CP - and T - Violating Effects in Neutrino Oscillations ? 1 Feb 1999

Neutrino oscillations with three families of leptons are described with the help of a unitary neutrino mixing matrix U in analogy to the Standard Model quark mixing with the CKM matrix. If U contains a nontrivial phase and if all three neutrino mass eigenstates have a different mass, there will be CP-and T-violating asymmetries at distances L which are large compared to E/D 2 , where D 2 is the largest difference of neutrino mass squares. We give explicit expressions for these L-dependent asymmetries in a frame which is able to describe the present solar and atmospheric oscillation observations. The recent strong evidence for neutrino oscillations in atmospheric neutrino production [1] has amplified the interest in the basic properties of these oscillations. The observed strength of the neutral weak interaction of atmospheric neutrinos, in the π 0 /e ratio [2], does not require the assumption of sterile neutrinos but allows a complete description in an extended Standard Model of elementary particles. Without changing anything in the principles of the model, the extension can easily be made by adding three SU(2) singlets of right-handed neutrinos — ν eR , ν µR , and ν τ R — to the set of elementary fermions. This leads to a fourth mass matrix M ν in addition to M ℓ , M Q , and M q for charged leptons ℓ, up-and down-type quarks Q and q. The diagonalization of M ℓ leads to the Yukawa term m e ee + m µ µµ + m τ τ τ in the Lagrangian, and M ν cannot be diagonalized at the same time. The SU(2) partners of e, µ, and τ have to be linear superpositions of mass eigenstates ν 1 , ν 2 , and ν 3. In very close analogy to the CKM matrix of quark mixing [3, 4], the right-handed neutrino singlet fields require a unitary transformation U between the two triplets in family space,