LeptonicCPviolation studies at MiniBooNE in the (3+2) sterile neutrino oscillation hypothesis

We investigate the extent to which leptonic $CP$-violation in ($3+2$) sterile neutrino models leads to different oscillation probabilities for ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{e}$ and ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e}$ oscillations at MiniBooNE. We are using a combined analysis of short-baseline (SBL) oscillation results, including the LSND and null SBL results, to which we impose additional constraints from atmospheric oscillation data. We obtain the favored regions in MiniBooNE oscillation probability space for both ($3+2$) $CP$-conserving and ($3+2$) $CP$-violating models. We further investigate the allowed $CP$-violation phase values and the MiniBooNE reach for such a $CP$ violation measurement. The analysis shows that the oscillation probabilities in MiniBooNE neutrino and antineutrino running modes can differ significantly, with the latter possibly being as much as 3 times larger than the first. In addition, we also show that all possible values of the single $CP$-violation phase measurable at short baselines in ($3+2$) models are allowed within 99% CL by existing data.