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 $\mathrm{\mid }{U}_{e4}{\mathrm{\mid }}^2$ and $\mathrm{\mid }{U}_{\mu 4}{\mathrm{\mid }}^2$ for a mainly sterile neutrino mass eigenstate ${\nu }_4$. Using the excellent agreement among $\mathcal{F}t$ 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$R^{(D)}{e/\tau}$,andthebranchingratios$BR(B^+\rightarrow e^+\nu_e)$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.