More on Fake GUT

TL;DR

This paper explores the 'fake GUT' framework where apparent matter unification is explained by a chiral gauge group, presenting concrete models and their implications for proton decay patterns.

Contribution

It provides detailed realizations of fake GUT models based on extended gauge groups, expanding on previous theoretical proposals.

Findings

Concrete models based on SU(5)×U(2)_H and SU(5)×SU(3)_H are constructed.

These models predict different proton decay patterns compared to traditional GUTs.

The framework shows that SM matter unification can be explained without embedding into unified representations.

Abstract

It is remarkable that the matter fields in the Standard Model (SM) are apparently unified into the $\mathrm{SU}(5)$ representations. A straightforward explanation of this fact is to embed all the SM gauge groups into a simple group containing $\mathrm{SU}(5)$, i.e., the grand unified theory (GUT). Recently, however, a new framework "fake GUT" has been proposed. In this new framework, the apparent matter unification can be explained by a chiral gauge group $G$, $ G \supset \mathrm{SU}(5)$. We emphasize that the SM matter fields are not necessarily embedded into the chiral representations to explain the apparent unification. In this paper, we discuss details of concrete realizations of the fake GUT model. We first study the model based on $\mathrm{SU}(5) \times \mathrm{U}(2)_H$, where $\mathrm{SU}(3)_c$ in the SM is from $\mathrm{SU}(5)$ while $\mathrm{SU}(2)_L\times \mathrm{U}(1)_Y$ are from the diagonal subgroups of $\mathrm{SU}(5) \times \mathrm{U}(2)_H$. We also extend this model to the one based on a semi-simple group, $\mathrm{SU}(5) \times \mathrm{SU}(3)_H$, so that $\mathrm{U}(2)_H$ is embedded in $\mathrm{SU}(3)_H$. We also show that this framework predicts rather different decay patterns of the proton, compared to the conventional GUT.