Soft processes at the LHC, II: soft-hard factorisation breaking and gap survival

We calculate the probability that the rapidity gaps in diffractive processes survive both eikonal and enhanced rescattering. We present arguments that enhanced rescattering, which violates soft-hard factorisation, is not very strong. Accounting for NLO effects, there is no reason to expect that the black-disc regime is reached at the LHC. We discuss the predictions for the survival of the rapidity gaps for exclusive Higgs production at the LHC.