  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.
