Singularities of the Regge-Pole Model at Mass Zero

Abstract

We consider the behavior of a Regge-pole expansion when the mass of a physical particle tends to zero. If this variation of the mass is obtained by letting some parameter $\ensuremath{\lambda}$ vary, it is found that the analytic form of the residues must change discontinuously when the mass passes through zero. We call such an effect a transition, by analogy with statistical mechanics. Some consequences are given concerning the reliability of perturbation expansion, zero-mass pions and their Toller classification, and the Pomeranchuk singularity.