the negative-parity $h(0^-)$ state is strongly suppressed in comparison with the production of the $h(0^+)$ state. Similarly it follows that the central diffractive exclusive production of $2^{++}$ states is also suppressed in some topical cases; for example, $2^{++}$ states formed from heavy quark pairs (in the non-relativistic model) [@KMRmm; @TEN] or $2^{++}$ ‘gravitons’ in models with extra dimensions in which their coupling to gluons has a point-like nature (with no derivatives) so they are not produced via the $J_z=0$ two-gluon state [@INC]. Also these processes can provide a unique opportunity to determine the quantum numbers of pair-produced new strongly-interacting objects [@INC]. For example, comparatively light gluinos and squarks can be distinguished by the respective $\beta^3$ and $\beta$ threshold behaviour, where $\beta$ is the particle velocity.

Example: dynamics of $h(0^\pm)$ Higgs production {#sec:3}
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So far we have discussed the structure of the production amplitudes for pp p + h + p, \[eq:rat1\] where $h$ has a given $J^P$, which follow from general principles. To go further we need to consider the dynamics of the process. We study $h(0^\pm)$ Higgs production as a topical example. The general rules imply that the central vertices behave as

[l l l]{} g\_[ik]{}\^[h(0\^+)]{} & \~& 