Electroweak form factors of theΔ(1232)resonance

Abstract

$\mathrm{Nucleon}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1232)$ 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 $\ensuremath{\nu}$-proton and $\ensuremath{\nu}$-neutron channel data are discussed in a unified statistical model. A new parametrization of the $N\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1232)$ vector form factors is proposed. In the case of model with deuteron nuclear effects fit to neutrino scattering data gives the axial mass ${M}_{A\mathrm{\ensuremath{\Delta}}}={0.85}_{\ensuremath{-}0.08}^{+0.09}\text{ }\text{ }\mathrm{GeV}$ and ${C}_{5}^{A}(0)={1.10}_{\ensuremath{-}0.14}^{+0.15}$ 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 ${M}_{A\mathrm{\ensuremath{\Delta}}}=0.8{1}_{\ensuremath{-}0.09}^{+0.09}\text{ }\text{ }\mathrm{GeV}$ and ${C}_{5}^{A}(0)=0.9{3}_{\ensuremath{-}0.13}^{+0.13}$.