In this article, we give a brief review of the origin of the neutrino mass in some interesting non-linear supersymmetric models with R-symmetry. These models are able to address and solve the most important problems of particle physics and provide mechanisms for neutrino mass generation and their mixing parameters in agreement with the current experimental data. Their prediction could be experimentally tested in the near future by collider experiments.

In this article, we present a detailed study of the masses of all gauge bosons, as well as explaing recent experimental data regarding the W-boson mass presented by the CDF collaboration and even possible changes that these data can bring to experimental measurements of the masses of Z-boson mass in the context of the Minimal Supersymmetric SU(3)_C⊗ SU(3)_L⊗ U(1)_N Model. We also intend to show a phenomenological analysis of possible mixtures of gauge bosons in this model. We will show that our numerical predictions for the masses of the physical gauge bosons are within the current experimental limits.

In this lectures, we give a review about the Minimal Supersymmetric Standard Model (MSSM) with R -Parity Violation because it provides an attractive way to generate neutrino masses, lepton mixing angles in acconcordance to present neutrino data.

We build a supersymmetric model based on the gauge group [Formula: see text], where [Formula: see text] is a new charge and [Formula: see text] and [Formula: see text] are the usual baryonic and leptonic numbers, respectively. The model has three right-handed neutrinos with nonidentical [Formula: see text] charges. The type-I seesaw mechanism is implemented for the generating masses for all the neutrinos. There are good candidates for dark matter and due to a Majorana phase at sneutrinos masses it is possible to induce leptogenesis in this model.

We will present within the context of the supersymmetric models with SU(3)_C× SU(2)_L× U(1)_Y^'× U(1)_B-L gauge symmetry an explanation for the new data on the W-boson mass recently presented by the CDF collaboration. We will also study the neutral boson sector of this model.

We build a supersymmetric model with SU(2)_L⊗ SU(2)_R⊗ U(1)_(B-L) electroweak gauge symmetry, where SU(2)_L is the left-handed currents while SU(2)_R is the right-handed currents and B and L are the usual baryonic and leptonic numbers. We can generate an universal seesaw mechanism to get masses for all the usual fermions in this model, it means quarks and leptons, and also explain the mixing experimental data. We will also to study the masses of the Gauge Bosons and also the masses of all usual scalars of this model.

We build a supersymmetric model with [Formula: see text] gauge symmetry, with a global [Formula: see text] symmetry. The [Formula: see text] symmetry is necessary to keep the proton stable at least at tree level. There is also a global [Formula: see text] symmetry, where [Formula: see text] and [Formula: see text] are the usual baryonic and leptonic numbers, respectively. We introduce three nonidentical right-handed neutrinos plus new scalars fields. After symmetry breaking, the right-handed neutrinos together with one left-handed neutrino get Majorana masses via the seesaw mechanism. The other two left-handed neutrinos get their Majorana masses at 1-loop level. We will also explain the mixing angle in the neutrino sector in agreement with the experimental data and we get several interesting candidates to the observed dark matter.

We give a review about the Minimal Supersymmetric Standard Model with three right-handed neutrinos (MSSM3RHN). We, first introduce the minimal set of fields to built this model in their superfields formalism. After it, we build the lagrangian of the model in the superspace formalism and also introduce the soft terms to break SUSY. We show how to get masses to the neutrinos and sneutrinos in this model.

We consider an extension of the standard electroweak model with three Higgs doublets and global B-L and ℤ_2 symmetries. Two of the scalar doublets are inert due to the ℤ_2 symmetry. We calculated all the mass spectra in the scalar and lepton sectors and accommodate the leptonic mixing matrix as well. We also include an analysis of the scalar sector, showing that the potential is limited from below, and we obtain the masses of the scalar sector. Furthermore we consider the effects of the model on the anaomalous magnetic dipole of charged leptons and the μ→ eγ decay. We also present the SUSY version of the model with global B-L.

In this lectures, we give a review about the Minimal Supersymmetric Standard Model (MSSM) and the General Singlet Extensions of the MSSM (GSEMSSM). We, first introduce the minimal set of fields to built both models. Then we introduce their superfields and using them we build the lagrangian of those models in the superspace formalism. We show how to get the mass spectrum of those model in the $R$-parity scenarios and we also show how to get some Feynman Rules with the Gauge Bosons.

In this paper, we give a brief review of the Minimal Supersymmetric Standard Model (MSSM) and "μ from ν" Supersymmetric Standard Model (μνSSM). Then we propose a generalization of μνSSM in order to explain the recent ATLAS, CMS and LHCb results. This "new" μνSSM generalizes the superpotential W_suppot of μνSSM by including two terms that generate a mixing among leptons, gauginos and higgsinos while keeping the charginos and neutralinos masses unchanged. Also, it is potentially interesting for cosmological applications as it displays flat directions of the superpotential and a viable leptogenesis mechanism.

We consider a model with three Higgs doublet in a discrete B - L×ℤ_3 discrete symmetries. Two of the scalar doublets are inert due to the ℤ_3 symmetry. We calculated all the mass spectra in the scalar and lepton sectors and accommodate the leptonic mixing matrix as well.

We build a supersymmetric version with [Formula: see text] gauge symmetry, where [Formula: see text] is a new charge and [Formula: see text] and [Formula: see text] are the usual baryonic and leptonic numbers. The model has three right-handed neutrinos with identical [Formula: see text] charges, and can accommodate all fermion masses at the tree level. In particular, the type I seesaw mechanism is implemented for the generation of the active neutrino masses. We obtain the mass spectra of all sectors and for the scalar one we also give the flat directions allowed by the model.

We build a supersymmetric version with $SU(3)_C\otimes SU(2)_L\otimes U(1)_{Y^\prime}\otimes U(1)_{B-L}$ gauge symmetry, where $Y^\prime$ is a new charge and $B$ and $L$ are the usual baryonic and leptonic numbers. The model has three right-handed neutrinos with identical $B-L$ charges, and can accommodate all fermion masses at the tree level. In particular, the type-I seesaw mechanism is implemented for the generation of the active neutrino masses. We obtain the mass spectra of all sectors and for the scalar one we also give the flat directions allowed by the model.

We recall the many obstacles which seemed, long ago, to prevent supersymmetry from possibly being a fundamental symmetry of Nature. We also present their solutions, leading to the construction of the supersymmetric extensions of the Standard Model. Finally we discuss briefly the early experimental searches for supersymmetry.

In a previous work we applied a discrete symmetry (2') in order to light fermions acquire mass only at one loop level. This symmetry and the assumption of alignment between fermions and sfermions allow us to avoid FCNC problems. Here a more general hypothesis of flavor mixing in the sfermion sector of MSSM is considered and we show that the s quark is heavier than u,d quarks due to different content of sfermions contributions. Our results are in agreement with the experimental constraint on the values of sfermions masses.

Gluinos are expected to be one of the most massive sparticles (supersymmetric partners of usual particles) which constitute the Minimal Supersymmetric Standard Model (MSSM). The gluinos are the partners of the gluons and they are color octet fermions, due this fact they can not mix with the other particles. Therefore in several scenarios, given at SPS convention, they are the most massive particles and their nature is a Majorana fermion. Therefore their production is only feasible at a very energetic machine such as the Large Hadron Collider (LHC). Being the fermion partners of the gluons, their role and interactions are directly related with the properties of the supersymmetric QCD (sQCD). We review the mechanisms for producing gluinos at the LHC and investigate the total cross section and differential distributions, making an analysis of their uncertainties, such as the gluino and squark masses, as obtained in several scenarios, commenting on the possibilities of discriminating among them.

We point out the production of the charginos and neutralinos in electron-electron process in several supersymmetric models, in order to show that the International Linear Collider can discover double charged charginos if these particles really exist in nature.

On this article we show explicity that Supersymmetric Left-Right Models already satisfy the R-parity. They also respect $L$-parity and $B$-parity.

We consider the minimal supersymmetric extension of the 3-3-1 model and we study the mass spectra in the scalar sector of this model without the antisextet. We show that all our lightest scalars are in agreement with the experimental limits.