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

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 ν_μ+ν_μ disappearance search result. We find a best fit of Δm₄₁²=1.75 eV² with Δχ_null-min²/d.o.f. of $50.61/4$. We find that the combined IceCube and short baseline data constrain θ₃₄ to <80^∘(<6^∘) at 90% C.L. for Δm₄₁²≈2(6) eV², which is improved over present limits. Incorporating the IceCube information provides the first constraints on all entries of the $3+1$ mixing matrix.