Dark Matter Phenomenology and Higgs Vacuum Stability in A Scotogenic Extension of Inert Higgs Doublet Dark Matter Model

DOI : 10.17577/IJERTCONV10IS07002

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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 Guwahati-781014, 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

  1. 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 one-loop

    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 SM-fields are even while field 2


    of this model.

    KeywordsBeyond Standard Model, Dark matter, Vacuum Stability.


    Ni are odd. The Yukawa lagrangian for the model is

    N i i N i i i 2 ¯ i (1)

    L = N¯ N m /2 N¯c N +y N l +h. c


    The scalar lagrangian is given by

    The Standard Model (SM) of particle physics is an


    2 + m2 +


    adequate description of the fundamental interactions in nature at the energies probed by the Large Hadron Collider (LHC) [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


    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



    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




    = 1

    (RGE) which is an indication of possible instability of the Higgs vacuum.


    2 2 (H 0 +iA0)


    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 Higgs-boson with mass mh . The inert doublet consists of a neutral CP – even scalar H 0 ,

    model has been carried out in [10-13]. In addition to DM, this

    framework could also explain the origin of light neutrino

    a pseudo-scalar A0

    , and a pair of charged scalars H±


    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 ±

    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 ,


    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 ± =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


    model, and in Fig.1 we have shown a plot of variation of relic

    0 2


    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 spin-independent cross


    3 + 4 + 5




    3 + 4 5



    o SI varying with DM mass, which is consistent with



the experimental bounds from XENON1T experiment [15, 16]. In Fig. 2 the red points represent the experimental points from XENON1T experiment for spin-independent 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


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.


direct detection cross-section 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].


Fig. 1. Plot of variation of relic density h


with DM mass

1 ,2> 0, 2 1 2 +3> 0,

2 1 2 + 3 + 4 2(5 )>0


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 one-loop renormalization group

Fig. 2. Plot of variation of Spin-independent cross section


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 one-loop 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.



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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