  We study analytical properties of the hard exclusive processes amplitudes. We
found that QCD factorization for deeply virtual Compton scattering and hard
exclusive vector meson production results in the subtracted dispersion relation
with the subtraction constant determined by the Polyakov-Weiss $D$-term. The
relation of this constant to the fixed pole contribution found by Brodsky,
Close and Gunion and defined by parton distributions is proved, while its
manifestation is spoiled by the small $x$ divergence. The continuation to the
real photons limit is considered and the numerical correspondence between
lattice simulations of $D$-term and low energy Thomson amplitude is found.
