Scaling laws in high-energy neutrino reactions

Abstract

Bjorken has proposed that the structure functionsF1,F2,F3 of deep inelastic neutrino scattering are functions of ω=−2Mν/q2 only. These scaling laws are studied in Veneziano-like models and are found to emerge naturally for the scattering of neutrinos on a neutron or of antineutrinos on a proton, together with the Callan-Gross sum rule for\(\int\limits_1^\infty d \omega F_2 /\omega ^2 \), the Gross-Llewellyn Smith sum rule for\(\int\limits_1^\infty d \omega F_3 /\omega ^2 \) and the relationF1=1/2ωF2. (It is assumed that certain equal-time commutators of currents contain no operator Schwinger terms). The models suggest the possibility that the structure functions for the scattering of neutrinos on a proton, or of antineutrinos on a neutron, are small in the deep inelastic limit.