Closing the SU(3)L U(1)X symmetry at the electroweak scale

We show that some models with SU(3)C SU(3)L U(1)X gauge symmetry can be realized at the electroweak scale and that this is a consequence of an approximate global SU(2)L+R symmetry. This symmetry implies a condition among the vacuum expectation value of one of the neutral Higgs scalars, the U(1)X's coupling constant, gX, the sine of the weak mixing angle sin θW, and the mass of the W boson, MW. In the limit in which this symmetry is valid it avoids the tree level mixing of the Z boson of the standard model with the extra Z′ boson. We have verified that the oblique T parameter is within the allowed range indicating that the radiative corrections that induce such a mixing at the 1-loop level are small. We also show that a SU(3)L+R custodial symmetry implies that in some of the models we have to include sterile (singlets of the 3-3-1 symmetry) right-handed neutrinos with Majorana masses, since the seesaw mechanism is mandatory to obtain light active neutrinos. Moreover, the approximate SU(2)L+R SU(3)L+R symmetry implies that the extra nonstandard particles of these 3-3-1 models can be considerably lighter than it had been thought before so that new physics can be really just around the corner. © 2006 The American Physical Society.