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We calculate the probability that the rapidity gaps in diffractive processessurvive both eikonal and enhanced rescattering. We present arguments thatenhanced rescattering, which violates soft-hard factorization, is not verystrong. Accounting for NLO effects, there is no reason to expect that the blackdisc regime is reached at the LHC. We discuss the predictions for the survivalof the rapidity gaps for exclusive Higgs production at the LHC.

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