Theoretical Overview on the Flavor Issues of Massive Neutrinos

We present an overview on some basic properties of massive neutrinos and focus on their flavor issues, including the mass spectrum, flavor mixing pattern and CP violation. The lepton flavor structures are explored by taking account of the observed value of the smallest neutrino mixing angle \theta_{13}. The impact of \theta_{13} on the running behaviors of other flavor mixing parameters is discussed in some detail. The seesaw-induced enhancement of the electromagnetic dipole moments for three Majorana neutrinos is also discussed in a TeV seesaw scenario.Comment: References added. arXiv admin note: text overlap with arXiv:1203.1672, arXiv:1201.2543, arXiv:1203.311

First determination of the Jarlskog invariant of CP violation from the moduli of the CKM matrix elements

We find that the precision and accuracy of current experimental data on the moduli of nine Cabibbo-Kobayashi-Maskawa (CKM) quark flavor mixing matrix elements allows us to numerically determine the correct size of the Jarlskog invariant of CP violation from four of them in eight different ways for the first time. This observation implies a remarkable self-consistency of the correlation between CP-conserving and CP-violating quantities of the CKM matrix as guaranteed by its unitarity.Comment: 8 page

Resolving the octant of theta_{23} via radiative mu-tau symmetry breaking

We point out that the observed neutrino mixing pattern at low energies is very likely to originate from the 3 times 3 lepton flavor mixing matrix U which possesses the exact mu-tau permutation symmetry |U_{mu i}| = |U_{tau i}| (for i=1,2,3) at a superhigh energy scale Lambda_{mu tau} \sim 10^{14} GeV. The deviation of theta_{23} from 45^\circ and that of delta from 270^\circ in the standard parametrization of U are therefore a natural consequence of small mu-tau symmetry breaking via the renormalization-group equations (RGEs) running from Lambda_{mu tau} down to the electroweak scale Lambda_{EW} \sim 10^2 GeV. In fitting current experimental data we find that the RGE-corrected value of theta_{23} is uniquely correlated with the neutrino mass ordering: theta_{23} \simeq 42.4^\circ reported by Capozzi et al (or theta_{23} \simeq 48.9^\circ reported by Forero et al) at Lambda_{EW} can arise from theta_{23} = 45^\circ at Lambda_{mu tau} in the minimal supersymmetric standard model if the neutrino mass ordering is inverted (or normal). Accordingly, the preliminary best-fit results of delta at Lambda_{EW} can also evolve from delta = 270^\circ at Lambda_{mu tau} no matter whether the massive neutrinos are Dirac or Majorana particles.Comment: 12 pages, 3 tables, 2 figures, minor changes, references updated, accepted for publication in Phys. Rev.

A Pythagoras-like theorem for CP violation in neutrino oscillations

It is well known that the golden appearance channels of neutrino oscillations are $\nu^{}_{\mu} \to \nu^{}_{e}$ and $\overline{\nu}^{}_{\mu} \to \overline{\nu}^{}_{e}$, and their probabilities in vacuum are determined by three CP-conserving flavor mixing factors ${\cal R}^{}_{ij} \equiv {\rm Re} (U^{}_{\mu i} U^{}_{e j} U^{*}_{\mu j} U^{*}_{e i})$ and the universal Jarlskog invariant of CP violation ${\cal J}^{}_{\nu} \equiv (-1)^{i+j} {\rm Im} (U^{}_{\mu i} U^{}_{e j} U^{*}_{\mu j} U^{*}_{e i})$ (for $i, j = 1, 2, 3$ and $i < j$) with $U$ being the $3 \times 3$ Pontecorvo-Maki-Nakagawa-Sakata matrix. We show that the magnitude of ${\cal J}^{}_{\nu}$ can be calculated from ${\cal J}^{2}_{\nu} = {\cal R}^{}_{12} {\cal R}^{}_{13} + {\cal R}^{}_{12} {\cal R}^{}_{23} + {\cal R}^{}_{13} {\cal R}^{}_{23}$ which holds as a natural consequence of the unitarity of $U$, and this Pythagoras-like relation provides a novel cross-check of the result of ${\cal J}^{}_{\nu}$ that will be directly measured in the next-generation $\nu^{}_{\mu} \to \nu^{}_{e}$ and $\overline{\nu}^{}_{\mu} \to \overline{\nu}^{}_{e}$ oscillation experiments. Terrestrial matter effects on ${\cal J}^{}_{\nu}$ and ${\cal R}^{}_{ij}$ are also discussed.Comment: 14 pages, 6 figure

Impacts of the observed theta_{13} on the running behaviors of Dirac and Majorana neutrino mixing angles and CP-violating phases

The recent observation of the smallest neutrino mixing angle $\theta_{13}$ in the Daya Bay and RENO experiments motivates us to examine whether $\theta_{13} \simeq 9^\circ$ at the electroweak scale can be generated from $\theta_{13} = 0^\circ$ at a superhigh-energy scale via the radiative corrections. We find that it is difficult but not impossible in the minimal supersymmetric standard model (MSSM), and a relatively large $\theta_{13}$ may have some nontrivial impacts on the running behaviors of the other two mixing angles and CP-violating phases. In particular, we demonstrate that the CP-violating phases play a crucial role in the evolution of the mixing angles by using the one-loop renormalization-group equations of the Dirac or Majorana neutrinos in the MSSM. We also take the "correlative" neutrino mixing pattern with $\theta_{12} \simeq 35.3^\circ$, $\theta_{23} = 45^\circ$ and $\theta_{13} \simeq 9.7^\circ$ at a presumable flavor symmetry scale as an example to illustrate that the three mixing angles can receive comparably small radiative corrections and thus evolve to their best-fit values at the electroweak scale if the CP-violating phases are properly adjusted.Comment: RevTeX 16 pages, 3 figures, 4 tables, more discussions added, references updated. Accepted for publication in Phys. Rev.