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Register a new userGeneralized Friedberg-Lee model for neutrino masses and leptonic CP violation from mu-tau symmetry breaking
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Assuming the Majorana nature of massive neutrinos, we generalize the Friedberg-Lee neutrino mass model to include CP violation in the neutrino mass matrix M_ u. The most general case with all the free parameters of M_ u being complex is discussed. We show that a favorable neutrino mixing pattern (with theta_12 approx 35.3^circ, theta_23=45^circ, theta_13 eq 0^circ and delta=90^circ) can naturally be derived from M_ u, if it has an approximate or softly-broken mu-tau symmetry. We also point out a different way to obtain the nearly tri-bimaximal neutrino mixing pattern with delta=0^circ and non-vanishing Majorana phases.
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The $mu$-$tau$ exchange symmetry in the neutrino mass matrix and its breaking as a perturbation are discussed. The exact $mu$-$tau$ symmetry restricts the 2-3 and 1-3 neutrino mixing angles as $theta_{23} = pi/4$ and $theta_{13} = 0$ at a zeroth order level. We claim that the $mu$-$tau$ symmetry breaking prefers a large CP violation to realize the observed value of $theta_{13}$ and to keep $theta_{23}$ nearly maximal, though an artificial choice of the $mu$-$tau$ breaking can tune $theta_{23}$, irrespective of the CP phase. We exhibit several relations among the deviation of $theta_{23}$ from $pi/4$, $theta_{13}$ and Dirac CP phase $delta$, which are useful to test the $mu$-$tau$ breaking models in the near future experiments. We also propose a concrete model to break the $mu$-$tau$ exchange symmetry spontaneously and its breaking is mediated by the gauge interactions radiatively in the framework of the extended gauge model with $B-L$ and $L_mu - L_tau$ symmetries. As a result of the gauge mediated $mu$-$tau$ breaking in the neutrino mass matrix, the artificial choice is unlikely, and a large Dirac CP phase is preferable.
We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the FL symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via see-saw mechanism. If the right-handed neutrinos transform non-trivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale see-saw mechanism. Second, we present two models with the $SO(3)times U(1)$ global flavour symmetry in the lepton sector. After the flavour symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via see-saw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the $SO(3)times U(1)$ flavour symmetry breaking.
We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the Standard Model with a generalized supersymmetry breaking sector. If the usual superpotential Yukawa couplings are forbidden by the additional gauge symmetry (such as a U(1)), effective Dirac mass terms involving the wrong Higgs field can arise either at tree level due to hard supersymmetry breaking fermion Yukawa couplings, or at one-loop due to nonanalytic or nonholomorphic soft supersymmetry breaking trilinear scalar couplings. As both of these operators are naturally suppressed in generic models of supersymmetry breaking, the resulting neutrino masses are naturally in the sub-eV range. The neutrino magnetic and electric dipole moments resulting from the radiative mechanism also vanish at one-loop order.
The neutrino masses and mixings indicated by current neutrino oscillation experiments suggest that the neutrino mass matrix possesses an approximate $mu-tau$ exchange symmetry. In this study, we explore the neutrino parameter space and show that if a small $mu-tau$ symmetry breaking is considered, the Majorana $CP$ phases must be unequal and non-zero independently of the neutrino mass scale. Moreover, a small $mu-tau$ symmetry breaking favors quasi-degenerate masses. We also show that Majorana phases are strongly correlated with the Dirac $CP$ violating phase. Within this framework, we obtain robust predictions for the values of the Majorana phases when the experimental indications for the Dirac $CP$ phase are used.
We perform a global analysis of neutrino oscillation data, including high-precision measurements of the neutrino mixing angle theta_13 at reactor experiments, which have confirmed previous indications in favor of theta_13>0. Recent data presented at the Neutrino 2012 Conference are also included. We focus on the correlations between theta_13 and the mixing angle theta_23, as well as between theta_13 and the neutrino CP-violation phase delta. We find interesting indications for theta_23< pi/4 and possible hints for delta ~ pi, with no significant difference between normal and inverted mass hierarchy.
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