In this work we build a gauge model based on the SU(3)c$\bigotimes${}SU(3)L$\bigotimes${}U(1)N symmetry with heavy neutrinos and show that we can have two weakly interacting cold dark matter candidates in its spectrum. This is achieved by noticing that a global U(1) symmetry can be imposed on the model in such a way that the stability of the dark matter is guaranteed. We obtain their relic abundance and analyze their compatibility with recent direct detection experiments, also exploring the possibility of explaining the two events reported by CDMSII. An interesting outcome of this 3-3-1 model, concerning direct detection of these WIMPs, is a strong bound on the symmetry breaking scale, which imposes it to be above 3~TeV.

Motivated by the upcoming Higgs analyses, we investigate the importance of the complementarity of the Higgs boson chase on the low-mass weakly interacting massive particle (WIMP) search in direct detection experiments and the gamma-ray emission from the Galactic Center measured by the Fermi-LAT telescope in the context of the SU(3)c$\bigotimes${}SU(3)L$\bigotimes${}U(1)N. We obtain the relic abundance, thermal cross section, and the WIMP-nucleon cross section in the low-mass regime and network them with the branching ratios (BRs) of the Higgs boson in the model. We conclude that the Higgs boson search has a profound connection to the dark matter problem in our model, in particular for the case that (MWIMPMH/2 and, consequently, ruling out any attempt to explain the Fermi-LAT observations, although still offering a region of the parameter space consistent with the current bounds. Lastly, we show that our model has a Standard Model-like Higgs boson for the regime that MWIMP>MH/2, by computing the BRs into bb, $\gamma${}$\gamma${} and $\tau${}$\tau${}.

We show that Peccei-Quinn and lepton number symmetries can be a natural outcome in a 3-3-1 model with right-handed neutrinos after imposing a $Z_{11}\otimes Z_2$ symmetry. This symmetry is suitably accommodated in this model when we augment its spectrum by including merely one singlet scalar field. We work out the breaking of the Peccei-Quinn symmetry, yielding the axion, and study the phenomenological consequences. The main result of this work is that the solution to the strong CP problem can be implemented in a natural way, implying an invisible axion phenomenologically unconstrained, free of domain wall formation, and constituting a good candidate for the cold dark matter.

The simplest non-Abelian gauge extension of the electroweak standard model, the SU(3)c$\bigotimes${}SU(3)L$\bigotimes${}U(1)N, known as the 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 into 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 common lore in the literature of neutrino mass generation is that the canonical seesaw mechanism beautifully offers an explanation for the tiny neutrino mass but at the cost of introducing right-handed neutrinos at a scale that is out of range for the current experiments. The inverse seesaw mechanism is an interesting alternative to the canonical one once it leads to tiny neutrino masses with the advantage of being testable at the TeV scale. However, this last mechanism suffers from an issue of naturalness concerning the scale responsible for such small masses, namely, the parameter $\mu${} that is related to lepton number violation and is supposed to be at the keV scale, much lower than the electroweak one. However, no theoretical framework was built that offers an explanation for obtaining this specific scale. In this work, we propose a variation of the inverse seesaw mechanism by assuming a minimal scalar and fermionic set of singlet fields, along with a Z5$\bigotimes${}Z2 symmetry, that allows a dynamical explanation for the smallness of $\mu${}, recovering the neat canonical seesaw formula and with right-handed (RH) neutrinos free to be at the electroweak scale, thus testable at LHC and current neutrino experiments.