# Neutrino-induced single-pion production: Kinematics and Cross Section

## TL;DR

This paper discusses the kinematics and cross section formulas for neutrino-induced single-pion production in the energy range relevant to neutrino oscillation experiments, providing a framework for understanding these interactions.

## Contribution

It introduces a detailed formalism for the kinematics and cross section calculations of neutrino-induced single-pion production, applicable to various $2\rightarrow4$ processes.

## Key findings

- Provides explicit kinematic formulas for neutrino-induced SPP.
- Derives cross section expressions relevant for neutrino energies of hundreds of MeV to a few GeV.
- Framework applicable to other similar scattering processes.

## Abstract

In the energy range of present and future accelerator-based neutrino-oscillation experiments, single-pion production (SPP) is one of the main contributions to the neutrino-nucleus scattering cross section. For these neutrino energies, ranging from several hundreds of MeV to a few GeV, the SPP on the nucleus is usually described by the reaction in which the incoming lepton couples to one bound nucleon in the nucleus, producing a pion and the knock-out nucleon, along with the residual system and the scattered lepton in the final state. Here, the kinematics and cross section formula for this process are discussed, although the formalism can be applied to other $2\rightarrow4$ processes.