Geometrical description of binary reactions and large p/sub perpendicular to / phenomena

The authors study consequences of defining the impact parameter as being the variable conjugate to transverse relative c.m. momentum, p /sub perpendicular to /. The dynamical information carried by these are intimately connected to the behaviour of 90 degrees scattering. In particular, impact parameter dynamics is a priori qualitatively different from direct channel angular momentum dynamics. A phenomenological study of elastic pi /sup +or-/p and pp data at fixed values of longitudinal momentum, p/sub ///, leads to a generalized geometrical scaling hypothesis. In contrast with the power behaviour predicted by parton models, the data suggest exponential behaviour of the scaling amplitudes at fixed p/sub /// of the type e/sup Rp perpendicular to / with R approximately=1 fm. Correspondingly, these amplitudes are described by a pair of complex conjugate singularities on the imaginary axis in the impact parameter plane. (29 refs).