Radiative (anti)neutrino energy spectra from muon, pion, and kaon decays

TL;DR

This paper evaluates radiative corrections to (anti)neutrino energy spectra from muon, pion, and kaon decays, providing analytical forms and assessing their impact on neutrino flux predictions for current and future experiments.

Contribution

It offers detailed $ ext{O}(\alpha)$ radiative correction calculations and analytical energy spectra for meson and muon decays, improving flux predictions for neutrino experiments.

Findings

Radiative corrections introduce continuous spectral components near the endpoint.

These corrections can alter flux-averaged cross sections by about 6×10^{-5}.

Flux modifications around the peak are at the 3-4 permille level.

Abstract

To describe low-energy (anti)neutrino fluxes in modern coherent elastic neutrino-nucleus scattering experiments as well as high-energy fluxes in precision-frontier projects such as the Enhanced NeUtrino BEams from kaon Tagging (ENUBET) and the Neutrinos from STORed Muons (nuSTORM), we evaluate (anti)neutrino energy spectra from radiative muon ($\mu^- \to e^- \bar{\nu}_e \nu_\mu (\gamma),~\mu^+ \to e^+ {\nu}_e \bar{\nu}_\mu (\gamma)$), pion $\pi_{\ell 2}$ ($\pi^- \to \mu^- \bar{\nu}_\mu (\gamma),~\pi^+ \to \mu^+ {\nu}_\mu (\gamma)$), and kaon $K_{\ell 2}$ ($K^- \to \mu^- \bar{\nu}_\mu (\gamma),~K^+ \to \mu^+ {\nu}_\mu (\gamma)$) decays. We compare detailed $\mathrm{O} \left( \alpha \right)$ distributions to the well-known tree-level results, investigate electron-mass corrections and provide energy spectra in analytical form. Radiative corrections introduce continuous and divergent spectral components near the endpoint, on top of the monochromatic tree-level meson-decay spectra, which can change the flux-averaged cross section at $6\times 10^{-5}$ level for the scattering on $^{40}\mathrm{Ar}$ nucleus with (anti)neutrinos from the pion decay at rest. Radiative effects modify the expected (anti)neutrino fluxes from the muon decay around the peak region by $3-4$ permille, which is a precision goal for next-generation artificial neutrino sources.