CKM and Tri-bimaximal MNS Matrices in a SU(5) x (d)T Model

We propose a model based on SU(5) x {}^{(d)}T which successfully gives rise to near tri-bimaximal leptonic mixing as well as realistic CKM matrix elements for the quarks. The Georgi-Jarlskog relations for three generations are also obtained. Due to the {}^{(d)}T transformation property of the matter fields, the b-quark mass can be generated only when the {}^{(d)}T symmetry is broken, giving a dynamical origin for the hierarchy between m_{b} and m_{t}. There are only nine operators allowed in the Yukawa sector up to at least mass dimension seven due to an additional Z_{12} x Z'_{12} symmetry, which also forbids, up to some high orders, operators that lead to proton decay. The resulting model has a total of nine parameters in the charged fermion and neutrino sectors, and hence is very predictive. In addition to the prediction for \theta_{13} \simeq \theta_{c}/3 \sqrt{2}, the model gives rise to a sum rule, \tan^{2}\theta_{\odot} \simeq \tan^{2} \theta_{\odot, \mathrm{TBM}} - {1/2} \theta_{c} \cos\beta, which is a consequence of the Georgi-Jarlskog relations in the quark sector. This deviation could account for the difference between the experimental best fit value for the solar mixing angle and the value predicted by the tri-bimaximal mixing matrix.Comment: 11 pages; v2: additional references added; minor modifications made; conclusion unchanged; v3: version to appear in Phys. Lett.

Neutrino Mass Matrix from S_4 Symmetry

The cubic symmetry S_4 contains A_4 and S_3, both of which have been used to study neutrino mass matrices. Using S_4 as the family symmetry of a complete supersymmetric theory of leptons, it is shown how the requirement of breaking S_4 at the seesaw scale without breaking supersymmetry enforces a special form of the neutrino mass matrix which exhibits maximal nu_mu - nu_tau mixing as well as zero U_e3. In addition, (nu_e + nu_mu + nu_tau)/sqrt{3} is naturally close to being a mass eignestate, thus predicting tan^2 theta_12 to be near but not equal to 1/2.Comment: 11 pages, no figur

Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model

Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We modify the Dirichlet and Neumann boundary conditions with the fully $O(D, D)$ description from the doubled gauge fields. We perform the one-loop $\beta$ function for the constant background fields to find low energy effective theory without using the strong constraints. The low energy theory can also be $O(D,D)$ invariant as the double sigma model. We use the other one way to construct different boundary conditions from the projectors. Finally, we combine the antisymmetric background field with the field strength to redefine a different $O(D, D)$ generalized metric. We use this generalized metric to construct a consistent double sigma model with the classical and quantum equivalence. We show the one-loop $\beta$ function for the constant background fields and obtain the normal sigma model after integrating out the dual coordinates.Comment: 32 pages, minor changes, references adde