Analytic Continuation in Helicity and O(2,1) Expansions

Abstract

We discuss the analytic continuation of an azimuthal angular variable in a scattering process to a channel where it may take on large imaginary values. The asymptotic behavior of the many-particle amplitude for large values of that variable is shown to be governed by singularities in an analytically continued helicity amplitude. The procedure is analogous to the usual Regge-Sommerfeld-Watson transformation relating large-$cos\theta$ behavior to singularities in analytically continued angular momentum amplitudes.