  When comparing recent experimental data from the H1 and ZEUS Collaborations
at HERA for diffractive dijet production in deep-inelastic scattering (DIS) and
photoproduction with next-to-leading order (NLO) QCD predictions using
diffractive parton densities, good agreement is found for DIS. However, the
dijet photoproduction data are overestimated by the NLO theory, showing that
factorization breaking occurs at this order. While this is expected
theoretically for resolved photoproduction, the fact that the data are better
described by a global suppression of direct and resolved contribution by about
a factor of two comes as a surprise. We therefore discuss in some detail the
factorization scheme and scale dependence between direct and resolved
contributions and propose a new factorization scheme for diffractive dijet
photoproduction.
