Possible Failure of the Pomeranchuk Theorem-Shrinkage of the Forward Elastic Peak

Assuming constant but unequal asymptotic total cross sections ${\sigma }_{\pm }\left(\infty \right)$ leads to a ${\left(\ln s\right)}^2$ shrinkage of the forward elastic peak. Moreover, under rather general assumptions, $\frac{d{\sigma }^{\mathrm{el}}}{\mathrm{dt}}$ exhibits and infinitude of oscillations in $t$ as $s\to \infty$, a result derived earlier by Finkelstein within the Regge-cut model.