Analytic Structure of Multiparticle Amplitudes in Complex Helicity

Abstract

By studying the partial-wave expansions of multiparticle amplitudes we argue that analytic properties in complex helicity are just a reflection of the familiar analytic structure in angular momentum. We give a criterion which determines when an asymptotic behavior in an azimuthal angle (conjugate to the helicity) can be reached in a physical process. Our discussion centers around the five- and six-point functions; the latter, being relevant for single-particle inclusive processes, is considered in detail. One of the interesting features of analytic structure in $\lambda$ is that it depends in detail on what other variables one chooses in addition to the azimuthal angle conjugate to it. That singularity structure is found by examining the partial-wave analysis appropriate to the chosen variables. Finally, a discussion of signature in many-particle amplitudes is given.