  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.
