3+1and3+2sterile neutrino fits

Abstract

We present the results of fits of short-baseline neutrino-oscillation data in $3+1$ and $3+2$ neutrino-mixing schemes. In spite of the presence of a tension in the interpretation of the data, $3+1$ neutrino mixing is attractive for its simplicity and for the natural correspondence of one new entity (a sterile neutrino) with a new effect (short-baseline oscillations). The allowed regions in the oscillation parameter space can be tested in near-future experiments. In the framework of $3+2$ neutrino mixing, there is less tension in the interpretation of the data, at the price of introducing a second sterile neutrino. Moreover, the improvement of the parameter goodness of fit is mainly a statistical effect due to an increase in the number of parameters. The $CP$ violation in short-baseline experiments allowed in $3+2$ neutrino mixing can explain the positive ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{e}$ signal and the negative ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e}$ measurement in the MiniBooNE experiment. For the $CP$-violating phase, we obtained two minima of the marginal ${\ensuremath{\chi}}^{2}$ close to the two values where $CP$ violation is maximal.