First Constraints on the Complete Neutrino Mixing Matrix with a Sterile Neutrino

Abstract

Neutrino oscillation models involving one extra mass eigenstate beyond the standard three ($3+1$) are fit to global short baseline experimental data and the recent IceCube ${\nu }_{\mu }+{\bar{\nu }}_{\mu }$ disappearance search result. We find a best fit of $\Delta m_{41}^2=1.75{\text{eV}}^2$ with $\Delta {\chi }_{null-min}^2$ (dof) of 50.61 (4). We find that the combined IceCube and short baseline data constrain ${\theta }_{34}$ to $<80^{\circ }(<6^{\circ })$ at 90\% C.L. for $\Delta m_{41}^2\approx 2(6){\text{eV}}^2$, which is improved over present limits. Incorporating the IceCube information provides the first constraints on all entries of the 3+1 mixing matrix.

7 pages, 4 figures

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