The $Q^2$ dependence of the hard diffractive photoproduction of vector   meson or photon and the range of pQCD validity
  We consider two coupled problems.   We study the dependence on photon virtuality $Q^2$ for the semihard quasi--elastic photoproduction of neutral vector mesons on a quark, gluon or real photon (at $s\gg p_{\bot}^2,\;Q^2; \; p_{\bot}^2\gg \mu^2 \approx (0.3$ GeV)$^2$). To this end we calculate the corresponding amplitudes (in an analytical form) in the lowest nontrivial approximation of perturbative QCD. It is shown that the amplitude for the production of light meson varies very rapidly with the photon virtuality near $Q^2=0$.   We estimate the bound of the pQCD validity region for such processes. For the real incident photon the obtained bound for the $\rho$ meson production is very high. This bound decreases fast with the increase of $Q^2$, and we expect that the virtual photoproduction at HERA gives opportunity to test the pQCD results. The signature of this region is discussed. For the hard Compton effect the pQCD should work good at not too high $p_{\bot}$, and this effect seems measurable at HERA. 
I.F. Ginzburg and D.Yu. Ivanov (Inst. of Math., Novosibisk)