The minimal GUT with inflaton and dark matter unification
Eur. Phys. J. C
The minimal GUT with inflaton and dark matter unification
Heng-Yu Chen 2
Ilia Gogoladze 2
Shan Hu 1
Tianjun Li 0 4
Lina Wu 0 3
0 Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences , Beijing 100190 , People's Republic of China
1 Department of Physics, Faculty of Physics and Electronic Sciences, Hubei University , Wuhan 430062 , People's Republic of China
2 Department of Physics and Astronomy, Bartol Research Institute, University of Delaware , Newark, DE 19716 , USA
3 School of Physical Electronics, University of Electronic Science and Technology of China , Chengdu 610054 , People's Republic of China
4 School of Physical Sciences, University of Chinese Academy of Sciences , No. 19A Yuquan Road, Beijing 100049 , People's Republic of China
Giving up the solutions to the fine-tuning problems, we propose the non-supersymmetric flipped SU (5) × U (1)X model based on the minimal particle content principle, which can be constructed from the four-dimensional S O(10) models, five-dimensional orbifold S O(10) models, and local F-theory S O(10) models. To achieve gauge coupling unification, we introduce one pair of vector-like fermions, which form a complete SU (5) × U (1)X representation. The proton lifetime is around 5 × 1035 years, neutrino masses and mixing can be explained via the seesaw mechanism, baryon asymmetry can be generated via leptogenesis, and the vacuum stability problem can be solved as well. In particular, we propose that inflaton and dark matter particles can be unified to a real scalar field with Z2 symmetry, which is not an axion and does not have the non-minimal coupling to gravity. Such a kind of scenarios can be applied to the generic scalar dark matter models. Also, we find that the vector-like particle corrections to the Bs0 masses might be about 6.6%, while their corrections to the K 0 and Bd0 masses are negligible.
1 Introduction
It is well known that a Standard Model (SM) like Higgs boson
(h) with mass mh = 125.09 ± 0.24 GeV was discovered at
the LHC [
1–3
], and thus the SM particle content has been
confirmed. Moreover, there are many possible directions for new
physics beyond the SM: supersymmetry, extra dimensions,
strong dynamics or say composite Higgs field, extra gauge
symmetries, and Grand Unified Theory (GUT), etc.
However, we do not have any new physics signal at the 13 TeV
Large Hadron Collider (LHC) yet. Therefore, we may need
to reconsider the principle for new physics beyond the SM,
and then propose promising models.
First, let us briefly review the convincing evidence for new
physics beyond the SM
• Dark Matter (DM) is a necessary ingredient of cosmology,
considering the cosmic microwave background (CMB) or the
rotation curves of spiral galaxies, etc [
4,5
].
• Dark energy (DE) is required due to the concordance of
data from cosmic microwave anisotropy [4], galaxy clusters
(see, e.g., [
6
]), and high-redshift Type-IA supernovae [
7,8
].
• The non-zero masses and mixing of neutrinos have been
found from the atmospheric [9] and solar neutrino
experiments [
10
], as well as the reactor anti-neutrino experiments
[
11
], etc.
• A larger fraction of baryonic matter is found compared to
anti-matter in the Universe, i.e., the cosmic baryon
asymmetry η = n B /nγ = 6.05 ± 0.07 × 10−10 [
5
].
• The nearly scale-invariant, adiabatic, statistically isotropic,
and Gaussian density fluctuations (see, e.g., [
12
]) point to
cosmic inflation, which can solve the horizon and flatness
problems of the Universe as well.
Second, there are two kinds of theoretical problems in the
SM: fine-tuning problems and aesthetic problems. The
finetuning problems are: (i) The cosmological constant problem:
why is the cosmological constant so tiny? (ii) The gauge
hierarchy problem: the SM Higgs boson mass square is not stable
against quantum corrections and has quadratic divergences,
while the electroweak scale is about 16 order smaller than
the reduced Planck scale MPl 2.43 × 1018 GeV. (iii) The
strong CP problem: the θ parameter of Quantum
Chromodynamics (QCD) is smaller than 10−10 from the measurements
of the neutron electric dipole moment [
13,14
]. (iv) The SM
fermion mass hierarchy problem: the electron mass is about
5 orders smaller than top quark mass. Also, the aesthetic
problems are: (i) there is no explanation for the structure of
gauge interactions; (ii) there is no explanation of fermion
mass structures; (iii) there is no explanation for charge
quantization; (iv) there is no realization of gauge coupling
unification. The aesthetic problems can be solved in Grand Unified
Theories (GUTs) if we can realize gauge coupling
unification. In addition, the SM Higgs quartic coupling becomes
negative around 109 GeV for central measured values of the
SM parameters. Thus, the SM Higgs vacuum is not stable,
which is called the stability problem [
15–17
]. Interestingly,
the measured Higgs mass roughly corresponds to the (...truncated)