Constraints on a sub-eV scale sterile neutrino from non-oscillation measurements

Anomalies in several short-baseline neutrino oscillation experiments suggest the possible existence of sterile neutrinos at about eV scale having appreciable mixing with the already known three neutrinos. We find that if such a light sterile neutrino exists, through a combined study of the leptonic decays of $\mu^-$, $\tau^-$, $\pi^-$ and $K^-$, some semi-leptonic decays of $\tau^-$ and the invisible decay width of the $Z$ boson, it is possible to constrain the relevant mixing matrix elements. Furthermore, we compare the constraints, derived by using the method presented here, with the experimental results obtained from short-baseline neutrino oscillation experiments. We find that a single light sterile neutrino cannot satisfy the existing short-baseline neutrino oscillation constraints and explain the anomalies mentioned above. Along the way we provide a number of experimentally clean observables which can be used to directly study the light sterile neutrino independently of the neutrino oscillation experiments.