Diffractive open charm production at HERA

We use perturbative QCD to calculate the cross sections sigma(L,T) for the diffractive production of open charm (<c(c)over bar>) from longitudinally and transversely polarised photons (or virtuality Q(2)) incident at high energy (root s) on a proton target. We study both the Q(2) and M-2 dependence of the cross sections, where hi is the invariant mass of the <c(c)over bar> pair. Surprisingly, the result for sigma(T), as well as for sigma(L), is perturbatively stable. We estimate higher-order corrections and find a sizeable enhancement of the cross sections. The cross sections depend on the square of the gluon density g(x, K-2), and we show that the observation of open charm at the HERA electron-proton collider can act as a sensitive probe of the gluon distribution for x = (Q(2) + M-2)/s and scale K-2 = (m(c)(2) + < k(T)(2) >)(1 + Q(2)/M-2) where the average quark transverse momentum squared < k(T)(2) > similar to m(c)(2). As compared to diffractive J/psi production, open charm has the advantage that it is independent of the non-perturbative ambiguities arising from the J/psi wave function. We estimate the fraction of diffractive events that arise from <c(c)over bar> production.