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We describe how unintegrated parton distributions can be calculated from conventional integrated distributions. We extend and improve the 'last-step' evolution approach, and explain why doubly-unintegrated parton distributions are necessary. We generalise k tfactorisation to (z, k t )-factorisation. We apply the formalism to inclusive jet production in deep-inelastic scattering, mainly at leading order, but we also study the extension to next-to-leading order. We compare the predictions with recent HERA data.

The double-diffractive production of χc and χ b mesons, with a rapidity gap on either side, is studied, using both the Regge formalism and the perturbative QCD approach. Due to the rather low scale, the exclusive double-diffractive process pp → p + χ + p is predicted to dominate, whereas the probability that the incoming protons dissociate is expected to be relatively small. We evaluate the corresponding χ production cross sections at the Tevatron and LHC energies. For the double-diffractive process with proton dissociation, it is possible to select events with large transverse momenta transferred through the rapidity gaps, by measuring the transverse energy, E ⊥ , flows in the proton fragmentation regions. Then the large E ⊥ provides a scale to justify the use of perturbative QCD, and to allow a spin-parity analysis of the centrally produced system to be performed, by studying the azimuthal angular correlations between the directions of the forward and backward E ⊥ flows. The central production of the new X(3872) charmonium state is considered.

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