New Criterion for Nonoscillating High-Energy Behavior of Scattering Amplitudes. II. Applications

The condition for nonoscillation of scattering amplitudes at high energy, proposed in a previous paper by the authors, is applied to show that (i) fast oscillations can be incorporated into the picture by taking into account the finite resolution of physical apparatus, (ii) finite-energy sum rules are equivalent to the fulfillment of the criterion, (iii) Regge cuts lead to nonoscillating behavior in our sense, (iv) the criterion may still be satisfied when the leading singularities in the complex $l$ plane are more general than the usual cuts and poles.