Study of single-pion production by weak charged currents in low-energy<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mi>d</mml:mi></mml:math>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 $\ensuremath{\nu}p\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}p{\ensuremath{\pi}}^{+}$, $\ensuremath{\nu}n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}p{\ensuremath{\pi}}^{0}$, and $\ensuremath{\nu}n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}n{\ensuremath{\pi}}^{+}$. An isospin decomposition shows that the ratio of $I=\frac{1}{2}$ to $I=\frac{3}{2}$ amplitudes is 0.68\ifmmode\pm\else\textpm\fi{}0.04 with a relative phase of (90.7\ifmmode\pm\else\textpm\fi{}4.6)\ifmmode^\circ\else\textdegree\fi{} for $M(N\ensuremath{\pi})&lt;1.4$ GeV. This agrees with theoretical models, particularly the detailed calculation of Adler. Using the data of the reaction $\ensuremath{\nu}p\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}p{\ensuremath{\pi}}^{+}$, the characteristic mass of the nucleon axial-vector elastic form factor is measured to be ${0.98}_{\ensuremath{-}0.03}^{+0.06}$ 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.