First constraints on light sterile neutrino oscillations from combined appearance and disappearance searches with the MicroBooNE detector

We present a search for eV-scale sterile neutrino oscillations in the MicroBooNE liquid argon detector, simultaneously considering all possible appearance and disappearance effects within the $3+1$ active-to-sterile neutrino oscillation framework. We analyze the neutrino candidate events for the recent measurements of charged-current $ν_e$ and $ν_μ$ interactions in the MicroBooNE detector, using data corresponding to an exposure of 6.37$\times$10$^{20}$ protons on target from the Fermilab booster neutrino beam. We observe no evidence of light sterile neutrino oscillations and derive exclusion contours at the $95\%$ confidence level in the plane of the mass-squared splitting $Δm^2_{41}$ and the sterile neutrino mixing angles $θ_{μe}$ and $θ_{ee}$, excluding part of the parameter space allowed by experimental anomalies. Cancellation of $ν_e$ appearance and $ν_e$ disappearance effects due to the full $3+1$ treatment of the analysis leads to a degeneracy when determining the oscillation parameters, which is discussed in this paper and will be addressed by future analyses.