  We study hard diffractive scattering in hadron-hadron collisions including,
on top of the standard Pomeron-initiated processes, contributions due to the
exchange of Reggeons. Using a simple model to describe the parton content of
the Reggeon, we compute di-jet production in single diffractive and central
diffractive events. We show that Reggeon contributions can be sizable at the
LHC, and even sometimes dominant, and we identify kinematic windows in which
they could be experimentally studied. We argue that suitable measurements must
be performed in order to properly constrain the model, and be able to correctly
account for Reggeon exchanges in the analysis of the many hard diffractive
observables to be measured at the LHC.
