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Register a new userLeptonic CP phases near the $mu-tau$ symmetric limit
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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.
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A sterile neutrino in the $3+1$ scheme, where the sterile accounts for neutrino anomalies not explained solely by the weak active neutrinos, arises as a natural source for the breaking of the $mu-tau$ symmetry suggested by oscillation neutrino data. We explore the predictions for the Dirac CP phases in this scenario, with and without sterile neutrino decay, and show that current limits on $delta_{CP}$ suggest a normal hierarchy and a lightest neutrino scale below 0.1~eV as the most plausible explanation for that, when Majorana phases are null. Other Dirac phases turn out to be non zero as well.
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.
The branching fractions of radiative leptonic $tau$ decays $(tau to l u bar{ u} gamma$, $l=e,mu)$ were recently measured by the Babar collaboration with a relative error of about 3%. The measurement of the branching ratio $mathcal{B} (tau to e bar{ u} u gamma)$, for a minimum photon energy of 10 MeV in the $tau$ rest frame, differs from our recent SM prediction by 3.5 standard deviations, whereas our result agrees with Babars value for $mathcal{B} (tau to mu bar{ u} u gamma)$. Our predictions also agree with the measurement of $mathcal{B} (mu to e bar{ u} u gamma)$ by the MEG collaboration. We also report on a recent proposal to test the $tau$ dipole moments via precise measurements of radiative leptonic $tau$ decays at high-luminosity $B$ factories.
We analyze the CP violation in the semileptonic | Delta S|=1 tau-decays in supersymmetric extensions of the standard model (SM) with R parity violating term. We show that the CP asymmetry of tau-decay is enhanced significantly and the current experimental limits obtained by CLEO collaborations can be easily accommodated. We argue that observing CP violation in semi leptonic tau-decay would be a clear evidence for R-parity violating SUSY extension of the SM.
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.
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