CPT violating neutrinos in the light of KamLAND and Super-K
  We show that a hierarchical CPT violating neutrino spectrum can simultaneously accommodate all published neutrino data, including the LSND result, with a total chi^2 which is almost identical to the CPT conserving best fit. In our scenario the oscillation signal seen by the KamLAND experiment in antineutrinos is independent of the LMA solar oscillation signal seen in neutrinos. A larger antineutrino mass splitting accounts for the LSND signal and also contributes to atmospheric oscillations. Because of this feature, there is some tension between our model and certain Super-K atmospheric results. Thus, if LSND did not exist, our model would survive only at the 99% confidence level; with LSND, our model is (essentially) statistically equivalent to the CPT conserving best fit. 
G. Barenboim, L. Borissov, and J. Lykken