By Akhmedov
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90). Notice that Ve and Vµ contain a common term due to NC interactions. As we already know, such common terms in the diagonal elements are of no consequence for neutrino oscillations; we can therefore omit them 6 . This gives √ 2 ∆m2 d νe − ∆m cos 2θ + 2 G F Ne sin 2θ0 νe 0 4E 4E . (91) = i ∆m2 ∆m2 ν ν dt sin 2θ0 cos 2θ0 µ µ 4E 4E This is the evolution equation which describes νe ↔ νµ oscillations in matter. The equation for νe ↔ ντ oscillations has the same form. In the two-flavour approximation, νµ ↔ ντ oscillations are not modified in matter since Vµ = Vτ ; however, in the full 3-flavour framework matter does influence the νµ ↔ ντ oscillations because of the mixing with νe , see sec.
76)-(78) are recovered. As we have already discussed, matter affects neutrino and antineutrino oscillations differently: for cos 2θ0 > 0 and ∆m2 > 0, it can enhance oscillations of neutrinos but always suppresses oscillations of antineutrinos, whereas in the case ∆m2 < 0 the situation is opposite. e. matter induces the CP violating effects. This is because the usual matter is itself CP (and also C and CPT) asymmetric since it consists of particles and not of antiparticles, or in general not of equal number of particles and antiparticles.
100) ceases to be valid. Similar situation takes place in the case of neutrino oscillations in a matter of constant density: if the MSW resonance condition is satisfied, the oscillation amplitude sin2 2θ0 = 1, no matter how small θ0; however, in the limit θ0 → 0 the phase of the second sin2 factor in eq. (95) vanishes, and no oscillations occur. We shall now turn to a more quantitative description of the neutrino conversion in the adiabatic regime, which will also allow us to establish the domain of applicability of the adiabatic approximation.