# Neutrino induced weak pion production off the nucleon and coherent pion production in nuclei at low energies

## TL;DR

This paper develops a microscopic model for neutrino-induced pion production off nucleons and nuclei, critiques existing models like Rein--Sehgal, and discusses limitations in predicting pion angular distributions at low energies.

## Contribution

It introduces a new microscopic model for pion production and critically evaluates the Rein--Sehgal model's approximations and limitations.

## Key findings

- The microscopic model provides detailed predictions for pion production.
- Rein--Sehgal model's approximations lead to flatter differential cross sections.
- Limitations affect the accuracy of angular distribution predictions.

## Abstract

We present a microscopic model for neutrino induced one-pion production off the nucleon and its implementation for the purpose of calculating coherent pion production in nuclei. We further criticize the use of the Rein--Sehgal model for coherent pion production by low energy neutrinos. In particular, we show how the approximations in that model give rise to a much flatter differential cross section in the $\eta=E_\pi(1-\cos\theta_\pi)$ variable. We discuss the limitations intrinsic to any approach based on the partial conservation of the axial current hypothesis and the inability of such models to properly determine the angular distribution of the outgoing pion with respect to the direction of the incoming neutrino. We show the effects of those limitation for the case of the $\frac{d\sigma}{d\eta}$ differential cross section.