On the sign of cos θ at the branch points of a partial wave amplitude in thes-plane

Abstract

The sign of the cosine of the scattering angle, cosθ, at the branch points of a relativistic two-body partial wave amplitude with arbitrary masses in the complexs-plane is determined. The results yield that as to the tops-sheet, (i) the sign of cosθ is the same at the complex conjugated branch points which lie off the reals-axis, and (ii) cosθ changes sign at the (direct channel) thresholds. The difference between the elastic and inelastic cases is emphasized. It is pointed out that in certain physical energy ranges, for some collisions (e.g. π + N → π + N), the directions near the backward direction can be considered as the most important ones, while for several other collisions (e.g. π + N → ϱ + N) the directions into the forward hemisphere have the strongest influence.