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Register a new userA renormalizable fermion mass model with the double tetrahedral group
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We present a renormalizable model for fermion masses based solely on the double tetrahedral group T. It does not include right handed neutrinos and majorana neutrino masses are generated radiatively. The scalar sector of the model involves three SU(2) doublets and a set of lepton number violating (charged) scalars needed to give mass to the neutrinos. In the quark sector the model leads to a Fritzsch type scenario that is consistent with all the existing data. In the lepton sector, the model leads to tribimaximal (and near tribimaximal) mixing, and an inverted mass hierarchy.
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A non-supersymmetric renormalizable $SO(10)$ model is investigated for its viability in explaining the observed fermion masses and mixing parameters along with the baryon asymmetry produced via thermal leptogenesis. The Yukawa sector of the model consists of complex $10_H$ and $overline{126}_H$ scalars with a Peccei-Quinn like symmetry and it leads to strong correlations among the Yukawa couplings of all the standard model fermions including the couplings and masses of the right-handed (RH) neutrinos. The latter implies the necessity to include the second lightest RH neutrino and flavor effects for the precision computation of leptogenesis. We use the most general density matrix equations to calculate the temperature evolution of flavoured leptonic asymmetry. A simplified analytical solution of these equations, applicable to the RH neutrino spectrum predicted in the model, is also obtained which allows one to fit the observed baryon to photon ratio along with the other fermion mass observables in a numerically efficient way. The analytical and numerical solutions are found to be in agreement within a factor of ${cal O}(1)$. We find that the successful leptogenesis in this model does not prefer any particular value for leptonic Dirac and Majorana CP phases and the entire range of values of these observables is found to be consistent. The model specifically predicts (a) the lightest neutrino mass $m_{ u_1}$ between 2-8 meV, (b) the effective mass of neutrinoless double beta decay $m_{beta beta}$ between 4-10 meV, and (c) a particular correlation between the Dirac and one of the Majorana CP phases.
We propose a low scale renormalizable left-right symmetric theory that successfully explains the observed SM fermion mass hierarchy, the tiny values for the light active neutrino masses, the lepton and baryon asymmetries of the Universe, as well as the muon and electron anomalous magnetic moments. In the proposed model the top and exotic quarks obtain masses at tree level, whereas the masses of the bottom, charm and strange quarks, tau and muon leptons are generated from a tree level Universal Seesaw mechanism, thanks to their mixings with the charged exotic vector like fermions. The masses for the first generation SM charged fermions arise from a radiative seesaw mechanism at one loop level, mediated by charged vector like fermions and electrically neutral scalars. The light active neutrino masses are produced from a one-loop level inverse seesaw mechanism. Our model is also consistent with the experimental constraints arising from the Higgs diphoton decay rate. We also discuss the $Z^prime$ and heavy scalar production at a proton-proton collider.
In the context of a renormalizable supersymmetric SO(10) Grand Unified Theory, we consider the fermion mass matrices generated by the Yukawa couplings to a $mathbf{10} oplus mathbf{120} oplus bar{mathbf{126}}$ representation of scalars. We perform a complete investigation of the possibilities of imposing flavour symmetries in this scenario; the purpose is to reduce the number of Yukawa coupling constants in order to identify potentially predictive models. We have found that there are only 14 inequivalent cases of Yukawa coupling matrices, out of which 13 cases are generated by $Z_n$ symmetries, with suitable $n$, and one case is generated by a $Z_2 times Z_2$ symmetry. A numerical analysis of the 14 cases reveals that only two of them---dubbed A and B in the present paper---allow good fits to the experimentally known fermion masses and mixings.
A mechanism is suggested by which the dynamics of confinement could be responsible for the fermion mass matrix. In this approach the large top quark Yukawa coupling is generated naturally during confinement, while those of the other quarks and leptons stem from non-renormalizable couplings at the Planck scale and are suppressed. Below the confinement scale(s) the effective theory is minimal supersymmetric $SU(5)$ or the supersymmetric standard model. Particles in the $bar 5$ representations of $SU(5)$ are fundamental while those in the $10$ and $5$ are composite. The standard model gauge group is weakly coupled and predictions of unification can be preserved. A hierarchy in confinement scales helps generate a hierarchical spectrum of quark and lepton masses and ensures the Kobayashi-Maskawa matrix is nearly diagonal. However, the most natural outcome is that the strange quark is heavier than the charm quark; additional structure is required to evade this conclusion. No attempt has been made to address the issues of $SU(5)$ breaking, SUSY breaking, doublet/triplet splitting or the $mu$ parameter. While the models presented here are neither elegant nor complete, they are remarkable in that they can be analyzed without uncontrollable dynamical assumptions.
We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2 chain, which is a one-dimensional generalization of the two dimensional Kitaev honeycomb model. Using the mean field theory, coupled with a gauge fixing procedure to implement the single occupancy constraint, we obtain the phase diagram of the model. We then show that it matches the exact results obtained earlier using the Majorana fermion representation. We also compute the spin-spin correlation in the gapless phase and show that it is a spin liquid. Finally, we map the one-dimensional model in terms of the slave fermions to the model of 1D p-wave superconducting model with complex parameters and show that the parameters of our model fall in the topological trivial regime and hence does not have edge Majorana modes.
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