Confronting the short-baseline oscillation anomalies with a single sterile neutrino and non-standard matter effects

We examine the MiniBooNE neutrino, MiniBooNE antineutrino and LSND antineutrino data sets in a two-neutrino $\stackrel{\tiny{(-)}}{\nu}_{\mu}\rightarrow\stackrel{\tiny{(-)}}{\nu}_e$ oscillation approximation subject to non-standard matter effects. We assume those effects can be parametrized by an $L$-independent effective potential, $V_s=\pm A_s$, experienced only by an intermediate, non-weakly-interacting (sterile) neutrino state which we assume participates in the oscillation, where $+/-$ corresponds to neutrino/antineutrino propagation. We discuss the mathematical framework in which such oscillations arise in detail, and derive the relevant oscillation probability as a function of the vacuum oscillation parameters $\Delta m^2$ and $\sin^22\theta_{\mu e}$, and the matter effect parameter $A_s$. We are able to successfully fit all three data sets, including the MiniBooNE low energy excess, with the following best-fit model parameters: $\Delta m^2=0.47$ eV$^2$, $\sin^22\theta_{\mu e}=0.010$, and $A_s=2.0\times10^{-10}$ eV. The $\chi^2$-probability for the best fit corresponds to 21.6%, to be compared to 6.8% for a fit where $A_s$ has been set to zero, corresponding to a (3+1) sterile neutrino oscillation model. We find that the compatibility between the three data sets corresponds to 17.4%, to be compared to 2.3% for $A_s=0$. Finally, given the fit results, we examine consequences for reactor, solar, and atmospheric oscillations. For this paper, the presented model is empirically driven, but the results obtained can be directly used to investigate various phenomenological interpretations such as non-standard matter effects.