We consider a multi-component dark matter model where the dark sector contains a scalar doublet and a complex scalar singlet. We impose a discrete $Z_4$ symmetry to ensure such that the lightest component of the doublet, $\tilde{A}$, and the singlet, $\tilde{S}$, are both stable. Interactions between the dark sectors impact significantly dark matter observables, they allow in particular to significantly relax the direct detection constraints on the model. To determine the parameter space that satisfies relic density, theoretical and collider constraints as well as direct and indirect detection limits, we perform two separate scans, the first includes the full parameter space of the model while the second is dedicated to scenarios with a compressed inert doublet spectrum. In the first case we find that the singlet is generally the dominant dark matter component while in the compressed case the doublet is more likely to be the dominant dark matter component. In both cases we find that the two dark matter particles can have masses that ranges from around $m_h/2$ to over the TeV scale. We emphasize the interplay between cosmological astrophysical and collider constraints and show that a large fraction of the parameter space that escapes current constraints is within the sensitivity reach of future detectors such as XENON-nT, Darwin or CTA. Important collider signatures are mostly found in the compressed spectrum case with the possibility of probing the model with searches for heavy stable charged particles and disappearing tracks. We also show that semi-annihilation processes such as $\tilde{S}\tilde{S}\to \tilde{A}Z$ could give the dominant signature in indirect detection searches.
We consider beyond the standard model embedding of inert Higgs doublet fields. We argue that inert Higgs doublets can arise naturally in grand unified theories where the necessary associated $Z_2$ symmetry can occur automatically. Several examples are discussed.
We present an extensive analysis of a model in which the (Majorana) Dark Matter candidate is a mixture between a SU(2) singlet and two SU(2) doublets. This kind of setup takes the name of singlet-doublet model. We will investigate in detail an extension of this model in which the Dark Matter sector interactions with a 2-doublet Higgs sector enforcing the complementarity between Dark Matter phenomenology and searches of extra Higgs bosons.
When the singlet-doublet fermion dark matter model is extended with additional $Z_2$--odd real singlet scalars, neutrino masses and mixings can be generated at one-loop level. In this work, we discuss the salient features arising from the combination of the two resulting simplified dark matter models. When the $Z_2$-lightest odd particle is a scalar singlet, $\operatorname{Br}(μ\to e γ)$ could be measurable provided that the singlet-doublet fermion mixing is small enough. In this scenario, also the new decay channels of vector-like fermions into scalars can generate interesting leptonic plus m…
The Inert Doublet Model and its extension with an additional complex singlet is considered. The CP violation aspects are analysed in the simplified case, with one SM-like Higgs doublet and a complex singlet.
Pseudoscalar and charged Higgs bosons production in the processes $μ^+ μ^-\to P^0_i Z^0$, $μ^+μ^- \to H^{\pm}W^{\mp}$ within the models with several Higgs doublets and singlets is considered.
We analyze a simple extension of the Standard Model where the dark matter particle is a Dirac fermion that is mixture of a singlet and an SU(2) doublet. The model contains only four free parameters: the singlet and the doublet masses and two new Yukawa couplings. Direct detection bounds in this model are very strong and require the dark matter particle to be singlet-like. As a result, its relic density has to be obtained via coannihilations with the doublet. We find that the dark matter mass should be below 750 GeV, that the singlet-doublet mass difference cannot exceed 9%, and that direct det…
Following the discovery of a Higgs boson, there has been renewed interest in the general 2-Higgs-Doublet Model (2HDM). A model with One Inert Doublet plus One Higgs Doublet (I(1+1)HDM), where one of the scalar doublets is "inert" (since it has no vacuum expectation value and does not couple to fermions) has an advantage over the 2HDM since it provides a good Dark Matter (DM) candidate, namely the lightest inert scalar. Motivated by the existence of three fermion families, here we consider a model with two scalar doublets plus one Higgs doublet (I(2+1)HDM), where the two scalar doublets are ine…
In this paper, we propose a scheme for neutrino mass generation. A Higgs singlet is introduced in the Standard Model of particle physics (SM). All of this new singlet and the charged and neutral Higgs fields in the original Higgs doublet are assumed to have nonzero vacuum expectation values (VEVs). The normal hierarchy of neutrino masses is evidently preferred in our scheme. The neutrino masses are explicitly calculated.
Inspired by the dark matter searches in the low mass region, we study the Type II two Higgs doublet model with a light gauge singlet WIMP stabilized by a Z_2 symmetry. The real singlet is required to only couple to the non-Standard Model Higgs. We investigate singlet candidates with different spins as well as isospin violating effect. The parameter space favored by LHC data in two Higgs doublet model and hadronic uncertainties in WIMP-nucleon elastic scattering are also taken into account. We find only the scalar singlet in the isospin conserving case leads to a major overlap with the region o…
Inert Doublet Model (IDM) is a minimal extension of the Standard Model with the second scalar doublet that may provide a Dark Matter candidate. In this paper we consider the different variants of the evolution of the Universe after inflation, that lead towards the Inert phase today.
We present a study of singlet-doublet vector-like leptonic dark matter (DM) in the framework of two Higgs doublet model (2HDM), where the dark sector is comprised of one doublet and one singlet vectorlike fermions (VLFs). The DM, that arises as an admixture of the neutral components of the VLFs, is stabilized by an imposed discrete symmetry $\mathcal{Z}_2^{'}$ . We test the viability of the model in the light of observations from PLANCK and recent limits on spin-independent direct detection experiments, and search for its possible collider signals. In addition, we also look for the stochastic …
We make a phenomenological study of a model with two inert doublets plus one Higgs doublet (I(2+1)HDM) which is symmetric under a Z$_2$ group, preserved after Electro-Weak Symmetry Breaking (EWSB) by the vacuum alignment $(0,0,v)$. This model may be regarded as an extension to the model with one inert doublet plus one Higgs doublet (I(1+1)HDM), by the addition of an extra inert scalar doublet. The neutral fields from the two inert doublets provide a viable Dark Matter (DM) candidate which is stabilised by the conserved $Z_2$ symmetry. We study the new Higgs decay channels offered by the scalar…
I give an overview on models that extend the Standard Model scalar sector by additional gauge singlets or multiplets. I discuss current constraints on such models, as well as possible signatures and discovery prospects at current and future colliders.
In the inert scalar doublet framework, we analyze what would be the effect of a $B-L$ asymmetry that could have been produced in the Universe thermal bath at high temperature. We show that, unless the "$λ_5$" scalar interaction is tiny, this asymmetry is automatically reprocessed in part into an inert scalar asymmetry that could be at the origin of dark matter today. Along this scenario, the inert mass scale lies in the few-TeV range and direct detection constraints require that the inert scalar particles decay into a lighter dark matter particle which, as the inert doublet, is odd under a $Z_…
Inert Doublet Model is a minimal extension of the Standard Model with the second scalar doublet that may provide a Dark Matter candidate. In this paper we consider different variants of the evolution of the Universe after inflation, that lead towards the Inert phase today. We extend our previous analysis, in particular by discussing the co-existence of minima and providing numerical examples of the evolutions of the mass parameters for the different types of the history of the Universe. We take into account the existing constraints, including the relict density data.
We study the effective potential and the Renormalization Group(RG) improvement to the effective potential of Higgs boson in a singlet-doublet fermion dark matter extension of the Standard Model(SM), and in general singlet-doublet fermion extension models with several copies of doublet fermions or singlet fermions. We study the stability of the electroweak vacuum with the RG improved effective potential in these models beyond the SM. We study the decay of the electroweak vacuum using the RG improved effective potential in these models beyond the SM. In this study we consider the quantum correct…
The Inert Doublet Model relies on a discrete symmetry to prevent couplings of the new scalars to Standard Model fermions. This stabilizes the lightest inert state, which can then contribute to the observed dark matter density. In the presence of additional approximate symmetries, the resulting spectrum of exotic scalars can be compressed. Here, we study the phenomenological and cosmological implications of this scenario. We derive new limits on the compressed Inert Doublet Model from LEP, and outline the prospects for exclusion and discovery of this model at dark matter experiments, the LHC, a…
We discuss the status of the Inert Doublet Model, a two-Higgs doublet model that obeys a discrete Z2 symmetry and provides a dark matter candidate. We discuss all current theoretical and experimental constraints on the model as well as discovery prospects at current and future colliders.
We examine simple extension of the standard model with a pair of fermions, one singlet and a doublet, in a common thread linking the dark matter problem with the smallness of neutrino masses associated with several exciting features. In the presence of a small bare Majorana mass term, the singlet fermion brings in a pseudo-Dirac dark matter capable of evading the strong spin-independent direct detection bound by suppressing the dark matter annihilation processes mediated by the neutral current. In consequence, the allowed range of mixing angle between the doublet and the singlet fermions gets …
We take the Lagrangian of Inert Doublet Model and with unitary gauge calculate all the possible interactions, after calculating the interactions we draw the corresponding Feynman diagrams.There after calculate the Scattering cross section of the processes that contribute in the decay or scattering of DM candidate. In the concluding chapter we calculate the one loop correction to the process $HH\to hh$ and see all the possible loop contribution at this scale.
The Inert Doublet Model is an extension of the Standard Model including one extra ``Inert scalar doublet'' and an exact $Z_2$ symmetry. The ``Inert scalar'' provides a new candidate for dark matter. We present a systematic analysis of the dark matter abundance assuming the standard freeze-out mechanism and investigate the potentialities for direct and gamma indirect detection. We show that the dark matter candidate saturates the WMAP dark matter density in two rather separate mass ranges, one between 40 and 80 GeV, the other one over 400 GeV. We also show that the model should be within the ra…
One of the simplest extensions of the Standard Model that explains the observed abundance of dark matter is the inert doublet model. In this theory a discrete symmetry ensures that the neutral component of an additional electroweak doublet scalar is stable, and constitutes a dark matter candidate. As massive bodies such as the Sun and Earth move through the dark matter halo, dark matter particles can become gravitationally trapped in their cores. Annihilations of these particles result in neutrinos, which can potentially be observed with neutrino telescopes. We calculate the neutrino detection…
In this work, we investigate the prospects for detecting the Inert Doublet Model via the trilepton channel at the LHC. We present a set of representative benchmark scenarios in which all applicable constraints are satisfied, and show that in some of these scenarios, it is possible to obtain a signal at the 5 sigma significance level or better with integrated luminosity of 300 fb^{-1}.
We consider the case of the Dark Two Higgs Doublet Model (D2HDM) where a $U(1)'$ symmetry group and an extra Higgs doublet are added to the Standard Model. This model leads to a gauge singlet particle as an interesting Dark Matter (DM) candidate. We obtain phenomenological constraints to the parameter space of the model considering the one necessary to produce the correct density of thermal relic dark matter $Ωh^2$. We find a relation between the masses of the DM matter candidate $m_S$ and $m_{Z'}$ that satisfy the relic density for given values of $\tanβ$.
The complex singlet-doublet model is a popular theory to account for dark matter and electroweak baryogenesis, wherein the Standard Model particle content is supplemented by a complex scalar gauge singlet, with certain discrete symmetries imposed. The scalar potential which results thereof can have seven different types of minima at tree-level, which may coexist for specific choices of parameters. There is therefore the possibility that a given minimum is not global but rather a local one, and may tunnel to a deeper extremum, thus causing vacuum instability. This rich vacuum structure is expla…
A minimal extension of the Standard Model (SM) by a vector-like fermion doublet and three right handed (RH) singlet neutrinos is proposed in order to explain dark matter and tiny neutrino mass simultaneously. The DM arises as a mixture of the neutral component of the fermion doublet and one of the RH neutrinos, both assumed to be odd under an imposed $\mathcal{Z}_2$ symmetry. Being Majorana in nature, the DM escapes from $Z$-mediated direct search constraints to mark a significant difference from singlet-doublet Dirac DM. The other two $\mathcal{Z}_2$ even heavy RH neutrinos give rise masses a…
We have explored properties of an extension of the Inert Doublet Model by the addition of an extra non-inert scalar doublet. The model offers a possibility of CP violation in the scalar sector and a candidate for the Dark Matter. Allowed regions in the plane spanned by the mass of the Dark-Matter particle and the lightest neutral Higgs particle have been identified, and constraints from direct and indirect-detection experiments have been studied. For favorable parameter regions one may observe long-lived charged particles produced at the LHC.
We extend the so-called singlet doublet dark matter model, where the dark matter is an admixture of a Standard Model singlet and a pair of electroweak doublet fermions, by a singlet scalar field. The new portal coupling of it with the dark sector not only contributes to the dark matter phenomenology (involving relic density and direct detection limits), but also becomes important for generation of dark matter mass through its vacuum expectation value. While the presence of dark sector fermions affects the stability of the electroweak vacuum adversely, we find this additional singlet is capable…
Recently, it was pointed out that the solar and atmospheric neutrino deficits can be explained by oscillations between electroweak doublet and singlet neutrinos in the model of Majorana neutrinos. However, since the model includes no flavor mixing, it cannot explain the recent LSND result. We extend the model to include the flavor mixing, and obtain the explanation of the LSND result together with the solar and atmospheric neutrino deficits. The requirement for the neutrinos to be the hot dark matter selects out only the vacuum oscillation solution to the solar neutrino deficit.
Gauge field theory of a horizontal symmetry of the group G = SU(2) X U(1) is developed so as to generalize the standard model of particle physics. All fermion and scalar fields are assumed to belong to doublets and singlets of the group in high energy regime. Mass matrices with four texture zeros of Dirac and Majorana types are systematically derived. In addition to seven scalar particles, the theory predicts existence of one peculiar vector particle which seems to play important roles in astrophysics and particle physics.
New results for the Inert Doublet Model (IDM) are discussed. It is very special among the $D$-symmetric 2HDMs, offering a good DM candidate. New unitarity constraints were derived for the IDM and SM-like light Higgs boson scenario in the Mixed Model.
We explore an extension of the fourth generation model with multi-Higgs doublets and three fermion singlets. The Standard Model neutrinos acquire mass radiatively at one loop level while the fourth generation neutrinos acquire a heavy tree-level mass. The model also contains several Dark Matter candidate whose stability is guaranteed by a $Z_2$ discrete symmetry. The possibility of CP violation in the scalar sector is also briefly discussed.
We give a survey on current constraints on the Inert Doublet Model parameter space, including all theoretical as well as experimental limits from collider and astrophysical data. For allowed regions in the parameter space, we provide total production cross sections for the pair-production of scalars at the 13 TeV LHC and propose benchmarks scenarios which should be investigated by the LHC experiments at Run II.
We study the Inert Higgs Doublet Model and its inert scalar Higgs $H$ as the only source for dark matter. It is found that three mass regions of the inert scalar Higgs can give the correct dark matter relic density. The low mass region (between 3 and 50 GeV) is ruled out. New direct dark matter detection experiments will probe the intermediate (between 60 and 100 GeV) and high (heavier than 550 GeV) mass regions. Collider experiments are advised to search for $D^\pm \to HW^\pm$ decay in the two jets plus missing energy channel.
The inert Higgs doublet model is an extension of the standard model with an extra scalar doublet. The extra doublet is $Z_2$ odd while all the other particles are $Z_2$ even, thus the model contains a dark matter candidate. It is known that the spin-independent cross section of the dark matter and the nucleon is highly suppressed for $m_{\text DM} \sim m_h/2$ at the tree level. In this talk, we show the loop corrections give the significant effects in this regime.
We examine the `singlet majoron model' first introduced by Chikashige, Mohapatra and Peccei as a simple extension of the standard model with massive Majorana neutrinos. We can explain both the solar and the atmospheric neutrino deficits by the oscillations between electroweak doublet and singlet neutrinos without flavor mixing. Furthermore, while some light neutrinos can be the hot dark matter, tau neutrino with mass of 8.9-24 MeV can be the cold dark matter through the interaction with the majoron. Thus, we can simultaneously explain the solar neutrino deficit, the atmospheric neutrino anomal…
We analyse the thermal evolution of the Universe in the Inert Doublet Model for three viable regions of Dark Matter mass: low, medium and high DM mass. Those three regions exhibit different behaviour in the possible types of evolution. We argue that the quartic self-couplings in IDM are significant parameters for the astrophysical analysis.
The Singlet-Doublet model of dark matter is a minimal extension of the Standard Model with dark matter that is a mixture of a singlet and a non-chiral pair of electroweak doublet fermions. The stability of dark matter is ensured by the typical parity symmetry, and, similar to a "Bino-Higgsino" system, the extra matter content improves gauge coupling unification. We revisit the experimental constraints on the Singlet-Doublet dark matter model, combining the most relevant bounds from direct (spin independent and spin dependent) and indirect searches. We show that such comprehensive analysis sets…
The vacuum structure of the inert doublet model is analysed at the one-loop level using the effective potential formalism, to verify the validity of tree-level predictions for the properties of the global minimum. An inert minimum (with massive fermions) and an inert-like minimum (with massless fermions) can coexist at tree level. But the one-loop analysis reveals that the allowed parameter space for the coexistence of more than one minimum is larger than the tree-level expected one. It is also shown that for some choices of parameters, the global minimum found at the one-loop level may be ine…
The Inert Doublet Model (IDM) is a simple extension of the Standard Model (SM) that aims to address the naturalness problem, electroweak baryogenesis and accommodate a viable dark matter (DM) candidate, along with a rich phenomenlogy in terms of collider signatures. In this note, we address the constraints on the IDM by recasting dilepton + missing energy searches performed for Supersymmetry at LHC run-1 using Madanalysis5.
Self-interacting dark matter (SIDM) with a light mediator is a promising scenario to alleviate the small-scale problems of the cold dark matter paradigm while being consistent with the latter at large scales, as suggested by astrophysical observations. This, however, leads to an under-abundant SIDM relic due to large annihilation rates into mediator particles, often requiring an extension of the simplest thermal or non-thermal relic generation mechanism. In this work, we consider a singlet-doublet fermion dark matter scenario where the singlet fermion with a light scalar mediator gives rise to…
We study an extension of the Inert Higgs Doublet Model (IHDM) by three copies of right handed neutrinos and heavy charged leptons such that both the inert Higgs doublet and the heavy fermions are odd under the $Z_2$ symmetry of the model. The neutrino masses are generated at one loop in the scotogenic fashion. Assuming the neutral scalar of the inert Higgs to be the dark matter candidate, we particularly look into the region of parameter space where dark matter relic abundance is primarily governed by the inert Higgs coupling with the leptons. This corresponds to tiny Higgs portal coupling of …
We study a three Higgs doublet model where one doublet is inert and the other two doublets are active. Flavor changing neutral currents are avoided at tree-level by imposing a softly broken $Z'_2$ symmetry and we consider type I and type II Yukawa structures. The lightest inert scalar is a viable Dark Matter (DM) candidate. A numerical scan of the free parameters is performed taking into account theoretical constraints such as positivity of the scalar potential and unitarity of $2 \rightarrow 2$ scattering amplitudes. The model is further constrained by experimental results such as $B$ physics…
We consider multi-component dark matter in a model where one dark matter component is feebly interacting (FIMP) while the second is weakly interacting (WIMP). The model contains an inert scalar doublet and a complex scalar singlet and features a discrete $Z_4$ symmetry. We determine the parameter space that satisfies theoretical constraints, collider constraints, relic density as well as direct and indirect detection limits. We discuss the possibility to probe the model through collider and astrophysical searches. We find that it is possible that the FIMP forms the dominant DM component, in th…
We have updated a recently proposed extension of the Inert Doublet Model. The extension amounts to the addition of an extra non-inert scalar doublet. The model thus offers a possibility of CP violation in the scalar sector and a candidate for the Dark Matter. The recent XENON100 direct-detection experiment excludes a considerable range of medium-low dark-matter masses, leaving only as viable very low masses of order 5-10 GeV, as well as the regions from \sim 60 to \sim 110 GeV, and above \sim 530 GeV. For favorable parameter regions one may observe related long-lived charged particles produced…
Although theoretically well-motivated as a minimal consistent Dark Matter (DM) model, the Inert Doublet Model (IDM) fell short in explaining the existence of DM in the intermediate mass region ($100-500$ GeV). We try to address this problem by introducing an additional vector dark matter. We show that the relic density of inert dark matter candidate can be enhanced significantly with new interactions in the intermediate mass region $100-500$ GeV in the multicomponent dark matter model when compared with the usual single component inert doublet model. We also show that we can get a reasonable e…
We investigate the parameter space of the Inert Doublet Model, which is a straightforward extension of the SM in the scalar sector. We apply a set of constraints both from the theoretical and experimental side to extract and determine allowed regions of parameter space. These constraints put strong limits on both masses and couplings of the new particles. We also present a set of benchmarks for the current LHC run. This work is based on [1, 2].
We study some implications of the presence of two inert scalar doublets which are charged under a dark Abelian gauge symmetry. Specifically, we investigate the effects of the new scalars on oblique electroweak parameters and on the interactions of the 125 GeV Higgs boson, especially its decay modes $h\toγγ,γZ$, and trilinear coupling, all of which will be probed with improved precision in future Higgs measurements. Moreover, we explore how the inert scalars may give rise to strongly first-order electroweak phase transition and also show its correlation with sizable modifications to the Higgs t…
The radiative neutrino mass model with an inert doublet scalar has been considered as a promising candidate which can explain neutrino masses, dark matter abundance and baryon number asymmetry if dark matter is identified with the lightest neutral component of the inert doublet. We reexamine these properties by imposing all the data of the neutrino oscillation, which are recently suggested by the reactor experiments. We find that the sufficient baryon number asymmetry seems not to be easily generated in a consistent way with all the data of the neutrino masses and mixing as long as the right-h…
We apply a formalism accounting for thermal effects (such as modified Sommerfeld effect; Salpeter correction; decohering scatterings; dissociation of bound states), to one of the simplest WIMP-like dark matter models, associated with an "inert" Higgs doublet. A broad temperature range T ~ M/20...M/10^4 is considered, stressing the importance and less-understood nature of late annihilation stages. Even though only weak interactions play a role, we find that resummed real and virtual corrections increase the tree-level overclosure bound by 1...18%, depending on quartic couplings and mass splitti…
In this work we consider a model for particle dark matter where an extra inert Higgs doublet and an additional scalar singlet is added to the Standard Model (SM) Lagrangian. The dark matter candidate is obtained from only the inert doublet. The stability of this one component dark matter is ensured by imposing a $Z_2$ symmetry on this additional inert doublet. The additional singlet scalar has a vacuum expectation value (VEV) and mixes with the Standard Model Higgs doublet resulting in two CP even scalars $h_1$ and $h_2$. We treat one of these scalars, $h_1$, to be consistent with the SM Higgs…
We consider an extension of the standard model (SM) with an inert Higgs doublet and three Majorana singlet fermions to address both origin and the smallness of neutrino masses and dark matter (DM) problems. In this setup, the lightest Majorana singlet fermion plays the role of DM candidate and the model parameter space can be accommodated to avoid different experimental constraints such as lepton flavor violating processes and electroweak precision tests. The neutrino mass is generated at one-loop level a la Scotogenic model and its smallness is ensured by the degeneracy between the CP-odd and…
The inert doublet model, a minimal extension of the Standard Model by a second higgs doublet with no direct couplings to quarks or leptons, is one of the simplest scenarios that can explain the dark matter. In this paper, we study in detail the impact of dark matter annihilation into three-body final state on the phenomenology of the inert doublet model. We find that this new annihilation mode dominates, in a relevant portion of the parameter space, over those into two-body final states considered in previous analysis. As a result, the computation of the relic density is modified and the viabl…
We study the production and decay of charged scalars, eta^\pm, in the context of a CP-Violating Inert-Doublet Model. The model is an extended version of the Inert Doublet Model with an extra Higgs doublet and provides new sources of CP violation and a dark matter candidate. As compared with the 2HDM, the particle spectrum contains two additional neutral scalars and a charged pair. These particles are subject to a Z_2 symmetry, but can be pair-produced in hadronic collisions. If a charged scalar is included in the pair, it decays to the stable dark-matter candidate (i.e., the lightest neutral i…
We extend the $SU(3)_c \times SU(2)_L \times U(1)_Y$ standard model by a $U(1)_{Y'}$ gauge symmetry. Three right-handed neutrinos are introduced to cancel the gauge anomaly. One Higgs singlet is responsible for spontaneously breaking the $U(1)_{Y'}$ symmetry while the standard model Higgs doublet does not carry any $U(1)_{Y'}$ charges. The down-type quarks, up-type quarks, charged leptons and neutral neutrinos obtain their Dirac masses through four types of dimension-5 operators constructed by the fermion doublets and singlets with the Higgs doublet and singlet. This effective theory is realiz…
We consider a model for the Higgs sector with two scalar doublets and a broken $Z_2$ symmetry, the Stealth Doublet Model, where the $Z_2$ symmetry is manifest in the Yukawa sector but broken by the scalar potential. This model can be seen as a generalization of the Inert Doublet Model. One of the doublets is the Higgs doublet that participates in electroweak symmetry breaking and couples to fermions. The other doublet does not couple to fermions at tree level and does not acquire a vacuum expectation value. The broken $Z_2$ symmetry leads to interesting phenomenology such as mixing between the…
