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 $(c\overline{c})$ from longitudinally and transversely polarised photons (of virtuality $Q^2$) incident at high energy $(\sqrt{s})$ on a proton target. We study both the $Q^2$ and $M^2$ dependence of the cross sections, where $M$ is the invariant mass of the $c\overline{c}$ 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 {\it 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 $K^2 = (m_c^2 + \langle k_T^2 \rangle) (1 + Q^2/M^2)$ where the average quark transverse momentum squared $\langle k_T^2 \rangle \sim m_c^2$. 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 $c\overline{c}$ production.