Operator-product expansions, neutrino scattering, and the dimension of the symmetry-breaking Hamiltonian

The structure functions W₄ and W₅ in inelastic neutrino-nucleon scattering are analyzed, using Wilson operator-product expansions. The ν dependence of the structure functions in the Bjorken scaling limit is related to the dimensions (Δᵢ) of the terms in the SU (3) ⊗ SU (3)-breaking Hamiltonian. Restrictions due to positive definiteness are used. Several applications of the analysis are made: (1) If the axial-vector current behaves as a canonical pion field, then there must exist a field of dimension ≤0. (2) A "maximal-contribution assumption" implies that Δ₁, the largest of the Δᵢ, is ≥2. (3) A proposed experimental determination of Δ₁ is analyzed. (4) Implications for internal-symmetry structure of the vanishing of W_L are discussed.