Weak interactions at high energies and complex angular momenta

Abstract

It has been suggested that weak interactions at high energies, Gs > 1 ( G is the Fermi coupling constant, √ s is the c.m.s. energy), become strong so that the partial waves can reach their unitary limit. This hypothesis is the opposite one to the assumption that there exists some special mechanism (e.g. the intermediate W-meson) which cuts off the increase of the partial waves at comparatively small energies s ⪡ G −1, in which case the interaction could remain weak up to very high energies. Elastic lepton scattering and some of other leptonic reactions (e + + e − ⇌ μ + + μ −) are considered by means od complex angular momentum theory provided Gs ⪢ 1. The main difference with the usual strong interactions consists in the possibility of the exchange of massless particles in the cross t-channel. This results (i) in the appearance of the singularity at t = 0 in Regge trajectories and residues and (ii) in the condensation of the Regge poles at t → 0 in the j-plane along the imaginary axis Re j = 0. For inelastic processes such as e + + e − → μ + + μ − the latter singularities could be the leading ones and the elastic cross section has then a specific oscillating behaviour at small momentum transfer. In the case of elastic lepton scattering due to s-channel unitarity there must exist some additional singularity in the right-half j-plane at t = 0. The total leptonic cross section satisfies therefore the inequality σ tot > const · s −1 when s → ∞.