Nonplanar Helicity-Pole Couplings: Duality and the Feynman Graph. I

We study, in the spirit of Gribov's Reggeon calculus, a particular nonplanar elastic six-point amplitude which contributes to the helicity-pole limit ($s,M^2\to \infty ,\frac{s}{M^2}\to \infty , \mathrm{and} t$ fixed) of the single-particle distribution. We find "third double-spectral function" effects analogous to those which appear in 2-2 amplitudes. In particular we find (1) nonsense-triple-Regge-wrong-signature fixed poles, and (2) the triple-Pomeranchukon vertex to be finite at $t=0\mathrm{}$ if the slope of the trajectory is nonzero and its intercept unity. In addition, we conjecture an asymptotic link between the high-energy Regge limits of ${\phi }^3$ theory amplitudes and the high-energy Regge behavior of dual-tree and dual-loop amplitudes.