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Register a new userHierarchical majorana neutrinos from democratic mass matrices
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Masaki J. S. Yang
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In this paper, we obtain the light neutrino masses and mixings consistent with the experiments, in the democratic texture approach. The essential ansatz is that $ u_{Ri}$ are assumed to transform as right-handed fields $bf 2_{R} + 1_{R}$ under the $S_{3L} times S_{3R}$ symmetry. The symmetry breaking terms are assumed to be diagonal and hierarchical. This setup only allows the normal hierarchy of the neutrino mass, and excludes both of inverted hierarchical and degenerated neutrinos. Although the neutrino sector has nine free parameters, several predictions are obtained at the leading order. When we neglect the smallest parameters $zeta_{ u}$ and $zeta_{R}$, all components of the mixing matrix $U_{rm PMNS}$ are expressed by the masses of light neutrinos and charged leptons. From the consistency between predicted and observed $U_{rm PMNS}$, we obtain the lightest neutrino masses $m_{1}$ = (1.1 $to$ 1.4) meV, and the effective mass for the double beta decay $vev{m_{ee}} simeq$ 4.5 meV.
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In this work we analyze the corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining large reactor mixing angle $theta_{13}$ and checking the consistency with other neutrino mixing angles. The corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrix of the form $R_{ij}cdot U cdot R_{kl}$ where $R_{ij}$ is rotation in ij sector and U is any one of these special matrices. We showed the rotations $R_{13}cdot U cdot R_{23}$, $R_{12}cdot U cdot R_{13}$ for BM and $R_{13}cdot U cdot R_{13}$ for TBM perturbative case successfully fit all neutrino mixing angles within $1sigma$ range. The perturbed PMNS matrix $R_{12}cdot U cdot R_{13}$ for DC, TBM and $R_{23}cdot U cdot R_{23}$ for TBM case is successful in producing mixing angles at 2$sigma$ level. The other rotation schemes are either excluded or successful in producing mixing angles at $3sigma$ level.
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The Majorana neutrino $psi_{M}(x)$ when constructed as a superposition of chiral fermions such as $ u_{L} + Coverline{ u_{L}}^{T}$ is characterized by $ ({cal C}{cal P}) psi_{M}(x)({cal C}{cal P})^{dagger} =igamma^{0}psi_{M}(t,-vec{x})$, and the CP symmetry describes the entire physics contents of Majorana neutrinos. Further specifications of C and P separately could lead to difficulties depending on the choice of C and P. The conventional $ {cal C} psi_{M}(x) {cal C}^{dagger} = psi_{M}(x)$ with well-defined P is naturally defined when one constructs the Majorana neutrino from the Dirac-type fermion. In the seesaw model of Type I or Type I+II where the same number of left- and right-handed chiral fermions appear, it is possible to use the generalized Pauli-Gursey transformation to rewrite the seesaw Lagrangian in terms of Dirac-type fermions only; the conventional C symmetry then works to define Majorana neutrinos. In contrast, the pseudo C-symmetry $ u_{L,R}(x)rightarrow Coverline{ u_{L,R}(x)}^{T}$ (and associated pseudo P-symmetry), that has been often used in both the seesaw model and Weinbergs model to describe Majorana neutrinos, attempts to assign a nontrivial charge conjugation transformation rule to each chiral fermion separately. But this common construction is known to be operatorially ill-defined and, for example, the amplitude of the neutrinoless double beta decay vanishes if the vacuum is assumed to be invariant under the pseudo C-symmetry.
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