  We emphasize the importance of tagging the outgoing forward protons to
sharpen the predictions for New Physics at the LHC (such as the diffractive
production of a light Higgs boson). The rescattering effects lead to a rich
distinctive structure of the cross section as a function of the transverse
momenta of the protons. We show that a study of the correlations between the
proton transverse momenta for double-diffractive production of central dijets
will provide a detailed check of the whole diffractive formalism. Adopting a
perturbative two-gluon structure of the Pomeron, we emphasize that 2++
quarkonium production, via Pomeron-Pomeron fusion, is strongly suppressed. This
offers a favourable production mechanism for non-qqbar states, such as
glueballs.
