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[over ¯]_{μ} disappearance search result. We find a best fit of Δm_{41}^{2}=1.75  eV^{2} with Δχ_{null-min}^{2}/d.o.f. of 50.61/4. We find that the combined IceCube and short baseline data constrain θ_{34} to <80°(<6°) at 90% C.L. for Δm_{41}^{2}≈2(6)  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.