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

Abstract

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