eV-scale sterile neutrino: A window open to non-unitarity?

An excess observed in the accelerator neutrino experiments in the $\nu_{\mu} \rightarrow \nu_{e}$ channel at high confidence level (CL) has been interpreted as due to eV-scale sterile neutrino(s). But, it has been suffered from the problem of ``appearance-disappearance tension'' at the similarly high CL because the measurements of the $\nu_{\mu} \rightarrow \nu_{\mu}$ channel do not observe the expected event number depletion corresponding to the sterile contribution in the appearance channel. We suggest non-unitarity as a simple and natural way of resolving the tension, which leads us to construct the non-unitary $(3+1)$ model. With reasonable estimation of the $\alpha$ parameters governing non-unitarity, which we argue growing when more sterile states added, we perform an illustrative analysis to illuminate if the tension can be resolved in this model. We have found the unique solution with $\sin^2 2\theta_{14} \approx 0.3$, which is consistent with the (reactors + Ga) data and is stable against variation of the appearance signature. This solution bridges between the two high CL signatures, BEST and LSND-MiniBooNE, and implies a large neutrino-antineutrino asymmetry, given the much less anomaly indicated in the antineutrino sector.