Relations Between Standard Model Parameters from $T^{'}$ Flavor Symmetry
Spontaneously broken flavor symmetry involving the binary tetrahedral group $T^{'}$ relates parameters in the standard model. In one example the CP violating Pontecorvo-Maki-Nakagawa-Sakata phase $\delta_{PMNS}$ and atmospheric mixing angle $\theta_{23}$ of neutrinos are related to the Cabibbo mixing angle $\Theta_C$ for quarks. A second formula relates a ratio of neutrino mass eigenvalues to the Cabibbo angle.
CKM and tri-bimaximal MNS matrices in a SU (5)× T ) (d model
Abstract We propose a model based on SU ( 5 ) × T ( d ) 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 T ( d ) transformation property of the matter fields, the b-quark mass can be generated only when the T ( d ) 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 × 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 θ 13 ≃ θ c / 3 2 , the model gives rise to a sum rule, tan 2 θ ⊙ ≃ tan 2 θ ⊙ , TBM − 1 2 θ c cos β , 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.
Optical rotatory dispersion and absolute configuration—III
Abstract Optical rotatory dispersion measurements on pyrrolidine, piperidine, and tetrahydro-isoquinoline alkaloids indicate that the absolute configuration of the α-asymmetric center may be assigned directly from the dispersion curve, provided either that the nitrogen atom is not protonated, or that the compound contains a chromophore absorbing above 200 mμ.