Regge Poles for Large Coupling Constants. I

Abstract

Since we define the Pomeranchon to be the leading singularity of the potential, and find that a high-energy particle resembles an expanding black disk if this singularity is located at $Jg1$, we study as a model the generation of such a singularity by the ladder diagrams in ${\ensuremath{\varphi}}^{3}$ theory. We find that, when the coupling constant is sufficiently large, there are Regge poles located at $Jg1$. Thus the Pomeranchon in this model is a Regge pole with $\ensuremath{\alpha}(0)g1$. This conclusion is reached by solving the Bethe-Salpeter equation to determine, in the strong coupling limit, the positions of the Regge (or Toller) poles at $t=0$. We find a family of approximately equally spaced Toller poles. The position of the leading singularity, but not the spacing, depends critically on whether the exchanged particle is massless or massive. Some numerical results are presented.