Neutrino oscillation data strongly support µ−τ symmetry as a good approximate flavor symmetry of the neutrino sector, which has to appear in any viable theory for neutrino mass-generation. The µ−τ breaking is not only small, but also the source of Dirac CP-violation. We conjecture that both discrete µ−τ and CP symmetries are fundamental symmetries of the seesaw Lagrangian (respected by interaction terms), and they are only softly broken, arising from a common origin via a unique dimension-3 Majorana mass-term of the heavy right-handed neutrinos. From this conceptually attractive and simple construction, we can predict the soft µ−τ breaking at low energies, leading to quantitative correlations between the apparently two small deviations θ 23 − 45 • and θ 13 − 0 • . This nontrivially connects the on-going measurements of mixing angle θ 23 with the upcoming experimental probes of θ 13 . We find that any deviation of θ 23 − 45 • must put a lower limit on θ 13 . Furthermore, we deduce the low energy Dirac and Majorana CP violations from a common soft-breaking phase associated with µ−τ breaking in the neutrino seesaw. Finally, from the soft CP breaking in neutrino seesaw we derive the cosmological CP violation for the baryon asymmetry via leptogenesis. We fully reconstruct the leptogenesis CP-asymmetry from the low energy Dirac CP phase and establish a direct link between the cosmological CP-violation and the low energy Jarlskog invariant. We predict new lower and upper bounds on the θ 13 mixing angle,• . In addition, we reveal a new hidden symmetry that dictates the solar mixing angle θ 12 by its group-parameter, and includes the conventional tri-bimaximal mixing as a special case, allowing deviations from it.

Existence of a mirror world in the universe is a fundamental way to restore the observed parity violation in weak interactions and provides the lightest mirror nucleon as a unique GeV-scale dark matter particle candidate. The visible and mirror worlds share the same spacetime of the universe and are connected by a unique space-inversion symmetry -the mirror parity (P ). We conjecture that the mirror parity is respected by the fundamental interaction Lagrangian, and study its spontaneous breaking from minimizing the Higgs vacuum potential. The domain wall problem is resolved by a unique soft breaking linear-term from the P -odd weak-singlet Higgs field. We also derive constraint from the Big-Bang nucleosynthesis. We then analyze the neutrino seesaw for both visible and mirror worlds, and demonstrate that the desired amounts of visible matter and mirror dark matter in the universe arise from a common origin of CP violation in the neutrino sector via leptogenesis. We derive the Higgs mass-spectrum and Higgs couplings with gauge bosons and fermions. We show their consistency with the direct Higgs searches and the indirect precision constraints. We further study the distinctive signatures of the predicted non-standard Higgs bosons at the LHC. Finally, we analyze the direct detections of GeV-scale mirror dark matter by TEXONO and CDEX experiments.

We conjecture that all CP violations (both Dirac and Majorana types) arise from a common origin in neutrino seesaw. With this conceptually attractive and simple conjecture, we deduce that µ−τ breaking shares the common origin with all CP violations. We study the common origin of µ − τ and CP breaking in the Dirac mass matrix of seesaw Lagrangian (with right-handed neutrinos being µ−τ blind), which uniquely leads to inverted mass-ordering of light neutrinos. We then predict a very different correlation between the two small µ−τ breaking observables θ 13 − 0• and θ 23 − 45• , which can saturate the present experimental upper limit on θ 13 . This will be tested against our previous normal mass-ordering scheme by the on-going oscillation experiments. We also analyze the correlations of θ 13 with Jarlskog invariant and neutrinoless ββ-decay observable. From the common origin of CP and µ − τ breaking in the neutrino seesaw, we establish a direct link between the low energy CP violations and the cosmological CP violation for baryon asymmetry. With these we further predict a lower bound on θ13 , supporting the on-going probes of θ13 at Daya Bay, Double Chooz and RENO experiments. Finally, we analyze the general model-independent Z2 ⊗ Z2 symmetry structure of the light neutrino sector, and map it into the seesaw sector, where one of the Z2's corresponds to the µ−τ symmetry Z µτ 2 and another the hidden symmetry Z s 2 (revealed in our previous work) which dictates the solar mixing angle θ12 . We derive the physical consequences of this Z s 2 and its possible partial violation in the presence of µ−τ breaking (without or with neutrino seesaw), regarding the θ12 determination and the correlation between µ−τ breaking observables.[ arXiv: 1104.2654 ]

We consider the rare top quark decays in the framework of the top-color-assisted technicolor ͑TC2͒ model. We find that the contributions of top-pions and top-Higgs-bosons predicted by the TC2 model can enhance the SM branching ratios by as much as 6 -9 orders of magnitude; i.e., in the extreme case, the orders of magnitude of branching ratios are Br(t→cg)ϳ10 Ϫ5 , Br(t→cZ)ϳ10 Ϫ5 , Br(t→c␥)ϳ10 Ϫ7 . With reasonable values of the parameters in the TC2 model, such rare top quark decays may be testable in future experiments. Therefore, rare top quark decays provide a unique way to test the TC2 model.

We study the lepton sector in the model based on the local gauge group SU (3)c ⊗SU (3)L ⊗U (1)X which do not contain particles with exotic electric charges. The seesaw mechanism and discrete A4 symmetry are introduced into the model to understand why neutrinos are especially light and the observed pattern of neutrino mixing. The model provides a method for obtaining the tri-bimaximal mixing matrix in the leading order. A non-zero mixing angle Ve3 presents in the modified mixing matrix.

Mirror universe is a fundamental way to restore parity symmetry in weak interactions. It naturally provides the lightest mirror nucleon as a unique GeV-scale asymmetric dark matter particle candidate. We conjecture that the mirror parity is respected by the fundamental interaction Lagrangian, and its possible soft breaking arises only from noninteraction terms in the gauge-singlet sector. We realize the spontaneous mirror parity violation by minimizing the vacuum Higgs potential, and derive the corresponding Higgs spectrum. We demonstrate that the common origin of CP violation in the visible and mirror neutrino seesaws can generate the right amount of matter and mirror dark matter via leptogenesis. We analyze the direct detections of GeV-scale mirror dark matter by TEXONO and CDEX experiments. We further study the predicted distinctive Higgs signatures at the LHC.

We introduce the fermion non-universality into the little Higgs models SU(5)/SO(5), SU(6)/Sp(6) and study the phenomenology of the new models. We find that if we change the transform property of the observed fermions under the extended [SU(2)×U(1)] 2 , the cancellation of the one-loop quadratically divergent correction to the Higgs mass arising from gauge bosons will not be changed, whereas the phenomenology at W -pole, Z-pole and low q 2 will be changed.