Breakdown of the Pomeranchuk Theorem and the Behavior of the Leading J -Plane Singularity

We prove that the leading J-plane singularity in the symmetric partial-wave amplitude FJ^_⁺(t) near $t=0$ should behave like α_±(t)=1±At1/2+ terms of higher order in t; namely, the Pomeranchuk pole (or cut) must be a pair of complex-conjugate poles (cuts) if the total cross sections σT^_p,a(s)s→∞→const and σT^_P(∞)≠σT^_ᵃ(∞), where p and a denote particle-particle and antiparticle-particle scattering, respectively. We use only unitarity and analyticity to prove this.