Standard Model with the additional $Z_6$ symmetry on the lattice

TL;DR

This paper explores a lattice-regularized Standard Model with an additional hidden $Z_6$ symmetry, analyzing its phase diagram and monopole configurations through numerical simulations of the full electroweak and strong interaction sectors.

Contribution

It introduces a lattice formulation of the Standard Model with the $Z_6$ symmetry and provides numerical results on its phase structure and monopole properties.

Findings

The phase diagram shows sensitivity to the $Z_6$ symmetry.

Monopole densities vary across phase transition lines.

Differences are observed between models with and without the $Z_6$ symmetry.

Abstract

An additional $Z_6$ symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently\cite{BVZ2003}. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In \cite{BVZ2004} we have reported our results on the numerical simulation of the Electroweak sector of the model. In this paper we report our results on the numerical simulation of the full ($SU(3)\otimes SU(2) \otimes U(1)$) model. The phase diagram of the model has been investigated using static quark and lepton potentials. Various types of monopoles have been constructed. Their densities appear to be sensitive to the phase transition lines. Differences between the realizations of the Standard Model which do or do not possess the mentioned $Z_6$ symmetry, are discussed.