Matter-induced T-invariance violation in neutrino oscillations requires an asymmetric matter potential along the neutrino path, and for Earth-bound experiments the effect is numerically tiny.
Leptonic commutators and clean T violation in neutrino oscillations
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abstract
A realistic medium- or long-baseline neutrino experiment may suffer from terrestrial matter effects which are likely to contaminate the genuine T-violating asymmetry between \nu_\alpha \to \nu_\beta and \nu_\beta \to \nu_\alpha oscillations. With the help of the commutators of lepton mass matrices in matter, we show that this kind of contamination is negligible for a variety of experiments provided the neutrino beam energy E and the baseline length L satisfy the condition 10^{-7} (L/km)^2 (GeV/E) << 1. The same observation is true for the CP-violating term of the asymmetry between \nu_\alpha \to \nu_\beta and \bar{\nu}_\alpha \to \bar{\nu}_\beta oscillations in matter.
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On T-Invariance Violation in Neutrino Oscillations and Matter Effects
Matter-induced T-invariance violation in neutrino oscillations requires an asymmetric matter potential along the neutrino path, and for Earth-bound experiments the effect is numerically tiny.