Dispersion relations and subtractions in hard exclusive processes

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.