Dispersion total photoproduction sum rules for nucleons and few-body nuclei revisited

The questions on the presense and quantitative role of the constant terms in the real part of the high-energy photon-nucleon and photon-nucleus amplitudes representing the contribution of the non-Regge (the fixed j=0-pole) singularities in the finite-energy sum rules (FESR) for the photoabsorption cross sections on nucleons and the lightest atomic nuclei are discussed and new testable relations are presented for relevant combinations of the Compton scattering amplitudes