Exclusive Higgs boson production at the CERN LHC: hard rescattering corrections

We examine, as a correction to the central exclusive Higgs boson production in $pp$ collisions at the LHC, the rescattering of gluonic ladders off the proton. As usual, at the lowest order the hard part of this process can be described as a fusion of two hard gluonic ladders. We calculate corrections to this hard amplitude which are due to rescattering of these ladders. These corrections, which contain high mass diffractive excitations of the proton, have not yet been taken into account by the usual soft survival probabilities. We find that the correction due to the exchange of a single hard rescattering is negative, large and infrared sensitive. As a first step towards a more reliable description we therefore replace the rescattering exchange by a unitarized amplitude using the BK equation which generates the saturation scale $Q_s(x)$. We also include a soft gap survival probability factor. We discuss the results and outline possible future strategies.