A 3-3-1 model with right-handed neutrinos based on the Δ(27)\Delta\left(27\right) family symmetry

We present the first multiscalar singlet extension of the 3-3-1 model with right-handed neutrinos, based on the $\Delta \left( 27\right)$ family symmetry, supplemented by the $Z_{4}\otimes Z_{8}\otimes Z_{14}$ flavor group, consistent with current low energy fermion flavor data. In the model under consideration, the light active neutrino masses are generated from a double seesaw mechanism and the observed pattern of charged fermion masses and quark mixing angles is caused by the breaking of the $\Delta \left( 27\right) \otimes Z_{4}\otimes Z_{8}\otimes Z_{14}$ discrete group at very high energy. Our model has only 14 effective free parameters, which are fitted to reproduce the experimental values of the 18 physical observables in the quark and lepton sectors. The obtained physical observables for the quark sector agree with their experimental values, whereas those ones for the lepton sector also do, only for the inverted neutrino mass hierarchy. The normal neutrino mass hierarchy scenario of the model is disfavored by the neutrino oscillation experimental data. We find an effective Majorana neutrino mass parameter of neutrinoless double beta decay of $m_{\beta \beta }=$ 22 meV, a leptonic Dirac CP violating phase of $34^{\circ }$ and a Jarlskog invariant of about $10^{-2}$ for the inverted neutrino mass spectrum.Comment: 22 pages. Final version published in European Physical Journal C. arXiv admin note: text overlap with arXiv:1601.03300, arXiv:1309.656

A variant of 3-3-1 model for the generation of the SM fermion mass and mixing pattern

We propose an extension of the 3-3-1 model with an additional symmetry group $Z_{2}\times Z_{4} \times U(1)_{L_g}$ and an extended scalar sector. To our best knowledge this is the first example of a renormalizable 3-3-1 model, which allows explanation of the SM fermion mass hierarchy by a sequential loop suppression: tree-level top and exotic fermion masses, 1-loop bottom, charm, tau and muon masses; 2-loop masses for the light up, down, strange quarks as well as for the electron. The light active neutrino masses are generated from a combination of linear and inverse seesaw mechanisms at two loop level. The model also has viable fermionic and scalar dark matter candidates.Comment: 35 pages, 4 figures. Version accepted for publication in JHE

On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras $sl(2,\mathbb{R})$ or $su(2)$ according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential. PACS: 03.65.-w; 03.65.Fd MSC: 81R05; 20C35; 22E70Comment: 49 pages. No figures. Version to appear in JP

The first Δ(27)\Delta(27) flavor 3-3-1 model with low scale seesaw mechanism

We propose a viable model based on the $SU(3)_C\times SU(3)_L\times U(1)_X$ gauge group, augmented by the $U(1)_{L_g}$ global lepton number symmetry and the $\Delta(27) \times Z_3\times Z_{16}$ discrete group, capable of explaining the Standard Model (SM) fermion masses and mixings, and having a low scale seesaw mechanism which can be tested at the LHC. In addition the model provides an explanation for the SM fermion masses and mixings. In the proposed model, small masses for the light active neutrinos are generated by an inverse seesaw mechanism caused by non renormalizable Yukawa operators and mediated by three very light Majorana neutrinos and the observed hierarchy of the SM fermion masses and mixing angles is produced by the spontaneous breaking of the $\Delta(27) \times Z_{3}\times Z_{16}$ symmetry at very large energy scale. This neutrino mass generation mechanism is not presented in our previous 3-3-1 models with $\Delta(27)$ group (Nucl.Phys. B913 (2016) 792-814 and Eur.Phys.J. C76 (2016) no.5, 242), where the masses of the light active neutrinos arise from a combination of type I and type II seesaw mechanisms (Nucl.Phys. B913 (2016) 792-814) as well as from a double seesaw mechanism (Eur.Phys.J. C76 (2016) no.5, 242). Thus, this work corresponds to the first implementation of the $\Delta(27)$ symmetry in a 3-3-1 model with low scale seesaw mechanism.Comment: 13 pages, 4 figures. Final version published in European Physical Journal