  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.
