Using MiniBooNE neutral current elastic cross section results to constrain 3+1 sterile neutrino models

The MiniBooNE Neutral Current Elastic (NCEL) cross section results are used to extract limits in the $\Delta m^{2}-\sin^{2}\vartheta_{\mu s}$ plane for a 3+1 sterile neutrino model with a mass splitting $0.1 \leq \Delta m^{2} \leq 10.0$ eV$^{2}$. GENIE is used with a cross section model close to the one employed by MiniBooNE to make event rate predictions using simulations on the MiniBooNE target material CH$_{2}$. The axial mass is a free parameter in all fits. Sterile modifications to the flux and changes to the cross section in the simulation relate the two and allow limits to be set on sterile neutrino mixing using cross section results. The large axial mass problem makes it necessary for experiments to perform their own axial mass fits, but a prior fit to the same dataset could mask a sterile oscillation signal if the sterile and cross section model parameters are not independent. We find that for the NCEL dataset there are significant correlations between the sterile and cross section model parameters, making a fit to both models simultaneously necessary to get robust results. Failure to do this results in stronger than warranted limits on the sterile parameters. The general problems that the current uncertainty on charged-current quasi-elastic (CCQE) and NCEL cross sections at MiniBooNE energies pose for sterile neutrino measurements are discussed.