# Neutrino pion-production on a nucleon

## TL;DR

This paper uses heavy baryon chiral perturbation theory including the $$ resonance to analyze the axial charged-current in neutrino-nucleon interactions at low energies, revealing deviations from PCAC predictions.

## Contribution

It demonstrates that chiral perturbation theory predicts deviations from PCAC, suggesting the need to modify existing neutrino-nucleon models for accurate scattering amplitude calculations.

## Key findings

- At leading order, Adler theorems are satisfied.
- At next-to-leading order, deviations from PCAC are predicted.
- Implications for neutrino-nucleus scattering models.

## Abstract

Heavy baryon chiral perturbation theory ($\chi$PT), where the $\Delta$ resonance is included, is used in order to examine the axial charged-current component of the weak interaction process at low neutrino energies. At leading chiral order the Adler theorems, derived using PCAC, are satisfied. At next-to-leading chiral order this effective field theory goes beyond these theorems. I will show that $\chi$PT generates deviation from the PCAC predictions, which means that some neutrino-nucleon models that are used in evaluating neutrino nucleus scattering amplitudes, might need modifications.