Constraints on Sterile Neutrinos in the MeV to GeV Mass Range

Abstract

A detailed discussion is given of the analysis of recent data to obtain improved upper bounds on the couplings $|U_{e4}|^2$ and $|U_{μ4}|^2$ for a mainly sterile neutrino mass eigenstate $ν_4$. Using the excellent agreement among ${\cal F}t$ values for superallowed nuclear beta decay, an improved upper limit is derived for emission of a $ν_4$. The agreement of the ratios of branching ratios $R^{(π)}_{e/μ}=BR(π^+ \to e^+ ν_e)/BR(π^+ \to μ^+ ν_μ)$, $R^{(K)}_{e/μ}$, $R^{(D_s)}_{e/τ}$, $R^{(D_s)}_{μ/τ}$, and $R^{(D)}_{e/τ}$, and the branching ratios $BR(B^+\rightarrow e^+ν_e)$ and $BR(B^+\rightarrow μ^+ν_μ)$ decays with predictions of the Standard Model, is utilized to derive new constraints on $ν_4$ emission covering the $ν_4$ mass range from MeV to GeV. We also discuss constraints from peak search experiments probing for emission of a $ν_4$ via lepton mixing, as well as constraints from pion beta decay, CKM unitarity, $μ$ decay, leptonic $τ$ decay, and other experimental inputs.