We systematically study the renormalizable three-term polynomial inflation in the supersymmetric and non-supersymmetric models. The supersymmetric inflaton potentials can be realized in supergravity theory, and only have two independent parameters. We show that the general renormalizable supergravity model is equivalent to one kind of our supersymmetric models. We find that the spectral index and tensor-to-scalar ratio can be consistent with the Planck and BICEP2 results, but the running of spectral index is always out of the $2sigma$ range. If we do not consider the BICEP2 experiment, these inflationary models can be highly consistent with the Planck observations and saturate its upper bound on the tensor-to-scalar ratio ($r le 0.11$). Thus, our models can be tested at the future Planck and QUBIC experiments.
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 numbers 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.
The 8 $times$ 8 matrix representation of SO(8) Symmetry has been defined by using the direct product of Pauli matrices and Gamma matrices. These 8 $times$ 8 matrices are being used to describe the rotations in SO(8) symmetry. The comparison of 8$times$8 matrices with octonions has also been shown. The transformations of SO(8) symmetry are represented with the help of Octonions and split Octonions spinors.
From the current ATLAS and CMS results on Higgs boson mass and decay rates, the NMSSM is obviously better than the MSSM. To explain the fine-tuning problems such as gauge hiearchy problem and strong CP problem in the SM, we point out that supersymmetry does not need to provide a dark matter candidate, i.e., R-parity can be violated. Thus, we consider three kinds of the NMSSM scenarios: in Scenarios I and II R-parity is conserved and the lightest neutralino relic density is respectively around and smaller than the observed value, while in Scenario III R-parity is violated. To fit all the experimental data, we consider the chi^2 analyses, and find that the Higgs boson mass and decay rates can be explained very well in these Scenarios. Considering the small chi^2 values and fine-tuning around 2-3.7% (or 1-2%), we obtain the viable parameter space with light (or relatively heavy) supersymmetric particle spectra only in Scenario III (or in Scenarios I and II). Because the singlino, Higgsinos, and light stop are relatively light in general, we can relax the LHC supersymmetry search constraints but the XENON100 experiment gives a strong constraint in Scenarios I and II. In all the viable parameter space, the anomalous magnetic moment of the muon (g_{mu} - 2)/2 are generically small. With R-parity violation, we can increase (g_{mu} - 2)/2, and avoid the contraints from the LHC supersymmetry searches and XENON100 experiment. Therefore, Scenario III with R-parity violation is more natural and realistic than Scenarios I and II.
An attempt has been made to investigate the global SU(2) and SU(3) unitary flavor symmetries systematically in terms of quaternion and octonion respectively. It is shown that these symmetries are suitably handled with quaternions and octonions in order to obtain their generators, commutation rules and symmetry properties. Accordingly, Casimir operators for SU(2)and SU(3) flavor symmetries are also constructed for the proper testing of these symmetries in terms of quaternions and octonions.
Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann lambda matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann lambda matrices of SU(3)symmetry and octonion basis elements. Consequently, the quantum chromo dynamics (QCD) has been reformulated and it is shown that the theory of strong interactions could be explained better in terms of non-associative octonion algebra. Further, the octonion automorphism group SU(3) has been suitably handled with split basis of octonion algebra showing that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields which are responsible for the existence of two gauge potentials respectively associated with electric charge and magnetic monopole and supports well the idea that the colored quarks are dyons.
Varying the Standard Model (SM) fermion Yukawa couplings universally by a generic positive scale factor ($F_{Yu}$), we study the phenomenological fit to the current available experimental results for the Higgs boson search at hadron colliders. We point out that the Higgs production cross section and its decay branching ratio to $gammagamma$ can be varied oppositely by $F_{Yu}$ to make their product almost invariant. Thus, our scenario and the SM Higgs are indistinguishable in the inclusive $Hto gammagamma$ channel. The current measurements on direct Yukawa coupling strength in the $Hto bbar{b}/tautau$ channel are not precise enough to fix the scale factor $F_{Yu}$. The most promising is the vector-boson-fusion channel in which the CMS has already observed possible suppression effect on the Yukawa couplings. Further more, the global $chi^2$ fit of the experimental data can get the optimal value by introducing a suppression factor $F_{Yu}sim1/2$ on the SM Yukawa couplings.
In this paper, Grand Unified theories are discussed in terms of quaternions and octonions by using the relation between quaternion basis elements with Pauli matrices and Octonions with Gell Mann lambda matrices. Connection between the unitary groups of GUTs and the normed division algebra has been established to re-describe the SU(5)gauge group. We have thus described the SU(5)gauge group and its subgroup SU(3)_{C}times SU(2)_{L}times U(1) by using quaternion and octonion basis elements. As such the connection between U(1) gauge group and complex number, SU(2) gauge group and quaternions and SU(3) and octonions is established. It is concluded that the division algebra approach to the the theory of unification of fundamental interactions as the case of GUTs leads to the consequences towards the new understanding of these theories which incorporate the existence of magnetic monopole and dyon.
Starting with the quaternionic formulation of isospin SU(2) group, we have derived the relations for different components of isospin with quark states. Extending this formalism to the case of SU(3) group we have considered the theory of octonion variables. Accordingly, the octonion splitting of SU(3) group have been reconsidered and various commutation relations for SU(3) group and its shift operators are also derived and verified for different iso-spin multiplets i.e. I, U and V- spins. Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and models of strong and electroweak interactions
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.
