Constraints on sterile neutrinos in the MeV to GeV mass range

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 ${\cal F}t$ values for superallowed nuclear beta decay, an improved upper limit is derived for emission of a $\nu_4$. The agreement of the ratios of branching ratios $R^{(\pi)}_{e/\mu}=BR(\pi^+ \to e^+ \nu_e)/BR(\pi^+ \to \mu^+ \nu_\mu)$, $R^{(K)}_{e/\mu}$, $R^{(D_s)}_{e/\tau}$, $R^{(D_s)}_{\mu/\tau}$, and $R^{(D)}_{e/\tau}$, and the branching ratios $BR(B^+\rightarrow e^+\nu_e)$ and $BR(B^+\rightarrow \mu^+\nu_\mu)$ 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.