Model dependence of the polarization asymmetries in weak pion production off the nucleon

TL;DR

This paper investigates how polarization asymmetries in weak pion production depend on the underlying models, highlighting their potential to probe axial form factors and resonance contributions in neutrino-nucleon interactions.

Contribution

It compares two phenomenological models to analyze polarization observables, revealing their sensitivity to axial form factors and resonance phases in weak pion production.

Findings

Polarization and target spin asymmetries are effective for extracting the $C_5^A$ axial form factor.

These asymmetries are sensitive to the phase between resonance and nonresonance amplitudes.

Polarization observables can test SPP models and the axial content of the $ riangle(1232)$ resonance.

Abstract

The work presents the studies of the polarization observables in the single pion production (SPP) induced by the interaction of the muon neutrino (antineutrino) with nucleons. The SPP cross-sections and spin asymmetries are computed within two phenomenological models. One is basing on the nonlinear sigma model \cite{Hernandez:2007qq}; the other has origin in linear sigma model~\cite{Fogli:1979cz}. Firstly, we show that the final nucleon polarization and target spin asymmetries are good observables to obtain information about the $C_5^A$ axial form factor. Secondly, we demonstrate that the nucleon polarization and the target spin asymmetries are sensitive to the relative phase between resonance and nonresonance amplitudes. We conclude that the polarization of the final nucleon and the target spin asymmetry are promising observables for testing SPP models, including studies of the axial content of $\Delta(1232)$ resonance and unitarization procedures.