Leptonic CP Violation and Wolfenstein Parametrization for Lepton Mixing

We investigate a general structure of lepton mixing matrix resulting from the SU$_F$(3) gauge family model with an appropriate vacuum structure of SU$_F$(3) symmetry breaking. It is shown that the lepton mixing matrix can be parametrized by using the Wolfenstein parametrization method to characterize its deviation from the tri-bimaximal mixing. A general analysis for the allowed leptonic CP-violating phase $\delta_e$ and the leptonic Wolfenstein parameters $\lambda_e$, $A_e$, $\rho_e$ is carried out based on the observed lepton mixing angles. We demonstrate how the leptonic CP violation correlates to the leptonic Wolfenstein parameters. It is found that the phase $\delta_e$ is strongly constrained and only a large or nearly maximal leptonic CP-violating phase $|\delta_e| \simeq 3\pi/4 \sim \pi/2$ is favorable when $\lambda_e > 0.15$. In particular, when taking $\lambda_e$ to be the Cabbibo angle \gl_e\simeq \lambda \simeq 0.225, a sensible result for leptonic Wolfenstein parameters and CP violation is obtained with $A_e=1.40$, $\rho_e=0.20$, \delta_{e}\sim 101.76\;^o, which is compatible with the one in quark sector. An interesting correlation between leptons and quarks is observed, which indicates a possible common origin of masses and mixing for the charged-leptons and quarks.Comment: 18 pages, 5 figures, sources of CP-violating phases are clarified, references adde

E-Courant algebroids

In this paper, we introduce the notion of $E$-Courant algebroids, where $E$ is a vector bundle. It is a kind of generalized Courant algebroid and contains Courant algebroids, Courant-Jacobi algebroids and omni-Lie algebroids as its special cases. We explore novel phenomena exhibited by $E$-Courant algebroids and provide many examples. We study the automorphism groups of omni-Lie algebroids and classify the isomorphism classes of exact $E$-Courant algebroids. In addition, we introduce the concepts of $E$-Lie bialgebroids and Manin triples.Comment: 29 pages, no figur

Dirac structures of omni-Lie algebroids

Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid \dev E\oplus \jet E is necessarily a Lie algebroid together with a representation on $E$. We study the geometry underlying these Dirac structures in the light of reduction theory. In particular, we prove that there is a one-to-one correspondence between reducible Dirac structures and projective Lie algebroids in \huaT=TM\oplus E; we establish the relation between the normalizer $N_{L}$ of a reducible Dirac structure $L$ and the derivation algebra \Der(\pomnib (L)) of the projective Lie algebroid \pomnib (L); we study the cohomology group $\mathrm{H}^\bullet(L,\rho_{L})$ and the relation between $N_{L}$ and $\mathrm{H}^1(L,\rho_{L})$; we describe Lie bialgebroids using the adjoint representation; we study the deformation of a Dirac structure $L$, which is related with $\mathrm{H}^2(L,\rho_{L})$.Comment: 23 pages, no figure, to appear in International Journal of Mathematic

Scheme for deterministic Bell-state-measurement-free quantum teleportation

A deterministic teleportation scheme for unknown atomic states is proposed in cavity QED. The Bell state measurement is not needed in the teleportation process, and the success probability can reach 1.0. In addition, the current scheme is insensitive to the cavity decay and thermal field.Comment: 3 pages, no figur