Abstract
The exponential parameterization of Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrino is used for comparative analysis of different neutrino mixing data. The UPMNS matrix is considered as the element of the SU(3) group and the second order matrix polynomial is constructed for it. The inverse problem of constructing the logarithm of the mixing matrix is addressed. In this way the standard parameterization is related to the exponential parameterization exactly. The exponential form allows easy factorization and separate analysis of the rotation and the CP violation. With the most recent experimental data on the neutrino mixing (May 2016), we calculate the values of the exponential parameterization matrix for neutrinos with account for the CP violation. The complementarity hypothesis for quarks and neutrinos is demonstrated to hold, despite significant change in the neutrino mixing data. The values of the entries of the exponential mixing matrix are evaluated with account for the actual degree of the CP violation in neutrino mixing and without it. Various factorizations of the CP violating term are investigated in the framework of the exponential parameterization.
Highlights
Mixing in the lepton sector of the Standard Model (SM) means that a charged W-boson interacts with mass states of charged leptons e, μ, τ and with neutrino states ν1, ν2, ν3
With the most recent data on the CP violation in the lepton sector [51] this approach yields the entries for the unitary mixing matrix, which deviate far from the experimental values. To overcome this difficulty of the exponential parameterization with complex exponents in just the (1, 3) and (3, 1) entries, we develop in the following a precise account for the CP violation by means of the matrix logarithm technique, described in Sect
The exponential parameterization of the mixing matrix for the neutrinos is applied for the comparative analysis of the mixing data from tri-bimaximal parameterization, data of the year 2014 and May 2016, the latter with account for the CP violation
Summary
I =1,2,3 to the way it is done for quarks by the CKM matrix. Mixing in the lepton sector of the SM means that a charged W-boson interacts with mass states of charged leptons e, μ, τ and with neutrino states ν1, ν2, ν3. The authors discussed the unified description between different kinds of parameterizations for quark and lepton sectors: the standard parameterizations, the Wolfenstein-like parameterizations and the triminimal parameterizations in the context of the quark–lepton complementarity (QLC) hypothesis [21,30]. The latter consists in the phenomenological relations of quark and lepton mixing angles θqi j and θi j in the standard parameterization: θ12 + θq12 = 45◦, θ23 + θq23 = 45◦. The exponential parameterization for quarks was proposed in [36]; a very similar parameterization for neutrinos was studied in [35] in the following form: Uexp = exp A,.
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