A detailed and general study of the fermionic structure of the 331 models with β arbitrary is carried out based on the criterion of cancellation of anomalies. We consider models with an arbitrary number of lepton and quark generations, but requiring to associate only one lepton and one quark SU (3) L multiplet for each generation, and at most one right-handed singlet per each left-handed fermion. We see that the number of quark left-handed multiplets must be three times the number of leptonic left-handed multiplets. Furthermore, we consider a model with four families and β = −1/ √ 3 where the additional family corresponds to a mirror fermion of the third generation of the Standard Model. We also show how to generate ansatzs about the mass matrices of the fermions according to the phenomenology. In particular, it is possible to get a natural fit for the neutrino hierarchical masses and mixing angles. Moreover, by means of the mixing between the third quark family and its mirror fermion, a possible solution for the A b F B discrepancy is obtained.

A complete study of the Higgs sector of the SU(3) c SU(3) L U(1) X model is carried out, obtaining all possible cases of vacuum expectation values that permit the spontaneous symmetry breaking pattern SU (3) We find the most general Higgs potentials that contain three Higgs triplets and one sextet. A detailed study of the scalar sector for different models with three Higgs triplets is done. The models end up in an electroweak two Higgs doublet model after the first symmetry breakdown; we find that the low energy limit depends on a trilinear parameter of the Higgs potential, and that the decoupling limit from the electroweak two Higgs doublet model to the minimal standard model can be obtained quite naturally.

We present a new supersymmetric version of the SU (3) ⊗ U (1) gauge model using a more economic content of particles. The model has a smaller set of free parameters than other possibilities considered before. The MSSM can be seen as an effective theory of this larger symmetry. We find that the upper bound of the ligthest CPeven Higgs boson can be moved up to 140 GeV.

Quantitative analysis of the damping of magnet oscillations by eddy currents in aluminum foil Am. J. Phys. 80, 804 (2012) Rolling magnets down a conductive hill: Revisiting a classic demonstration of the effects of eddy currents Am. J. Phys. 80, 800 (2012) A semiquantitative treatment of surface charges in DC circuits Am. J. Phys. 80, 782 (2012) Relation between Poisson and Schrödinger equations Am. J. Phys. 80, 715 (2012) Magnetic dipole moment of a moving electric dipole Am.The fact that the capacitance coefficients for a set of conductors are geometrical factors is derived in most electricity and magnetism textbooks. We present an alternative derivation based on Laplace's equation that is accessible to students in an intermediate course on electricity and magnetism. The properties of Laplace's equation permits us to determine many properties of the capacitance matrix. Some examples are given to illustrate the usefulness of these properties.

Simple, simpler, simplest: Spontaneous pattern formation in a commonplace system Am. J. Phys. 80, 578 (2012) Determination of contact angle from the maximum height of enlarged drops on solid surfaces Am. J. Phys. 80, 284 (2012) Aerodynamics in the classroom and at the ball park Am. J. Phys. 80, 289 (2012) The added mass of a spherical projectile Am.It is usual in introductory courses of mechanics to develop the work and energy formalism from Newton's laws. It has been shown how forces transform under a change of reference frame. No analogous study is usually done for the way in which work and energy transform under a change of reference frames. We analyze the behavior of energy and work under such transformations and explicitly show the expected invariance of the formalism under Galilean transformations for one particle and a system of particles. The case of noninertial systems is also analyzed and the fictitious work is characterized. In particular, we showed that the total fictitious work in the center of mass system vanishes even if the center of mass defines a noninertial frame. Some subtleties that arise from the formalism are illustrated by examples.