On Landau pole in the minimal 3-3-1 model

Abstract

We show that in 3-3-1 models the existence of a Landau-like pole in the coupling constant related to the $U(1{)}_X$ factor, $g_X$, in a certain value of ${\sin }^2{\theta }_W$, arises only assuming that the condition to match the gauge coupling constants of the standard model, $g_{2L}$, with that of the 3-3-1 model, $g_{3L}$, is valid for all energies. However, if we impose that this matching condition is valid only at a given energy, say $\mu =M_Z$, the pole arises when ${\sin }^2{\theta }_X({\mu }_{LP})=1$, which is the only weak mixing angle in the models. The value of ${\mu }_{LP}$ depends on the energy scales, ${\mu }_m$ and ${\mu }_{331}$, in which the matching and the 3-3-1 symmetry is fully realized, respectively. We also show that $g_{2L}$ and $g_{3L}$ have different running with energy. Therefore, differently from what is usually assumed in the literature, these couplings can not be considered equal for all energies. As a consequence, the fermion couplings with neutral vector bosons are different if we write them in terms of $\sin {\theta }_X$ instead of $\sin {\theta }_W$.

arXiv comment14 pages, 6 figures, version submitted for publication

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