797 research outputs found

    Pseudo-Dirac neutrinos from flavour dependent CP symmetry

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    Discrete residual symmetries and flavour dependent CP symmetries consistent with them have been used to constrain neutrino mixing angles and CP violating phases. We discuss here role of such CP symmetries in obtaining a pseudo-Dirac neutrino which can provide a pair of neutrinos responsible for the solar splitting. It is shown that if (a) 3×33\times 3 Majorana neutrino matrix MνM_\nu is invariant under a discrete Z2×Z2Z_2\times Z_2 symmetry generated by S1,2S_{1,2}, (b) CP symmetry XX transform MνM_\nu as XTMνX=MνX^T M_\nu X=M_\nu^*, and (c) XX and S1,2S_{1,2} obey consistency conditions XS1,2X=S2,1X S_{1,2}^* X^\dagger=S_{2,1}, then two of the neutrino masses are degenerate independent of specific forms of XX, S1S_1 and S2S_2. Explicit examples of this result are discussed in the context of Δ(6n2)\Delta(6 n^2) groups which can also be used to constrain neutrino mixing matrix UU. Degeneracy in two of the masses does not allow complete determination of UU but it can also be fixed once the perturbations are introduced. We consider explicit perturbations which break Z2×Z2Z_2\times Z_2 symmetries but respect CP. These are shown to remove the degeneracy and provide a predictive description of neutrino spectrum. In particular, a correlation sin2θ23sinδCP=±Im[p]\sin 2\theta_{23}\sin\delta_{CP}=\pm {\rm Im}[p] is obtained between the atmospheric mixing angle θ23\theta_{23} and the CP violating phase δCP\delta_{CP} in terms of a group theoretically determined phase factor pp. Experimentally interesting case θ23=π4\theta_{23}=\frac{\pi}{4}, δCP=±π2\delta_{CP}=\pm \frac{\pi}{2} emerges for groups which predict purely imaginary pp. We present detailed predictions of the allowed ranges of neutrino mixing angles, phases and the lightest neutrino mass for three of the lowest Δ(6n2)\Delta(6 n^2) groups with n=2,4,6n=2,4,6.Comment: 17 pages, 4 figures; Minor modification, published versio

    Generalized μ\mu-τ\tau symmetry and discrete subgroups of O(3)

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    The generalized μ\mu-τ\tau interchange symmetry in the leptonic mixing matrix UU corresponds to the relations: Uμi=Uτi|U_{\mu i}|=|U_{\tau i}| with i=1,2,3i=1,2,3. It predicts maximal atmospheric mixing and maximal Dirac CP violation given θ130\theta_{13} \neq 0. We show that the generalized μ\mu-τ\tau symmetry can arise if the charged lepton and neutrino mass matrices are invariant under specific residual symmetries contained in the finite discrete subgroups of O(3)O(3). The groups A4A_4, S4S_4 and A5A_5 are the only such groups which can entirely fix UU at the leading order. The neutrinos can be (a) non-degenerate or (b) partially degenerate depending on the choice of their residual symmetries. One obtains either vanishing or very large θ13\theta_{13} in case of (a) while only A5A_5 can provide θ13\theta_{13} close to its experimental value in the case (b). We provide an explicit model based on A5A_5 and discuss a class of perturbations which can generate fully realistic neutrino masses and mixing maintaining the generalized μ\mu-τ\tau symmetry in UU. Our approach provides generalization of some of the ideas proposed earlier in order to obtain the predictions, θ23=π/4\theta_{23}=\pi/4 and δCP=±π/2\delta_{\rm CP} = \pm \pi/2.Comment: 18 page

    Fermion Masses in SO(10) Models

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    We examine many SO(10) models for their viability or otherwise in explaining all the fermion masses and mixing angles. This study is carried out for both supersymmetric and non-supersymmetric models and with minimal (10+126ˉ10+\bar{126}) and non-minimal (10+126ˉ+12010+\bar{126}+120) Higgs content. Extensive numerical fits to fermion masses and mixing are carried out in each case assuming dominance of type-II or type-I seesaw mechanism. Required scale of the B-L breaking is identified in each case. In supersymmetric case, several sets of data at the GUT scale with or without inclusion of finite supersymmetric corrections are used. All models studied provide quite good fits if the type-I seesaw mechanism dominates while many fail if the type-II seesaw dominates. This can be traced to the absence of the bb-τ\tau unification at the GUT scale in these models. The minimal non-supersymmetric model with type-I seesaw dominance gives excellent fits. In the presence of a 45H45_H and an intermediate scale, the model can also account for the gauge coupling unification making it potentially interesting model for the complete unification. Structure of the Yukawa coupling matrices obtained numerically in this specific case is shown to follow from a very simple U(1) symmetry and a Froggatt-Nielsen singlet.Comment: 31 pages, 9 Tables, 4 figure

    Quasi-degenerate neutrinos in SO(10)

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    Quark lepton universality inherent in grand unified theories based on SO(10)SO(10) gauge group generically leads to hierarchical neutrino masses. We propose a specific ansatz for the structure of Yukawa matrices in SO(10)SO(10) models which differ from this generic expectations and lead to quasi degenerate neutrinos through the type-I seesaw mechanism. Consistency of this ansatz is demonstrated through a detailed fits to fermion masses and mixing angles all of which can be explained with reasonable accuracy in a model which uses the Higgs fields transforming as 10,12010,120 and 126\overline{126} representations of SO(10)SO(10). The proposed ansatz is shown to follow from an extended model based on the three generations of the vector like fermions and an O(3)O(3) flavour symmetry. Successful numerical fits are also discussed in earlier proposed models which used combination of the type-I and type-II seesaw mechanisms for obtaining quasi degenerate neutrinos. Large neutrino mixing angles emerge as a consequence of neutrino mass degeneracy in both these cases.Comment: 12 page

    Implications of partially degenerate neutrinos at a high scale in the light of KamLAND and WMAP

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    Electroweak radiative corrections can generate the neutrino (mass)2^2 difference required for the large mixing angle solution (LMA) to the solar neutrino problem if two of the neutrinos are assumed degenerate at high energy. We test this possibility with the existing experimental knowledge of the low energy neutrino mass and mixing parameters. We derive restrictions on ranges of the high scale mixing matrix elements and obtain predictions for the low energy parameters required in order to get the LMA solution of the solar neutrino problem picked out by KamLAND. We find that in the case of standard model this is achieved only when the (degenerate) neutrino masses lie in the range (0.7-2) \eV which is at odds with the cosmological limit m_{\nu}<0.23 \eV (at 9595 % C.L) established recently using WMAP results. Thus SM radiative corrections cannot easily generate the LMA solution in this scenario. However, the LMA solution is possible in case of the MSSM electroweak corrections with (almost) degenerate spectrum or with inverted mass hierarchy for limited ranges in the high scale parameters.Comment: 15 pages, LATEX includes five postscript figure
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