Kavli Affiliate: Satoshi Shirai
| First 5 Authors: Masahiro Ibe, Satoshi Shirai, Motoo Suzuki, Keiichi Watanabe, Tsutomu T. Yanagida
| Summary:
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 $mathrm{SU}(2)_Ltimes mathrm{U}(1)_Y$ 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.
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