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 ($$\mu^- \to e^- \bar{\nu}<em>e \nu</em>\mu (\gamma),~\mu⁺ \to e⁺ {\nu}<em>e \bar{\nu}</em>\mu (\gamma)$$), pion $\pi_{\ell 2}$ ($$\pi^- \to \mu^- \bar{\nu}<em>\mu (\gamma),~\pi⁺ \to \mu⁺ {\nu}</em>\mu (\gamma)$$), and kaon $K_{\ell 2}$ ($$K^- \to \mu^- \bar{\nu}<em>\mu (\gamma),~K⁺ \to \mu⁺ {\nu}</em>\mu (\gamma)$$) 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 $6\times 10<sup>{-5}$ level for the scattering on $<sup>{40}\mathrm{Ar}$ 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.