Dark matter stability can result from a residual matter-parity symmetry, following naturally from the spontaneous breaking of the gauge symmetry. Here we explore this idea in the context of the SU(3)c ⊗ SU(3)L ⊗ U(1)X ⊗ U(1)N electroweak extension of the standard model. The key feature of our new scotogenic dark matter theory is the use of a triplet scalar boson with anti-symmetric Yukawa couplings. This naturally implies that one of the light neutrinos is massless and, as a result, there is a lower bound for the 0νββ decay rate. I. INTRODUCTIONIn order to account for the existence of cosmological dark matter, we need new particles not present in the Standard Model (SM) of particle physics. Moreover, new symmetries capable of stabilising the corresponding candidate particle on cosmological scales are also required. Here we focus on the so-called Weakly Interacting Massive Particles, or WIMPs, as dark matter candidates. Within supersymmetric schemes, WIMP stability follows from having a conserved R-parity symmetry [1]. Our present construction does not rely on supersymmetry nor on the imposition of any ad hoc symmetry to stabilise dark matter. It is also a more complete theory setup, in the sense that it naturally generates neutrino masses as well. These arise radiatively, thanks to the exchange of new particles in the "dark" sector. The procedure is very well-motivated since neutrino masses are anyways necessary to account for neutrino oscillation data [2].Here we follow an alternative approach that naturally incorporates neutrino mass right from the beginning. This is provided by scotogenic dark matter schemes. These are "low-scale" models of neutrino mass [3] where dark matter emerges as a radiative mediator of neutrino mass generation. In this case, the symmetry stabilising dark matter is also responsible for the radiative origin of neutrino masses in a very elegant way [4]. Yet, in this case too, a dark matter stabilisation symmetry is introduced in an ad hoc manner. The need for such "dark" symmetry is a generic feature also of other scotogenic schemes, such as the generalization proposed in [5,6].Extending the SU(3) c ⊗ SU(2) L ⊗ U(1) Y gauge symmetry can provide a natural setting for a theory of dark matter where stabilisation can be automatic [7][8][9]. Such electroweak extensions involve the SU(3) L gauge symmetry, which also provides an "explanation" of the number of quark and lepton families from the anomaly cancellation requirement [10][11][12]. For recent papers using the SU(3) L gauge symmetry see . These theories can also, in

In this work, we analyze the generation of the higher-derivative Lorentz-violating Chern-Simons term at zero temperature and at finite temperature. We use the method of derivative expansion and the Matsubara formalism in order to consider the finite temperature effects. The results show that at zero temperature the induced higher-derivative Chern-Simons term is nonzero; in contrast, when the temperature reaches infinity, the coefficients of the induced term vanish. In addition, we also briefly study the question of large gauge invariance of this higher-derivative term as we as the conventional Chern-Simons term. We compute the exact induced action for both terms at finite temperature, however, in a particular gauge field background, and observe that they are, in fact, invariant under large gauge transformation. * Electronic address: julioleite,tmariz,wserafim@fis.ufal.br

We study the radiatively induced Lorentz-violating terms at finite temperature, namely, the higherderivative term and the Chern-Simons term. These terms are induced by integrating out the fermions coupled to the coefficient g κµν . The calculation of the resulting expressions is performed by using the derivative expansion and the Matsubara formalism. The Chern-Simons terms is nonzero only at finite temperature, whereas the higher-derivative term is finite at zero temperature, however, it goes to zero as the temperature grows to infinity. We also obtain a higher-derivative Chern-Simons term, nevertheless, it vanishes asymptotically. * Electronic address: julioleite,tmariz@fis.ufal.br

We develop a SUð3Þ C ⊗ SUð3Þ L ⊗ Uð1Þ X model where the number of fermion generations is fixed by cancellation of gauge anomalies, being a type of 3-3-1 model with new charged leptons. Similarly to the economical 3-3-1 models, symmetry breaking is achieved effectively with two scalar triplets so that the spectrum of scalar particles at the TeV scale contains just two CP even scalars, one of which is the recently discovered Higgs boson, plus a charged scalar. Such a scalar sector is simpler than the one in the Two Higgs Doublet Model, hence more attractive for phenomenological studies, and has no flavor changing neutral currents (FCNC) mediated by scalars except for the ones induced by the mixing of Standard Model (SM) fermions with heavy fermions. We identify a global residual symmetry of the model which guarantees mass degeneracies and some massless fermions whose masses need to be generated by the introduction of effective operators. The fermion masses so generated require less fine-tuning for most of the SM fermions and FCNC are naturally suppressed by the small mixing between the third family of quarks and the rest. The effective setting is justified by an ultraviolet completion of the model from which the effective operators emerge naturally. A detailed particle mass spectrum is presented, and an analysis of the Z 0 production at the LHC run II is performed to show that it could be easily detected by considering the invariant mass and transverse momentum distributions in the dimuon channel.