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T violation in neutrino oscillations in matter

We consider the interplay of fundamental and matter-induced T violation effects in neutrino oscillations in matter. After discussing the general features of these effects we derive a simple approximate analytic expression for the T-violating probability asymmetry ΔP^T_{ab} for three-flavour neutrino oscillations in a matter with an arbitrary density profile in terms of the two-flavour neutrino amplitudes. Explicit examples are given for the cases of a two-layer medium and for the adiabatic limit in the general case. We then discuss implications of the obtained results for long baseline experiments. We show, in particular, that asymmetric matter effects cannot hinder the determination of the fundamental CP and T-violating phase δ_{CP} in the long baseline experiments as far as the error in this determination is larger than 1% at 99% C.L. Since there are no T-violating effects in the two-flavour case, and in the limits of vanishing θ_{13} or Δm_{21}^2 the three-flavour neutrino oscillations effectively reduce to the two-flavour ones, studying the T-violating asymmetries ΔP^T_{ab} can in principle provide us with a complementary means of measuring θ_{13} and Δm_{21}^2.