Matter effects in upward-going muons and sterile neutrino oscillations

The angular distribution of upward-going muons produced by atmospheric neutrinos in the rock below the MACRO detector shows anomalies in good agreement with two flavor νμ→ντ oscillations with maximum mixing and Δm2 around 0.0024 eV2. Exploiting the dependence of magnitude of the matter effect on oscillation channel, and using a set of 809 upward-going muons observed in MACRO, we show that the two flavor νμ→νs oscillation is disfavored with 99% C.L. with respect to νμ→ντ.