Tests of the Conserved Vector Current and Partially Conserved Axial-Vector Current Hypotheses in High-Energy Neutrino Reactions

The following theorem is proved: Consider the high-energy neutrino reaction $\nu +\alpha \to l+\beta$, with $\alpha$ a nucleon or nucleus, $l$ a lepton ($e$ or $\mu$) and $\beta$ a system of strongly interacting particles. Suppose that the mass of $\alpha$ and the invariant mass of $\beta$ are not equal, and that the lepton mass is neglected. Then when the lepton emerges with its momentum parallel to that of the neutrino, the squared matrix element, averaged over lepton spin, depends only on the divergences of the vector and the axial-vector currents. Tests of the conserved vector current and the partially conserved axial-vector current hypotheses, based on the theorem, are proposed.