 Open Access
 Authors : Nilavjyoti Hazarika, Kalpana Bora
 Paper ID : IJERTCONV10IS07002
 Volume & Issue : PANE – 2021 (Volume 10 – Issue 07)
 Published (First Online): 28062022
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Dark Matter Phenomenology and Higgs Vacuum Stability in A Scotogenic Extension of Inert Higgs Doublet Dark Matter Model
Nilavjyoti Hazarika*, Kalpana Bora
Department of Physics Gauhati University Guwahati781014, India
Abstract In this work we study the dark matter phenomenology and the condition of Higgs vacuum stability of the Inert Higgs Doublet Dark Matter Model with scotogenic extension. Apart from dark matter candidate this model also

MODEL
In this model in addition to SM Higgs 1
another SU(2)
allows the possibility of radiative neutrino mass in scotogenic framework. We sample over the parameter space consistent with theoretical constraints, as well as dark matter relic abundance and direct detection searches. We use oneloop
scalar doublet 2 is considered. In addition three copies of
fermions Ni ,i= 1,2,3 , apart from the SM particle content has been considered. We include additional discrete symmetry
renormalization group equations to explore the stability of the
Higgs vacuum in this model and its effects on the viable regions
Z2 under which all SMfields are even while field 2
and
of this model.
KeywordsBeyond Standard Model, Dark matter, Vacuum Stability.
I. INTRODUCTION
Ni are odd. The Yukawa lagrangian for the model is
N i i N i i i 2 Â¯ i (1)
L = NÂ¯ N m /2 NÂ¯c N +y N l +h. c
i
The scalar lagrangian is given by
The Standard Model (SM) of particle physics is an
1
2 + m2 +
2
adequate description of the fundamental interactions in nature at the energies probed by the Large Hadron Collider (LHC) [1,
1
1
V=m
1
2 2
2 2 ( 1 1 )
2]. However, there still remains certain issues which are confirmed by experimental observations but he SM is unable to solve with them. One such issue is the presence of
2
2
+ 2 ( ) +
2 2
(
3 1
)( )
1 2 2
)+ 5
[()2 +h. c ]
mysterious dark matter (DM), which according to the
observations from WMAP [3] and cosmic microwave background radiation by Planck [4], constitute about 26.5% of
+4 (1
2)( 2 1 2 1 2
(2)
1
Universe. In addition to DM, there also exists problem with the stability of electroweak vacuum within the SM since the electroweak vacuum becomes unstable at large scale (~1010 GeV) [58] for top quark mass mt = 173.2 GeV [13]. At this
After spontaneous symmetry the SM Higgs
inert doublet 2 is,
(
)
while the
scale the SM Higgs quartic coupling H becomes negative 0
(
),
HÂ±
= 1
(RGE) which is an indication of possible instability of the Higgs vacuum.
2
2 2 (H 0 +iA0)
(3)
In order to resolve the above mentioned issues, we need to go beyond the SM. In this work, we consider additional scalars which could serve as DM candidate and also stabilize the vacuum simultaneously. We extend the SM with a scotogenic extension of the inert higgs doublet model as proposed by Ma in 2006 [9]. Earlier works on inert doublet
The vacuum expectation value (vev) of the neutral component of the doublet 1 is denoted by v . The h state corresponds to the physical SM Higgsboson with mass mh . The inert doublet consists of a neutral CP – even scalar H 0 ,
model has been carried out in [1013]. In addition to DM, this
framework could also explain the origin of light neutrino
a pseudoscalar A0
, and a pair of charged scalars HÂ±
masses.
The paper is organized as follows. The model is described in section II with explanation to different model parameters. Section III sheds light on the dark matter phenomenology and vacuum stability. We then discuss the results in section IV and finally conclude in section V.
H A H Â±
m ,m m
with masses 0 0 and By minimising the
potential V in (2) we get the masses of different physical scalars including SM Higgs and inert particles as,
h 1
m2= 2 v2 ,
IV. RESULTS AND DISCUSSIONS
We have considered a scotogenic extension of SM with inert doublet model, such that the lightest of CP even scalar of the
2 2 3 2
mH Â± =m2 + 2 v m2 =m2 + v2
H L
inert doublet i.e H 0 with mass mDM is considered as the
DM candidate. We compute the relic abundance of DM in our
0 2
2 2 2
m A =m +L v
(4)
model, and in Fig.1 we have shown a plot of variation of relic
0 2
where,
density with dark matter mass. The black line represent the observed relic density as given in (5). In Fig. 2 we observe the possibility of generating correct spinindependent cross
L=
3 + 4 + 5
2
L
=
3 + 4 5
2
section
o SI varying with DM mass, which is consistent with
and

DARK MATTER PHENOMENOLOGY AND HIGGS VACUUM STABILITY
the experimental bounds from XENON1T experiment [15, 16]. In Fig. 2 the red points represent the experimental points from XENON1T experiment for spinindependent cross section. The blue points below the red curve satisfies the constraint of correct relic density. The parameters used are
In the model one of the scalars between H 0 and A0
mh= 125
GeV,
2= 0. 01
.Thus the model predicts DM
could serve as a DM candidate. In this work we consider CP –
even scalar H 0 as the DM candidate. The Z2 symmetry prevents the decay of the DM candidate to SM particles. As 2 is inert, no mixing between 1 and 2 is possible and the gauge eigenstates are same as the mass eigenstates for the Higgs bosons. The Z2 symmetry further prevents any such mixing through the Higgs portal. Hence, the Inert Higgs doublet does not couple to fermions.
In this work we constrain the parameter space of the model, by using the measured value of the DM relic abundance provided by the Planck experiment [2].
0.119 < p< 0 .121
DM (5)
We use the MicrOmegas package [14] to compute the
correct relic abundance for our DM candidate satisfying PLANCK constraints. Further we apply the limits on DM
mass above 800 GeV that could give correct relic density.
2
direct detection crosssection from XEXON1T [15, 16] experiment.
In order that the the potential (2) is bounded from below, the quartic couplings must satisfy the stability conditions [17].
DM
Fig. 1. Plot of variation of relic density h
m
with DM mass
1 ,2> 0, 2 1 2 +3> 0,
2 1 2 + 3 + 4 2(5 )>0
(6)
As already mentioned in section I, in SM the Higgs quartic coupling H becomes negative at a scale around 1010 GeV
yt O (1)
58], due to top quark Yukawa coupling
. The
addition of new scalars can stabilize the vacuum [1822] by providing a positive contribution to the beta function of H . For doing the analysis we use oneloop renormalization group
Fig. 2. Plot of variation of Spinindependent cross section
m
o SI with
equations by implementing the model in SARAH 4.14.3 [23] and the beta functions for various gauge, quartic and Yukawa couplings in the model are evaluated up to oneloop level.
DM mass DM
We also studied the role of the new scalars in the stability of the electroweak vacuum by performing an RG analysis for the Higgs quartic coupling. Fig. 3 shows he one loop running
of the Higgs quartic coupling H as a function of the energy scale . The blue curve represents the contribution from SM and the red line represents the contribution for the scotogenic extension of inert doublet model. It is found that with respect to the SM case, the additional scalars enhance the vacuum stability scale to ~ 10 8 GeV and makes H >0 near the Planck scale.
H
ACKNOWLEDGMENT
The authors thank the RUSA grant and FIST grants of Govt. of India for support in upgrading computer laboratory where this work was completed.
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