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 ($μ^- \to e^- \barν_e ν_μ(γ),~μ^+ \to e^+ ν_e \barν_μ(γ)$), pion $π_{\ell 2}$ ($π^- \to μ^- \barν_μ(γ),~π^+ \to μ^+ ν_μ(γ)$), and kaon $K_{\ell 2}$ ($K^- \to μ^- \barν_μ(γ),~K^+ \to μ^+ ν_μ(γ)$) decays. We compare detailed $\mathrm{O} \left( α\right)$ 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.