  The double-diffractive production of chi_c and chi_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 \to p + chi + p is predicted to dominate, whereas
the probability that the incoming protons dissociate is expected to be
relatively small. We evaluate the corresponding chi 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_\perp, flows in the proton fragmentation regions. Then the large
E_\perp 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_\perp flows. The central production of the new X(3872)
charmonium state is considered.
