Dispersion relations and subtractions in hard exclusive processes

We study analytical properties of the hard exclusive process 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 studied and proved for momentum transfers exceeding the typical hadronic scale. The continuation to the real photon limit is considered, and the numerical correspondence between lattice simulations of the D-term and low energy Thomson amplitude is found. For sufficiently large t the subtraction may be expressed in a form similar to that suggested earlier for real Compton scattering.