Possibility of an Infinite Sequence of Regge Recurrences

Abstract

We show that a Regge trajectory, $\ensuremath{\alpha}(s)$, cannot have the property $\mathrm{Re}\ensuremath{\alpha}(s)\ensuremath{\rightarrow}+\ensuremath{\infty}$ as $s\ensuremath{\rightarrow}+\ensuremath{\infty}$ without leading to inconsistencies with two features of dispersion theory and Regge pole theory: that both $\ensuremath{\alpha}(s)$ and the reduced residue function, $\ensuremath{\gamma}(s)$, are analytic in the cut plane with one cut, and that they and the partial wave amplitude, $a(l, s)$, for $\mathrm{Re}l=\ensuremath{-}\frac{1}{2}$, are bounded for large $|s|$ by $\mathrm{exp}[{|s|}^{\frac{1}{2}}\ensuremath{-}\ensuremath{\epsilon}]$.