Total Photo-Production Cross-Section at Very High Energy

In this paper we apply to photoproduction total cross-section a model we have proposed for purely hadronic processes and which is based on QCD mini-jets and soft gluon re-summation. We compare the predictions of our model with the HERA data as well as with other models. When we extend the model to cosmic ray energies, our model predicts substantially higher cross-sections at TeV energies than models based on factorization but lower than models based on mini-jets alone, without soft gluons. We discuss the origin of this difference and comment on the Froissart bound for photon induced processes.