Physics Letters B 746 (2015) 266–275
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Graviton modes in multiply warped geometry
Mathew Thomas Arun
a
, Debajyoti Choudhury
a
, Ashmita Das
b
, Soumitra SenGupta
b,∗
a
Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
b
Department of Theoretical Physics, Indian Association for the Cultivation of Sciences, 2A&B R.S.C. Mullick Road, Kolkata 700 032, India
a r t i c l e i n f o a b s t r a c t
Article history:
Received
30 March 2015
Accepted
5 May 2015
Available
online 7 May 2015
Editor:
J. Hisano
The negative results in the search for Kaluza–Klein graviton modes at the LHC, when confronted with
the discovery of the Higgs, have been construed to have severely limited the efficacy of the Randall–
Sundrum
model as an explanation of the hierarchy problem. We show, though, that the presence
of multiple warping offers a natural resolution of this conundrum through modifications in both the
graviton spectrum and their couplings to the Standard Model fields.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Despite the spectacular success of the Standard Model (SM) of
elementary particles, the search for new physics beyond the SM
continues. One of the primary motivations for this is to resolve
the well-known gauge hierarchy/naturalness problem in connec-
tion
with the fine tuning of the higgs mass against large radia-
tive
corrections. Among several proposals to address this problem,
models with extra spatial dimensions draw special attention. In
this context, the warped geometry model proposed by Randall
and Sundrum (RS) [1] turned out to be particularly successful for
(i) it resolves the gauge hierarchy problem without bringing in any
other intermediate scale in the theory in contrast to the large ex-
tra
dimensional models; (ii) the modulus of the extra dimensional
model can be stabilized to a desired value by the Goldberger–Wise
mechanism [2], and (iii) a similar warped solution can be ob-
tained
from a more fundamental theory like string theory where
extra dimensions appear naturally [3]. As a result, several search
strategies at the LHC were designed specifically [4–7] to detect the
indirect/direct signatures of these warped extra dimensions e.g.
through the dileptonic decays of Kaluza–Klein (KK) excitations of
the graviton which appear in these models at the TeV scale.
The
original RS model was defined as a slice of AdS
5
space with
an S
1
/Z
2
orbifolding and a pair of three-branes located at the
orbifold fixed points, viz. y = 0, π (with the SM fields being lo-
calized
on the last mentioned). The parameters characterizing the
*
Corresponding author.
E-mail
addresses: thomas.mathewarun@gmail.com (M.T. Arun),
debajyoti.choudhury@gmail.com (D. Choudhury), ashmita.phy@gmail.com (A. Das),
soumitraiacs@gmail.com (S. SenGupta).
theory are the 5-dimensional fundamental (gravitational) scale M
5
and the bulk cosmological constant
5
. The solution to Einstein’s
equations, on demanding a (1 +3)-dimensional Lorentz symmetry,
then leads to a warp-factor in the metric of the form exp(−k
5
r
c
y)
where r
c
is the compactification radius and k
5
=
−
5
/24 M
3
5
.
Clearly, the applicability of the semiclassical treatment (as opposed
to a full quantum gravity calculation) requires that the bulk cur-
vature
k
5
be substantially smaller than M
5
. An analogous string
theoretic argument [8] relating the D3 brane tension to the string
scale (related, in turn, to M
5
through Yang–Mills gauge couplings)
demands the same, leading to k
5
/M
5
0.1. On the other hand, too
small a value for this ratio would, typically, necessitate a consid-
erable
hierarchy between r
−1
c
and M
5
, thereby taking away from
the merits of the scenario. Thus, it is normally accepted that one
should consider only 0.01 ≤ k
5
/M
5
≤ 0.1. Indeed, this constraint
plays a crucial role in most of the phenomenological studies of this
scenario, and certainly for the aforementioned results reported by
the ATLAS and the CMS groups. Throughout our analysis we shall
impose an analogous condition on the bulk curvature as an im-
portant
restriction to ensure the applicability of our semiclassical
calculations.
In the context of the original RS model, the large exponential
warping is held responsible for the apparent lightness of the Higgs
vacuum expectation value v (and its mass), as perceived on our
brane, related as it is to some naturally high scale
v ∼ O(M
5
),
applicable at the other brane, through the relation
v =
ve
−π k
5
r
c
. (1)
Here
v is determined by the natural scale of higher dimensional
model ∼ five dimensional Planck scale M
5
and k
5
r
c
≈ 12 would
explain the hierarchy with r
c
being stabilized to this value by
http://dx.doi.org/10.1016/j.physletb.2015.05.008
0370-2693/
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.