The effective dimension-5 operators can be induced by quantum gravity or inspired by string and M theories. They have important impacts on grand unified theories. We investigate the group theoretic nature of them for the well known E(6) model. Consid
ering the breaking chains $E_{6}mapsto H=SO(10)times U_{V}(1)mapsto SU(5)times U_{V}(1)times U_{V}(1)mapsto SU(3)times SU(2)times U_{Z}(1)times U_{V}(1)times U_{V}(1)$ and $E_{6}mapsto H=SO(10)times U_{V}(1)mapsto SU(4)times SU_{L}(2)times SU_{R}(2)times U_{V}(1)mapsto SU(3)times SU_{L}(2)times SU_{R}(2)times U_{S}(1)times U_{V}(1)$, we derive and give all of the Clebsch-Gordan coefficients $Phi^{(r)}_{s,z}$ associated with $E_6$ breaking to the standard model. Some applications of the results are discussed shortly.
We propose a class of the two Higgs doublet Standard models (SMs) with a SM singlet and a class of supersymmetric SMs with two pairs of Higgs doublets, where the right-handed up/charm quarks and the right-handed top quark have different quantum numbe
rs under extra discrete symmetries. Thus, the right-handed up and charm quarks couple to one Higgs doublet field, while the right-handed top quark couples to another Higgs doublet. The quark CKM mixings can be generated from the down-type quark sector. As one of phenomenological consequences in our models, we explore whether one can accommodate the observed direct CP asymmetry difference in singly Cabibbo-suppressed D decays. We show that it is possible to explain the measured values of CP violation under relevant experimental constraints.
We calculate the dependence on intermediate scale of the gaugino mass ratios upon breaking of SO(10) into the SM via an intermediate group $H$. We see that the ratios change significantly when the intermediate scale is low (say, $10^8$ GeV or 1 Tev)
compared to the case when the two breakings occur at the same scale.
We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the FL symmetry spontaneously.
We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via see-saw mechanism. If the right-handed neutrinos transform non-trivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale see-saw mechanism. Second, we present two models with the $SO(3)times U(1)$ global flavour symmetry in the lepton sector. After the flavour symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via see-saw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the $SO(3)times U(1)$ flavour symmetry breaking.
We have investigated the effects of unparticles in decays $B to l u$. It is found that the direct CP violation in the decays, which is zero in SM, can show up due to the CP conserving phase intrinsic in unparticle physics. For $l=tau$, the direct CP
asymmetry can reach 30% for the scalar unparticle contribution, and 100% for the longitudinal vector unparticle contribution under the constraints of ${rm Br}(Btotau u)$ and $ u e$ elastic scattering. If both unparticle-lepton coupling universality and unparticle-quark coupling universality are assumed the constraint from $Br(pito mu u)$ leads that the direct CP violation in $Bto l u$ can only reach at most 8% and 1% for scalar and vector unparticle contributions respectively if $d_{cal U} < 2$. If the direct CP violation is observed in the future it would give strong evidence for the existence of unparticle stuff.
