Single Pion Production off Free Nucleons: Analysis of Photon, Electron, Pion and Neutrino Induced Processes

In this paper, I introduce a unified model for single-pion production across photo-, electro-, and neutrino-nucleon interactions, designed to be valid over a broad kinematic range that is crucial for accelerator-based neutrino experiments. This model includes vector and axial-vector nucleon transition form factors for all excited nucleons or resonances up to 2 GeV, as well as non-resonant backgrounds, within a meson dominance framework that adheres to QCD principles and ensures unitarity. This approach guarantees accurate asymptotic behaviour at high momentum transfer and effectively addresses the transition region. Additionally, the model employs the Conserved Vector Current and Partially Conserved Axial Current relations to provide reliable predictions at very low momentum transfer, tackling challenges encountered by current neutrino experiments. The unified model facilitates a comprehensive analysis by integrating all available data from electron, photon, pion, and neutrino scattering experiments. This integration enables a detailed investigation of nucleon structure within the resonance region and is particularly valuable for probing weak interactions, where neutrino-nucleon data are limited. The combined analysis allows for the simultaneous parameterisation and constraint of the model free parameters, while quantifying associated uncertainties, thus providing a robust and reliable framework for future neutrino measurements.