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

The sign of the cosine of the scattering angle, cos, 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 cos is the same at the complex conjugated branch points which lie off the reals-axis, and (ii) cos 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. + N + N), the directions near the backward direction can be considered as the most important ones, while for several other collisions (e.g. + N + N) the directions into the forward hemisphere have the strongest influence.The author would like to thank Professor G. Höhler for his kind hospitality at the Institut für theoretische Kernphysik, University of Karlsruhe. He is grateful to him and to the members of that Institute for valuable discussions. Correspondence with Dr. Jens Lyng Petersen, which gave rise to the present investigation, is also acknowledged.