reaction $pp\to pX^0p$, and to the proposal to look for the Higgs boson and other new particles in double-Pomeron-exchange processes, see, for example, [@BL]–[@INC]. Indeed it will be one of the main challenges of the LHC to identify the nature (including the spin–parity) of newly-discovered heavy objects. It appears to be very hard to find a spin–parity analyser using conventional approaches.

Models for double-Pomeron-exchange production of hadrons with different quantum numbers have been developed in recent years [@a4]–[@a8]. However in some papers [@a5; @a5a] the formulas of Reggeon theory were not fully consistent, while some results of the others follow simply from general rules of the Reggeon approach. In Section \[sec:2\] we first consider these rules and compare them with experimental observations [@a2], and with the results of the phenomenological analysis performed in Ref. [@a7]. Also the dynamics for the Pomeron–Pomeron–particle vertices is discussed.

In Section \[sec:3\] we illustrate how the general behaviour is distorted by the dynamics of the process, using $h(0^\pm)$ exclusive diffractive production as an example. Apart from subsection 3.1, where we discuss the uncertainties in the predicted cross sections, this section neglects the absorptive or unitary corrections. However at high energies these corrections are important (see, 