We present predictions for the diffractive production of $\\chi$ mesons in the
central rapidity region usually covered by collider detectors. The predicted
cross sections are based on the Bialas-Landshoff formalism for both exclusive
and
inclusive production and makes use of the
DPEMC Monte-Carlo simulation adapted with kinematics appropriate for small-mass
diffractive production. We compare generator-level results with a CDF
measurement for exclusive $\\chi$ production, and study background and other
scenarios
including the contribution
of inclusive $\\chi$ production. The results agree with the Tevatron data
and are extrapolated, highlighting the exclusive $\\chic$ production
at LHC energies. A possible new measurement at the Tevatron using the D\\O\\
forward detectors is investigated, taking advantage of the dominance of
exclusive production for high enough diffractive mass fraction.
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