LSND, SN1987A, and CPT violation

We point out that neutrino events observed at Kamiokande and IMB from SN1987A disfavor the neutrino oscillation parameters preferred by the LSND experiment. For Δm2>0 (the light side), the electron neutrinos from the neutronization burst would be lost, while the first event at Kamiokande is quite likely to be due to an electron neutrino. For Δm2<0 (the dark side), the average energy of the dominantly ν̄e events is already lower than the theoretical expectations, which would get aggravated by a complete conversion from ν̄μ to ν̄e. If taken seriously, the LSND data are disfavored independent of the existence of a sterile neutrino. A possible remedy is CPT violation, which allows different mass spectra for neutrinos and anti-neutrinos and hence can accommodate atmospheric, solar and LSND data without a sterile neutrino. If this is the case, Mini-BooNE must run in ν̄ rather than the planned ν mode to test the LSND signal. We speculate on a possible origin of CPT violation.