The simplest non-abelian gauge extension of the electroweak standard model, the SU (3) c ⊗ SU (3) L ⊗ U (1) N , known as 3-3-1 model, has a minimal version which demands the least possible fermionic content to account for the whole established phenomenology for the well known particles and interactions. Nevertheless, in its original form the minimal 3-3-1 model was proposed with a set of three scalar triplets and one sextet in order to yield the spontaneous breaking of the gauge symmetry and generate the observed fermion masses. Such a huge scalar sector turns the task of clearly identifying the physical scalar spectrum a clumsy labor. It not only adds an obstacle for the development of its phenomenology but implies a scalar potential plagued with new free coupling constants. In this work we show that the framework of the minimal 3-3-1 model can be built with only two scalar triplets, but still triggering the desired pattern of spontaneous symmetry breaking and generating the correct fermion masses. We present the exact physical spectrum and also show all the interactions involving the scalars, obtaining a neat minimal 3-3-1 model far more suited for phenomenological studies at the current Large Hadron Collider. *

The CPT-even gauge sector of the Standard Model Extension is composed of nineteen components comprised in the tensor (KF ) µνρσ , of which nine do not yield birefringence. In this work, we examine the Maxwell electrodynamics supplemented by these nine nonbirefringent CPT-even components in aspects related to the Feynman propagator and full consistency (stability, causality, unitarity). We adopt a prescription that parametrizes the nonbirefringent components in terms of a symmetric and traceless tensor, Kµν , and second parametrization that writes Kµν in terms of two arbitrary fourvectors, Uµ and Vν . We then explicitly evaluate the gauge propagator of this electrodynamics in a tensor closed way. In the sequel, we show that this propagator and involved dispersion relations can be specialized for the parity-odd and parity-even sectors of the tensor (KF ) µνρσ . In this way, we reassess some results of the literature and derive some new outcomes showing that the parity-even anisotropic sector engenders a stable, noncausal and unitary electrodynamics.

We study the muon anomalous magnetic moment (g − 2) μ in the context of the reduced minimal 3-3-1 model recently proposed in the literature. In particular, its spectrum contains a doubly charged scalar (H ±± ) and gauge boson (U ±± ), new singly charged vectors (V ± ) and a Z boson, each of which might give a sizeable contribution to the (g − 2) μ . We compute the 1-loop contributions from all these new particles to the (g − 2) μ . We conclude that the doubly charged vector boson provides the dominant contribution, and by comparing our results with the experimental constraints we derive an expected value for the scale of SU(3) L ⊗ U (1) N symmetry breaking v χ ∼ 2 TeV. We also note that, if the discrepancy in the anomalous moment is resolved in the future without this model then the constraints will tighten to requiring v χ 3.7 TeV with current precision, and they will entirely rule out the model if the expected precision is achieved by the future experiment at Fermilab.

In this work, we focus on some properties of the parity-even sector of the CPT-even electrodynamics of the standard model extension. We analyze how the six non-birefringent terms belonging to this sector modify the static and stationary classical solutions of the usual Maxwell theory. We observe that the parity-even terms do not couple the electric and magnetic sectors (at least in the stationary regime). The Green's method is used to obtain solutions for the field strengths E and B at first order in the Lorentz-covariance-violating parameters. Explicit solutions are attained for point-like and spatially extended sources, for which a dipolar expansion is achieved. Finally, it is presented an Earth-based experiment that can lead (in principle) to an upper bound on the anisotropic coefficients as stringent as (e κe−) ij < 2.9 × 10 −20 .

We build a gauge model based on the SU (3) c ⊗ SU (4) L ⊗ U (1) X symmetry where the scalar spectrum needed to generate gauge boson and fermion masses has a smaller scalar content than usually assumed in literature. We compute the running of its abelian gauge coupling and show that a Landau pole shows up at the TeV scale, a fact that we use to consistently implement those fermion masses that are not generated by Yukawa interactions, including neutrino masses. This is appropriately achieved by non renormalizable effective operators, suppressed by the Landau pole scale. Also, SU (3) c ⊗ SU (3) L ⊗ U (1) N models embedded in this gauge structure are bound to be strongly coupled at this same energy scale, contrary to what is generally believed, and neutrino mass generation is rather explained through the same effective operators used in the larger gauge group. Besides, their nice features, as the existence of cold dark matter candidates and the ability to reproduce the observed standard model Higgs-like phenomenology, are automatically inherited by our model. Finally, our results imply that this model is constrained to be observed or discarded soon, since it must be realized at the currently probed energy scale in LHC.