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In our recent paper [1] we formulated a predictive theory of neutrino masses by considering the interaction between the infrared sector of the effective theory of quantum gravity and the standard model fields. This allowed us to calculate, for the first time in the history of neutrino physics, the absolute scale of neutrino masses. From this theoretical framework, we obtained quantum-gravitational couplings/effective Majorana dimensionless couplings from the spherically symmetric vacuum solutions arising from the Bose-Einstein statistical modification to gravitation. In the present paper, we show that the same solutions can be obtained directly from the quantum interpretation of gravitational radiation arising from the thermodynamic modification to gravitation. Within this theoretical scheme, we show that the single-field inflationary model, GUTs, dark energy and matter-independent gravitational field of vacuum are all connected to the neutrino mass model.
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This years Physics Nobel prize for the discovery of neutrino oscillations which resolved the problem of the missing solar neutrinos and the atmospheric muon neutrinos implies that at least one of the three neutrino species has a tiny mass. The neutrino oscillations measure the mass difference squared, and the individual neutrino masses have yet to be accurately ascertained. Particle theory has so far not given a predictive picture for neutrino masses. Here we propose that the anthropic principle may be relevant, as it is frequently invoked to understand other aspects of the universe, including the precise values of fine structure constant or nuclear coupling constant or even the proton-electron mass ratio.
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 look for predictive flavour patterns of the effective Majorana neutrino mass matrix that are compatible with current neutrino oscillation data. Our search is based on the assumption that the neutrino mass matrix contains equal elements and a minimal number of parameters, in the flavour basis where the charged lepton mass matrix is diagonal and real. Three unique patterns that can successfully explain neutrino observables at the $3sigma$ confidence level with just three physical parameters are presented. Neutrino textures described by four and five parameters are also studied. The predictions for the lightest neutrino mass, the effective mass parameter in neutrinoless double beta decays and the CP-violating phases in the leptonic mixing are given.
We study a model for the mass matrices of the leptons. We are ablte to relate the mass eigenvalues of the charged leptons and of the neutrinos to the mxiing 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 of the neutrinos. We find 38 degrees, consistent with the experiments. The mixing element, connecting the first neutrino with the electron, is found to be 0.05.
The various experiments on neutrino oscillation evidenced that neutrinos have indeed non-zero masses but cannot tell us the absolute neutrino mass scale. This scale of neutrino masses is very important for understanding the evolution and the structure formation of the universe as well as for nuclear and particle physics beyond the present Standard Model. Complementary to deducing constraints on the sum of all neutrino masses from cosmological observations two different methods to determine the neutrino mass scale in the laboratory are pursued: the search for neutrinoless double $beta$-decay and the direct neutrino mass search by investigating single $beta$-decays or electron captures. The former method is not only sensitive to neutrino masses but also probes the Majorana character of neutrinos and thus lepton number violation with high sensitivity. Currently quite a few experiments with different techniques are being constructed, commissioned or are even running, which aim for a sensitivity on the neutrino mass of {cal O}(100) meV. The principle methods and these experiments will be discussed in this short review.
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