Pomeranchuk singularity in a class of Reggeon field theories suggested by direct-channel unitarity

Within the context of a generalized Reggeon calculus we study the infrared $J\to 1,t\to 0$ limit of a class of models whose "bare" structure arises from elastic amplitudes of the form $A(s,t)=s{\left(\ln \mathrm{s}\right)}^{\nu }{J}_{\nu }\left(a\sqrt{-t}\ln s\right)$. Such amplitudes are suggested by the implementation of $s$-channel unitarity via eikonalization of a "Born term," via absorption models, and via the multiperipheral bootstrap. We employ the renormalization group to study the renormalized Pomeranchuk singularity when the interaction involves a triple coupling. Our major result is that for $\nu =0\mathrm{}$ these theories are infrared-free. The total cross section behaves as $\frac{{\sigma }_T\mathrm{}\left(s\right)\mathrm{}\sim {\gamma }_1-{\gamma }_2}{\left[\right(\ln s\left){\left(\ln \ln s\right)}^{\frac{1}{2}}\right]}$, where ${\gamma }_1$ factorizes. Scaling laws for the Reggeon proper vertex functions are given.