Neutral-current neutrino production of Δ (1236)

We study the isovector vector and axial-vector neutral-current couplings by analyzing the neutral-current neutrino and antineutrino production of the Δ (1236) resonance. We use a quark model to predict the multipole structure and q2 dependence of the matrix elements. This model has been developed elsewhere for the charged-current case. We calculate and discuss relevant quantities: production cross sections as well as angular distribution of decay products. We show that measurable combinations of polarization density matrix elements are very sensitive to the relative magnitude and sign of the vector and axial-vector couplings. One can determine--up to an ambiguity--the vector and axial-vector couplings by measuring the neutrino and the antineutrino cross sections. The ambiguity can be solved by studying the angular distribution of the decay products. Moreover, both coupling could be determined also in a neutrino (or antineutrino) experiment alone by measuring the cross section and the polarization density matrix. Experiments must be performed at not too high energies, for which the vector-axial-vector interference term is sizeable. For pion neutrino production on nuclei, we point out that, if the recoil proton is observed, and if the π N mass is consistent with the Δ (1236) region, the nuclear charge-exchange corrections are lowered substantially with respect to the situation considered by Alder, Nussinov, and Paschos, in which only the pion is assumed to be observed