Hadronic description for the $\phi$-photoproduction near the threshold

The Pomeron-exchange plays an important role in the $\phi$-photoproduction from the nucleon. It describes well the increasing behavior of the production rate at high energies, a consequence of the Regge theory with the Pomeron trajectory $\alpha(t)$. Recently LEPS has reported a bump-like structure in $d\sigma/d t$ near the threshold energy. Within the Regge theory, the second Pomeron is examined, but it is difficult to reproduce such a narrow bump structure. Besides the Pomeron-exchange, we could expect hadronic processes relevant in the threshold region. In this work, we attempt a hadronic description for the $\phi$-photoproduction. Since the OZI mechanism suppresses Born diagrams at the tree level, we consider loop contributions. We pay special attention to the gauge invariant set of diagrams and momentum ($s, t$ and $u$) dependence of the amplitude. We discuss that some features of momentum dependence may help to understand the underlying reaction mechanism. We also discuss that some correlated loops may express effectively a meson exchange diagram, for instance, in the $t$-channel.