dependence of the vertex factors $f_{0^\pm}$ on $\vec p_{3\perp}\cdot \vec p_{4\perp}$, see [(\[eq:nightingale\])]{} and [(\[eq:ocelot\])]{}. However, it is evident from Fig. \[fig:4\] that this contribution does not give a large effect. What is more important is the suppression of $h(0^-)$ production in comparison to that for $h(0^+)$. The $h(0^-)$ amplitude is proportional to $\vec p_{3\perp}\times \vec p_{4\perp}$, where the dimensions must be compensated by some scale. In perturbative QCD this is the scale $Q_\perp^2$ arising from the gluon loop in Fig. \[fig:3\](a). Therefore the $h(0^-)$ cross section is reduced by a factor $\langle\, p_{3\perp}^2
p_{4\perp}^2 / 2Q_\perp^4\,\rangle$, that is by a factor of the order of 500 for typical $p_{i\perp}^2 \sim 1/2b
\sim 0.25~\GeV^2$ if $Q_\perp^2 \sim 4~\GeV^2$.

Absorptive corrections {#sec:4}
======================

In this section we consider how exclusive double-diffractive production is influenced by the absorptive (shadowing) effects, which arise from the multi-Pomeron diagrams of Fig. \[fig:2\]. To determine the suppression due to these absorptive corrections, it is convenient to work in impact parameter, $b$, space.

Absorptive effects for $h(0^+)$ production
------------------------------------------

The amplitude for the central production of an $h(0^+)$ state, via the double-Pomeron-exchange process $pp\to p +
h + p$, has the form T\^h(s,b\_1,b\_2,b) = ([-\_P(s,b\^2)]{}) T\_[PP]{}\^h(s\_1,s\_2,b\_1,b\_2), \[eq:snake\] 