Electroweak Form Factors of the $\Delta$(1232) Resonance

TL;DR

This paper models the electroweak form factors of the $ $Delta(1232) resonance using a chiral perturbation theory-based approach, fitting to electron and neutrino scattering data to extract new parametrizations and physical parameters.

Contribution

It introduces a new parametrization of the $N\to\Delta(1232)$ vector form factors and provides a unified analysis of neutrino and electron scattering data.

Findings

Extracted axial mass $M_{A\Delta}=0.85^{+0.09}_{-0.08}$ GeV.

Determined $C_5^A(0)=1.10^{+0.15}_{-0.14}$ consistent with Goldberger-Treiman.

Proposed a model incorporating nonresonant background terms from chiral perturbation theory.

Abstract

Nucleon $\to \Delta(1232)$ 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 $N\to\Delta(1232)$ vector form factors is proposed. Fit to neutrino scattering data gives axial mass $M_{A\Delta}=0.85{+0.09}{-0.08}\;$(GeV) and $C_5^A(0) = 1.10{+0.15}{-0.14}$ in accordance with Goldberger-Treiman relation as long as deuteron nuclear effects are considered.