High-energy neutrino-nucleon scattering, current algebra and partons

Abstract

The structure functions F j which describe high-energy neutrino-nucleon scattering are discussed. The analogue of the Callan-Gross result for electro-production is derived, viz. lim q 2→−∞ F 1 = lim q 2→−∞ F 1 = 0 with the algebra of field commutators and lim q 2→−∞ (F 2−ωF 1) = 0 with the quark model commutators. A sum rule for F 3 is derived assuming that F 3 satisfies an unsubtracted dispersion relation, as suggested by Regge theory. The breakdown of these current algebra results in perturbation theory is dicussed. The F i are also discussed in the ‘parton’ model, in which it is shown that F 3 is a measure of the average baryon number of the partons. In the ‘ quark-parton’ model of Bjorken and Paschos F 3 is small and our sum rule valid. In the ‘field theory parton’ model of Drell, Levy and Yan F 3 is large, in contradiction to Regge theory, and our sum rule invalid. This model predicts that anti-neutrino scattering vanishes in the backward direction.