Eur. Phys. J. C (2014) 74:2893
DOI 10.1140/epjc/s10052-014-2893-4
Regular Article - Theoretical Physics
Higgs quartic coupling and neutrino sector evolution in 2UED
models
Ammar Abdalgabar
1,a
, A. S. Cornell
1,b
, Aldo Deandrea
2,3,c
, Ahmad Tarhini
4,d
1
National Institute for Theoretical Physics, School of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa
2
Université de Lyon, 69622 Lyon, France
3
Université Lyon 1, CNRS/IN2P3, UMR5822 IPNL, 69622 Villeurbanne Cedex, France
4
Division of Physical Science and Engineering, King Abdullah University of Science and Technology (KAUST),
Thuwal 23955-6900, Saudi Arabia
Received: 17 February 2014 / Accepted: 5 May 2014 / Published online: 20 May 2014
© T he Author(s) 2014. This article is published with open access at Springerlink.com
Abstract Two compact universal extra-dimensional mod-
els are an interesting class of models for different theoret-
ical and phenomenological issues, such as the justification
of having three standard model fermion families, suppres-
sion of proton decay rate, dark matter parity from relics of
the six-dimensional Lorentz symmetry, origin of masses and
mixings in the standard model. However, these theories are
merely effective ones, with typically a reduced range of valid-
ity in their energy scale. We explore two limiting cases of the
three standard model generations all propagating in the bulk
or all localised to a brane, from the point of view of renormal-
isation group equation evolutions for the Higgs sector and for
the neutrino sector of these models. The recent experimental
results of the Higgs boson from the LHC allow, in some sce-
narios, stronger constraints on the cutoff scale to be placed,
from the requirement of the stability of the Higgs potential.
1 Introduction
The Higgs mechanism has intrigued both theorists and exper-
imentalists for a long time, being one of the central pieces in
the construction of the Standard Model (SM) and its exten-
sions. The Large Hadron Collider (LHC) was indeed built to
discover the missing pieces of the SM and to search for new
particles Beyond the Standard Model (BSM). The ATLAS
and CMS experiments announced last year the discovery of
a Higgs particle compatible with the SM expectations with a
mass of about 126 GeV [1,2], and updated results with more
a
e-mail: ammar.abdalgabar@students.wits.ac.za
b
e-mail: alan.cornell@wits.ac.za
c
e-mail: deandrea@ipnl.in2p3.fr
d
e-mail: tarhini.ahmad@gmail.com
data have been recently released (see for example [3,4]). As
we increase the energy scale above the Electro-Weak (EW)
scale, the quartic couplings may become smaller and even-
tually become negative, where, as a consequence, the poten-
tial becomes unbounded from below and the EW vacuum
becomes unstable. In the context of the SM this problem was
investigated a long time ago (see for example [5]) and con-
tinuously reinvestigated till recently (see for example [6]) as
Higgs data and more precise calculations became available.
This is also relevant for BSM and in particular those we
shall consider in the following, as this can give bounds on the
limit of validity of the effective theory. Among the models
which explore new physics that may operate near the TeV
scale, those with extra spatial dimensions [7] open many
possibilities for model building which can be constrained
[8] or explored in the near future. In this context there have
been many attempts to understand the origin of masses and
their mixings by using the Renormalisation Group Equa-
tions (RGEs) particularly for the Universal Extra Dimension
(UED) models and their possible extensions (see for exam-
ple [9] and references therein). In this case the problem of
vacuum stability and the triviality of the Higgs potential can
be quite relevant as running effects are more pronounced
in these models (with respect to the SM). For some recent
work concerning five- and six-dimensional UED models see
[10,11 ].
In particular, different models with two extra-dimensions
have been proposed, such as T
2
/Z
2
[8], the chiral square
T
2
/Z
4
[12,13 ], T
2
/(Z
2
× Z
2
) [14], S
2
/Z
2
[15], the flat
real projective plane RP
2
[16], and the real projective plane
starting from the sphere [17]. For example, in [16], the parity
assuring the stability of the dark matter candidate is due to a
remnant of the six-dimensional Lorentz symmetry after com-
pactification, as the model has no fixed points ( see [18]for
123