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Register a new userRenormalisable SO(10) models and neutrino masses and mixing
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We discuss some recent developments in SUSY Grand Unified Theories based on the gauge group SO(10). Considering renormalisable Yukawa couplings, we present ways to accommodate quark and lepton masses and and mixings.
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Assuming a Zee-like matrix for the right-handed neutrino Majorana masses in the see-saw mechanism, one gets maximal mixing for vacuum solar oscillations, a very small value for $U_{e3}$ and an approximate degeneracy for the two lower neutrino masses. The scale of right-handed neutrino Majorana masses is in good agreement with the value expected in a SO(10) model with Pati-Salam $SU(4)ts SU(2)ts SU(2)$ intermediate symmetry.
We report on the extrapolation of scalar mass parameters in the lepton sector to reconstruct SO(10) scenarios close to the unification scale. The method is demonstrated for an example in which SO(10) is broken directly to the Standard Model, based on the expected precision from coherent LHC and ILC collider analyses. In addition to the fundamental scalar mass parameters at the unification scale, the mass of the heaviest right-handed neutrino can be estimated in the seesaw scenario.
We discuss first the flavor mixing of the quarks, using the texture zero mass matrices. Then we study a similar model for the mass matrices of the leptons. We are able to relate the mass eigenvalues of the charged leptons and of the neutrinos to the mixing angles and can predict the masses of the neutrinos. We find a normal hierarchy - the masses are 0.004 eV, 0.01 eV and 0.05 eV. The atmospheric mixing angle is given by the mass ratios of the charged leptons and the neutrinos. we find about 40 degrees, consistent with the experiments. The mixing element, connecting the first neutrino wit the electron, is predicted to be 0.05. This prediction can soon be checked by the Daya Bay experiment.
We discuss the neutrino oscillations, using texture zero mass matrices for the leptons. The reactor mixing angle $theta^{}_{l}$ is calculated. The ratio of the masses of two neutrinos is determined by the solar mixing angle. We can calculate the masses of the three neutrinos: $m_1$ $approx$ 0.003 eV - $m_2$ $approx$ 0.012 eV - $m_3$ $approx$ 0.048 eV.
We discuss mass matrices with four texture zeros for the quarks and leptons. The three mixing angles for the quarks and leptons are functions of the fermion masses. The results agree with the experimental data. The ratio of the masses of the first two neutrinos is given by the solar mixing angle. The neutrino masses are calculated: $m_1$ $approx$ 0.004 eV, $m_2$ $approx$ 0.010 eV, $m_3$ $approx$ 0.070 eV.
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