Pomeron structure functions from HERA to Tevatron and LHC

The proton diffractive structure function $F_2^{D(3)}$ measured in the H1 and ZEUS experiments at HERA are analysed in terms of perturbative QCD in the perspective of the QCD extrapolation to the Tevatron and the LHC. It is shown that both data sets can be well described by a QCD analysis in which point-like parton distributions, evolving according to the next-leading DGLAP equations, are assigned to the leading and sub-leading Regge exchanges. For present data from H1 and ZEUS the gluon distributions are found to be quite different and we give the corresponding sets of quark and gluon parton distributions for the Pomeron, extracted from the two experiments. An extrapolation to the Tevatron range is compared with CDF data on single diffraction. Conclusions on factorization breaking between HERA and Tevatron critically depend on whether H1 (strong violation) or ZEUS (compatibility at low $\beta$) fits are taken into account. Using the double Pomeron formulation in central diffractive dijet production we show that the Tevatron mass fraction is much sensitive to the high $\beta$ tail of the gluon in the Pomeron, suggesting a new way of handling the otherwise badly known gluon distribution in the Pomeron. Extrapolation of the fits to very high $Q^2$ are given since they will be relevant for QCD and diffraction studies at the LHC.