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.
Highlights
In the Standard Model of particle physics, neutrinos are massless particles
We focus on the application to flux normalization at accelerator-based neutrino experiments in Secs
The correction to the electromagnetic energy spectrum is relatively flat over a wide energy, whereas the correction to the electron energy spectrum is logarithmically divergent below the electron end point; cf
Summary
Experiments with solar [1,2,3,4,5,6], atmospheric [7,8], reactor [9,10,11,12,13], and accelerator [14,15,16] neutrinos establish that neutrinos oscillate and have nonzero mass [17,18], providing a convincing example of physics beyond the Standard Model. Radiative corrections to elastic neutrino-electron scattering of order α were calculated first in Ref. Radiative corrections in elastic neutrino-electron scattering were discussed in Refs. As illustrative applications using accelerator neutrino beams [16,49,50,51], we consider the impact of radiative corrections on energy spectra and compare observables employing electron energy vs total electromagnetic energy. Appendix L displays fluxaveraged spectra in experimental conditions of DUNE, MINERvA, NOvA, and T2K experiments
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