Electron and neutron electric dipole moment in the 3-3-1 model with heavy leptons

We calculate the electric dipole moment for the electron and neutron in the framework of the 3-3-1 model with heavy charged leptons. We assume that the only source of $CP$ violation arises from a complex trilinear coupling constant and the three complex vacuum expectation values. However, two of the vacua phases are absorbed and the other two are equal up to a minus sign. Hence only one physical phase survives. In order to be compatible with the experimental data this phase has to be smaller than $10^{-6}$.Comment: 21 pages, 4 figures. Version published in PR

Schwinger's oscillator method, supersymmetric quantum mechanics and massless particles

We consider the Schwinger's method of angular momentum addition using the SU(2) algebra with both a fermionic and a bosonic oscillator. We show that the total spin states obtained are: one boson singlet state and an arbitrary number of spin-1/2 states, the later ones are energy degenerate. It means that we have in this case supersymmetric quantum mechanics and also the addition of angular momentum for massless particles. We review too the cases of two bosonic and fermionic oscillators.Comment: 11 pages,RevTe

Grand Unification and Proton Stability Near the Peccei-Quinn Scale

We show that in an $SU(2)\otimes U(1)$ model with a DSF-like invisible axion it is possible to obtain (i) the convergence of the three gauge coupling constants at an energy scale near the Peccei-Quinn scale; (ii) the correct value for $\sin^2\hat{\theta}_W(M_Z)$; (iii) the stabilization of the proton by the cyclic $Z_{13}\otimes Z_3$ symmetries which also stabilize the axion as a solution to the strong CP problem. Concerning the convergence of the three coupling constants and the prediction of the weak mixing angle at the $Z$-peak, this model is as good as the minimal supersymmetric standard model with $\mu_{\rm SUSY}=M_Z$. We also consider the standard model with six and seven Higgs doublets. The main calculations were done in the 1-loop approximation but we briefly consider the 2-loop contributions.Comment: 12 pages, 4 figure