We investigate the theoretical description of the central exclusive
production process, h1+h2 -> h1+X+h2. Taking Higgs production as an example, we
sum logarithmically enhanced corrections appearing in the perturbation series
to all orders in the strong coupling. Our results agree with those originally
presented by Khoze, Martin and Ryskin except that the scale appearing in the
Sudakov factor, mu=0.62 \sqrt{\hat{s}}, should be replaced with
mu=\sqrt{\hat{s}}, where \sqrt{\hat{s}} is the invariant mass of the centrally
produced system. We confirm this result using a fixed-order calculation and
show that the replacement leads to approximately a factor 2 suppression in the
cross-section for central system masses in the range 100-500 GeV.Comment: 41 pages, 19 figures; minor typos fixed; version published in JHE
