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Central exclusive production in hadron-hadron collisions at high energies, for example p + p -> p + X + p, where the “+” represents a large rapidity gap, is a valuable process for spectroscopy of mesonic states X. At collider energies the gaps can be large enough to be dominated by pomeron exchange, and then the quantum numbers of the state X are restricted. Isoscalar JPC = 0++ and 2++ mesons are selected, and our understanding of these spectra is incomplete. In particular, soft pomeron exchanges favor gluon-dominated states such as glueballs, which are expected in QCD but not yet well established. I will review some published data.

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