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->1,t->0 limit of a class of models whose "bare" structure arises from elastic amplitudes of the form A(s,t)=s(lns)^νJ_ν(asqrt-tlns). 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 ν=0 these theories are infrared-free. The total cross section behaves as σ_T(s)γ₁-γ₂/[(lns)(lnlns)¹/²], where γ₁ factorizes. Scaling laws for the Reggeon proper vertex functions are given.