We investigate the theoretical description of the central exclusive production process, $h_1 + h_2 to h_1+X+h_2$. Taking Higgs production as an example, we compute the subset of next-to-leading order corrections sensitive to the Sudakov factor appearing in the process. 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 show that the replacement leads to approximately a factor 2 suppression in the cross-section for central system masses in the range 100--500GeV.
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