# Nuclear Theory and Event Generators for Charge-Changing Neutrino Reactions

## TL;DR

This paper compares different spectral function models for charge-changing neutrino reactions, analyzing their impact on semi-inclusive cross sections and neutrino energy reconstruction to inform event generator choices.

## Contribution

It introduces a formalism for semi-inclusive cross sections using various spectral function models and compares their effects on neutrino reaction predictions.

## Key findings

- Semi-inclusive cross sections vary significantly between models.
- Spectral functions influence the shape of semi-inclusive cross sections.
- Average neutrino energy can be described by simple kinematic models across different spectral functions.

## Abstract

Semi-inclusive $CC\nu$ cross sections based on factorized cross sections are studied for a selection of spectral function models with the objective of facilitating the choice of models for use as input into event generators. The basic formalism for such cross sections is presented along with an introduction to constructing spectral functions for simple models based on the independent particle shell model (IPSM), the relativistic Fermi gas model (RFG) and a local density approximation (LDA) based on the RFG. Spectral functions for these models are shown for $^{16}$O along with a more sophisticated model which includes nucleon-nucleon interactions \cite{ALVAREZRUSO20181}. Inclusive and semi-inclusive cross sections are calculated for these models. Although the inclusive cross sections are all of similar size and shape, the semi-inclusive cross sections are subtantially different depending upon whether the spectral functions contain some features associated with the nuclear shell model or are based on the RFG and LDA models. Calculations of average values and standard deviations of the initial neutrino energy using the semi-inclusive cross section for the various models are presented and indicate that there may be simple kinematical descriptions of the average neutrino energy which is common to all of these models.