# Theory of elastic neutrino-electron scattering

## TL;DR

This paper provides comprehensive theoretical calculations and analytic expressions for elastic neutrino-electron scattering, including radiative corrections, to improve neutrino flux normalization and aid new physics searches.

## Contribution

It offers the most precise cross section values and detailed analytic formulas for radiative corrections within the Fermi effective theory, enhancing the accuracy of neutrino scattering predictions.

## Key findings

- Calculated total and differential cross sections with photon radiation
- Provided analytic expressions for electron and photon spectra
- Quantified theoretical uncertainties dominated by hadronic corrections

## Abstract

Theoretical predictions for elastic neutrino-electron scattering have no hadronic or nuclear uncertainties at leading order making this process an important tool for normalizing neutrino flux. However, the process is subject to large radiative corrections that differ according to experimental conditions. In this paper, we collect new and existing results for total and differential cross sections accompanied by radiation of one photon, $\nu e \to \nu e (\gamma)$. We perform calculations within the Fermi effective theory and provide analytic expressions for the electron energy spectrum and for the total electromagnetic energy spectrum as well as for double- and triple-differential cross sections with respect to electron energy, electron angle, photon energy, and photon angle. We discuss illustrative applications to accelerator-based neutrino experiments and provide the most precise up-to-date values of neutrino-electron scattering cross sections. We present an analysis of theoretical error, which is dominated by the $\sim 0.2 - 0.4\%$ uncertainty of the hadronic correction. We also discuss how searches for new physics can be affected by radiative corrections.