Exclusive production of $\omega$ meson in proton-proton collisions at high energies

First we calculate cross section for the $\gamma p \to \omega p$ reaction from the threshold to very large energies. At low energies the pion exchange is the dominant mechanism. At large energies the experimental cross section can be well described within the $k_{t}$-factorization approach by adjusting light-quark constituent mass. Next we calculate differential distributions for the $p p \to p p \omega$ reaction at RHIC, Tevatron and LHC energies for the first time in the literature. We consider photon-pomeron (pomeron-photon), photon-pion (pion-photon) as well as diffractive hadronic bremsstrahlung mechanisms. The latter are included in the meson/reggeon exchange picture with parameters fixed from the known phenomenology. Interesting rapidity distributions are predicted. The hadronic bremsstrahlung contributions dominate at large (forward, backward) rapidities. At small energies the photon-pomeron contribution is negligible compared to the bremsstrahlung contributions. It could be, however, easily identified at large energies at midrapidities. Absorptions effects are included and discussed. Our predictions are ready for verification at RHIC and LHC.