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

TL;DR

This paper analyzes the Landau pole issue in minimal 3-3-1 models, showing it depends on the energy scale at which gauge coupling matching is imposed, and highlights differences in the running of gauge couplings and fermion interactions.

Contribution

It demonstrates that the Landau pole in the 3-3-1 model depends on the matching energy scale and that gauge couplings run differently, challenging previous assumptions of their equality at all energies.

Findings

The Landau pole arises at different energies depending on the matching condition.

Gauge couplings $g_{2L}$ and $g_{3L}$ run differently with energy.

Fermion couplings to neutral bosons differ when expressed in terms of $ heta_X$ versus $ heta_W$.

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 $.