# Impact of final state interactions on neutrino-nucleon pion production cross sections extracted from neutrino-deuteron reaction data

## TL;DR

This paper investigates how final state interactions affect neutrino-induced pion production data from deuteron reactions, providing corrected cross sections to improve neutrino-nucleus models for oscillation experiments.

## Contribution

It introduces a theoretical model incorporating FSI effects to accurately extract elementary neutrino-nucleon pion production cross sections from deuteron data.

## Key findings

- FSI significantly reduce the spectra over the quasi-free peak region.
- A recipe is developed to extract elementary process information from deuteron data.
- Corrected cross sections improve neutrino-nucleus reaction models.

## Abstract

The current and near-future neutrino oscillation experiments require significantly improved neutrino-nucleus reaction models. Neutrino-nucleon pion production data play a crucial role to validate corresponding elementary amplitudes that go into such neutrino-nucleus models. Thus the currently available data extracted from charged-current neutrino-deuteron reaction data ($\nu_\mu d\to \mu^-\pi NN$) must be corrected for nuclear effects such as the Fermi motion and final state interactions (FSI). We study $\nu_\mu d\to \mu^-\pi NN$ with a theoretical model including the impulse mechanism supplemented by FSI from $NN$ and $\pi N$ rescatterings. An analysis of the spectator momentum distributions reveals that the FSI effects significantly reduce the spectra over the quasi-free peak region, and leads to a useful recipe to extract information of elementary $\nu_\mu N\to \mu^-\pi N$ processes using $\nu_\mu d\to \mu^-\pi NN$ data, with the important FSI corrections taken into account. We provide $\nu_\mu N\to \mu^-\pi N$ total cross sections by correcting the deuterium bubble chamber data for the FSI and Fermi motion. The results will bring a significant improvement on neutrino-nucleus reaction models for the near-future neutrino-oscillation experiments.