Abstract
The exponential parameterization of Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrino is discussed. The exponential form allows easy factorization and separate analysis of the CP-violating and Majorana terms. Based upon the recent experimental data on the neutrino mixing, the values for the exponential parameterization matrix for neutrinos are determined. The matrix entries for the pure rotational part in charge of the mixing without CP-violation are derived. The complementarity hypothesis for quarks and neutrinos is demonstrated. The comparison of the results, based on most recent and on old data is held. The CP-violating parameter value is estimated, based on the so far imprecise experimental indications, regarding CP-violation for neutrinos. The unitarity of the exponential parameterisation and the CP-violating term transform is confirmed. The transform of the neutrino mass state vector by the exponential matrix with account for CP-violation is shown.
Highlights
I =1,2,3 where VP M N S is the unitary PMNS mixing matrix [11]
Note that the obtained value of 44◦ differs from 45◦ by ≈2 %, which is within the margin of errors of the original experimental data sets, which determines the entries of the exponential mixing matrix and the rotation vectors directions
The exponential parameterization of the mixing matrix for neutrinos is explored with account of the present experimental data
Summary
I =1,2,3 where VP M N S is the unitary PMNS mixing matrix [11]. L ton mixing presumes that a charged W-boson can couple to any mass state of charged leptons (e, μ, τ ) with any mass state of neutrino. The PMNS matrix is fully determined by four parameters: three mixing angles θ12, θ23, θ13, and the phase δ, in charge of the CP violation description [15]. The experimental values of the mixing angles are relatively well determined [15,16,21–. Contrary to quark mixing angles, these are not small and the expansion in series of the only small parameter is not possible. Determined absolute values for the elements of the PMNS matrix read as follows [15]:. There are indications that the CP-violating phase may have a non-zero value; very approximately it is supposed to be as large as δ ≈ 300◦ (see [26,27])
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