Scaling Symmetry of Scattering Amplitudes

We introduce and study a possible symmetry relation among the scattering amplitudes of two reactions whose corresponding masses are related by a common factor σ (mi′mi=σ for all  i). We discuss two major physical examples of this symmetry involving electromagnetic and weak interactions. We consider the possibility of this symmetry in strong interactions at high energies and deduce from it interesting predictions on the asymptotic behavior of cross sections.