Diffractive PDFs and factorisation tests at HERA

The HERA collider at DESY (Hamburg) has provided Deep Inelastic Scattering (DIS) of elec- trons off protons in the years 1992-2007 for the H1 and ZEUS experiments with a centre of mass energy up to 318 GeV. Diffractive dissociation of photons in the reaction γ (∗) p → X p, constitute a large fraction (∼ 10%) of the visible cross section in deep inelastic scattering (DIS), and the process can be seen as a reaction where the colliding proton emerges intact in the interaction. Different experimental methods have been developed by the H1 and ZEUS experiments to select diffractive events: by detecting the final state proton with forward proton spectrometers or thanks to to the peculiar topology of diffractive events, by requiring a large rapidity gap in the main de- tector between the leading proton (or the low-mass baryonic system) and the photon dissociation system X. The ZEUS and H1 collaborations have performed next-to-leading-order (NLO) QCD fit to the inclusive diffractive data extracting diffractive parton densities (DPDFs). As a direct test of the QCD factorisation theorem, dijet cross sections have been compared to the NLO or- der QCD predictions, based on recent DPDFs obtained by H1 and ZEUS. New sets of DPDFs are obtained through a simultaneous fit to the inclusive and dijet diffractive cross sections. The analysis allows for a precise determination of both the quark and gluon distributions over a wide z range: the precision on the gluon density at high momentum fractions is improved compared to previous extractions since data on diffractive dijets allow to constrain the gluon density. Finally, recent factorization tests on diffractive dijets in photoproduction are presented and discussed in the following.