensor structure of the $f_2$ meson
interactions. Phenomenological informations together with tensor meson
dominance and vector meson dominance assumptions are used to estimate the $f_2$
meson's coupling constants. For $2\pi$ exchange, the loop terms including
intermediate $\pi N$ and $\omega N$ channels are calculated using the coupling
constants determined from the study of pion photoproduction. It is found that
our model with $f_2$ and $2\pi$ exchanges can successfully replace the commonly
used $\sigma$ exchange model that suffers from the big uncertainty of the
coupling constants. We found that the two models can be distinguished by
examining the single and double spin asymmetries.
