$\mathrm{Nucleon}\to \mathrm{\Delta }(1232)$ transition electroweak form factors are discussed in a single pion production model with nonresonant background terms originating from a chiral perturbation theory. Fits to electron-proton scattering $F_2$ as well as neutrino scattering bubble chamber experimental data are performed. Both $\nu$-proton and $\nu$-neutron channel data are discussed in a unified statistical model. A new parametrization of the $N\to \mathrm{\Delta }(1232)$ vector form factors is proposed. In the case of model with deuteron nuclear effects fit to neutrino scattering data gives the axial mass $M_{A\mathrm{\Delta }}={0.85}_{-0.08}^{+0.09}\mathrm{GeV}$ and $C_5^A(0)={1.10}_{-0.14}^{+0.15}$ in accordance with the Goldberger-Treiman relation. However, the consistency is spoiled when the deuteron effects are omitted; i.e., in this case the fit gives the axial mass $M_{A\mathrm{\Delta }}=0.81_{-0.09}^{+0.09}\mathrm{GeV}$ and $C_5^A(0)=0.93_{-0.13}^{+0.13}$.

• Received 21 July 2014

DOI:https://doi.org/10.1103/PhysRevD.90.093001