A detailed discussion is given of the analysis of recent data to obtain improved upper bounds on the couplings $|U_{e4}{|}^2$ and $|U_{\mu 4}{|}^2$ for a mainly sterile neutrino mass eigenstate ${\nu }_4$. Using the excellent agreement among the $\mathcal{F}t$ values (products of kinematic rate factors times half-lives with radiative corrections included) for superallowed nuclear beta decays, an improved upper limit is derived for emission of a ${\nu }_4$. The agreement of the ratios of branching ratios $R_{e/\mu }^{(\pi )}=\mathrm{BR}({\pi }^{+}\to e^{+}{\nu }_e)/\mathrm{BR}({\pi }^{+}\to {\mu }^{+}{\nu }_{\mu })$, $R_{e/\mu }^{(K)}$, $R_{e/\tau }^{(D_s)}$, $R_{\mu /\tau }^{(D_s)}$, and $R_{e/\tau }^{(D)}$, and the branching ratios $\mathrm{BR}(B^{+}\to e^{+}{\nu }_e)$ and $\mathrm{BR}(B^{+}\to {\mu }^{+}{\nu }_{\mu })$ decays with predictions of the Standard Model is utilized to derive new constraints on ${\nu }_4$ emission covering the ${\nu }_4$ mass range from MeV to GeV. We also discuss constraints from peak search experiments probing for emission of a ${\nu }_4$ via lepton mixing, as well as constraints from pion beta decay, CKM unitarity, $\mu$ decay, leptonic $\tau$ decay, and other experimental inputs.

• Received 24 September 2019

DOI:https://doi.org/10.1103/PhysRevD.100.073011

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Published by the American Physical Society