Watson's theorem and the $N\Delta(1232)$ axial transition

TL;DR

This paper improves a model for neutrino-induced pion production by restoring unitarity through Watson's theorem, leading to a more accurate determination of the $N\u03b4$ axial form factors consistent with theoretical predictions.

Contribution

The authors enhance an existing model by imposing Watson's theorem, resulting in a more precise extraction of the $N\u03b4$ axial form factors from experimental data.

Findings

Larger $C_5^A(0)$ value obtained, aligning with Goldberger-Treiman relation.

Model improvement yields better agreement with theoretical predictions.

Enhanced unitarity treatment refines axial form factor determination.

Abstract

We present a new determination of the $N\Delta$ axial form factors from neutrino induced pion production data. For this purpose, the model of Hernandez {\it et al.} [Phys. Rev. D76, 033005 (2007)] is improved by partially restoring unitarity. This is accomplished by imposing Watson's theorem on the dominant vector and axial multipoles. As a consequence, a larger $C_5^A(0)$, in good agreement with the prediction from the off-diagonal Goldberger-Treiman relation, is now obtained.