Violation of the Pomeranchuk Theorem and Zeros of the Scattering Amplitudes

Assuming constant but unequal asymptotic total cross sections for particle-particle and particle-antiparticle collisions, it is proved within axiomatic field theory that the scattering amplitude must have infinitely many zeros in a certain narrow angular region of the $t$ plane containing the physical region $t\le 0$. It is shown further that this region cannot be made narrower without additional assumptions. These results are also valid for a more general class of scattering amplitudes, including those saturating the Froissart bound.