Active to sterile neutrino oscillations: Coherence and MINOS results

We study the $\nu_\mu - \nu_s$ oscillation effects in the near detector of the MINOS experiment. Conceptually, the MINOS search for sterile neutrinos with mass $\sim 1$ eV realizes an interesting situation of partial decoherence of the neutrino state at the production. This corresponds to a difference of energies of the two mass eigenstates that is comparable with or bigger than the width of the initial state (pion). We show that these effects modify the MINOS bound on mixing of sterile neutrino for $\Delta m^2_{41} \aprge 0.5$ eV$^2$ and make the experiment insensitive to oscillations with $\Delta m^2_{41} \gtrsim 15$ eV$^2$. Oscillations with $\Delta m^2_{41} = (1 - 3)$ eV$^2$ could explain some deficit of events observed in the low energy bins in the near detector and correspondingly the excess of events in the far detector.