Physics with tagged forward protons at the LHC

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.