Study of single-pion production by weak charged currents in low-energy $\nu d$ interactions

This paper gives the results of a study of single-pion production by the weak charged current utilizing the wide-band muon-type-neutrino beam at the Argonne Zero Gradient Synchrotron. The data were obtained from hydrogen and deuterium fillings of the 12-ft bubble chamber. The methods of event selection and separation from background are given as are the details of the corrections and systematic effects in the data sample. The energy-dependent cross sections and differential distributions are presented for the three single-pion production reactions $\nu p\to {\mu }^{-}p{\pi }^{+}$, $\nu n\to {\mu }^{-}p{\pi }^0$, and $\nu n\to {\mu }^{-}n{\pi }^{+}$. An isospin decomposition shows that the ratio of $I=\frac{1}{2}$ to $I=\frac{3}{2}$ amplitudes is 0.68±0.04 with a relative phase of (90.7±4.6)° for $M\left(N\pi \right)<\mathrm{}1.4\mathrm{}$ GeV. This agrees with theoretical models, particularly the detailed calculation of Adler. Using the data of the reaction $\nu p\to {\mu }^{-}p{\pi }^{+}$, the characteristic mass of the nucleon axial-vector elastic form factor is measured to be ${0.98}_{-0.03\mathrm{}}^{+0.06\mathrm{}}$ GeV when analyzed within the context of the Adler model. The data are also compared to other parametrizations of the nucleon axial-vector form factor.