In TGD framework padic length scale hypothesis might explain these findings. I wrote already earlier hasty impressions about the situation but found that there were too many misunderstanding involved so that I decided to remove the blog page in a desperate attempt to keep some of my respectability (of course I know that I have lost it long time ago so that the manouvre came quite too late);-).
The basic vision is that the p-adic length scale of neutrino can vary so that the mass squared scale comes as octaves. Mixing matrices would be universal. The large discrepancy between LSND and MiniBoone results contra solar neutrino results could be understood if electron and muon neutrinos have same p-adic mass scale for solar neutrinos but for LSND and MiniBoone the mass scale of either neutrino type is scaled up. The sterile neutrino suggested as an explanation of the findings would be p-adically scaled up variant of ordinary neutrino having standard weak interactions. This scaling up can be different for neutrinos and antineutrinos as suggested by the fact that the anomaly is present only for antineutrinos.
The different values of Δ m2 for neutrinos and antineutrinos in MINOS experiment can be understood if the p-adic mass scale for neutrinos increases by one unit. The breaking of CP and CPT would be spontaneous and realized as a choice of different p-adic mass scales and could be understood in zero energy ontology. Similar mechanism would break supersymmetry and explain large differences between the mass scales of elementary fermions, which for same p-adic prime would have mass scales differing not too much.
I do not bother to type the formulas in html format and give a link to a short pdf file Could neutrinos appear in several p-adic mass scales?, where a serious analysis of the findings is discussed. See also the chapter p-Adic Mass calculations: New Physics of "p-Adic Length scale Hypothesis and Dark Matter Hierarchy".