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

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.

Comments: 14 pages, 2 figures. v2: journal version; minor corrections