Light-Cone Algebra, Field-Current Identity, and Deep-Inelastic Scattering

Abstract

We reproduce the full content of the Fritzsch-Gell-Mann light-cone algebra (originally derived using the quark model) for deep-inelastic lepton-nucleon scattering using currents given by the field-current identity. These currents are modified by dilaton clothing from the usual low-energy vector-dominance form by the principles of scale invariance to possess a scale dimension three (which is the dimension of the currents in the quark model). The calculation is performed by the technique of an effective Lagrangian to be used to first nonvanishing order, and the forms of the interactions needed to maintain the lightcone algebra are determined. The usual quark-parton results are explicitly obtained, e.g., the vanishing of ${q}^{2}{\ensuremath{\sigma}}_{L}$ in the deep-inelastic limit, the relations between electron and neutrino structure functions, etc. The Callan-Gross sum rule is examined and shown to be consistent with the above results.