Najimuddin Khan, Subhendu Rakshit
The inert scalar doublet model of dark matter can be valid up to the Planck scale. We briefly review the bounds on the model in such a scenario and identify parameter spaces that lead to absolute stability and metastability of the electroweak vacuum.
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We study several aspects of electroweak vacuum metastability when an extra gauge singlet scalar, a viable candidate for a dark matter particle, is added to the standard model of particle physics, which is assumed to be valid up to the Planck scale. Phase diagrams are drawn for different parameter spaces, and based on that, we graphically demonstrate how the confidence level, at which stability of electroweak vacuum is excluded, depends on such new physics parameters.
We study the stability of the electroweak vacuum in low-scale inflation models whose Hubble parameter is much smaller than the instability scale of the Higgs potential. In general, couplings between the inflaton and Higgs are present, and hence we study effects of these couplings during and after inflation. We derive constraints on the couplings between the inflaton and Higgs by requiring that they do not lead to catastrophic electroweak vacuum decay, in particular, via resonant production of the Higgs particles.
We analyse effective potential around the electroweak (EW) scale in the Standard Model extended with a heavy scalar doublet. We show that the additional scalars can have a strong impact on vacuum stability. Although the additional heavy scalars may improve the behaviour of running Higgs self-coupling at large field values, we prove that they can destabilise the vacuum due to EW-scale effects. A new EW symmetry conserving minimum of the effective potential can appear rendering the electroweak symmetry breaking minimum meta- or unstable. However, for the case of the inert doublet model (IDM) wit…
Spontaneous symmetry breaking, gauge hierarchy and electroweak vacuum metastability
该研究针对正希格斯质量参数情形推导电弱真空亚稳性新边界，可解释希格斯质量符号与自发对称性破缺，TeV能标新物理会降低边界，还给出了模型的真空质量依赖寿命。
We make an attempt to identify regions in a Type II Two-Higgs Doublet Model, which correspond to a metastable electroweak vacuum with lifetime larger than the age of the universe. We analyse scenarios which retain perturbative unitarity up to Grand unification and Planck scales. Each point in the parameter space is restricted using Data from the Large Hadron Collider (LHC) as well as flavor and precision electroweak constraints. We find that substantial regions of the parameter space are thus identified as corresponding to metastability, which compliment the allowed regions for absolute stabil…
We consider the possibility that the gauge hierarchy is a byproduct of the metastability of the electroweak vacuum, i.e., that whatever mechanism is responsible for the latter also sets the running Higgs mass to a value smaller than its natural value by many orders of magnitude. This perspective is motivated by the early-time framework for eternal inflation put forth recently, which favors vacua that are relatively short-lived, but applies more generally to any theoretical approach predicting that our vacuum should be metastable. We find that the metastability of the electroweak vacuum, togeth…
On electroweak metastability and Higgs inflation
研究通过非最小耦合使希格斯场在高能级处变平，从而实现电弱亚稳态在膨胀中的可行性。
Current measurements of Standard Model parameters suggest that the electroweak vacuum is metastable. This metastability has important cosmological implications, because large fluctuations in the Higgs field could trigger vacuum decay in the early universe. For the false vacuum to survive, interactions which stabilize the Higgs during inflation -- e.g., inflaton-Higgs interactions or non-minimal couplings to gravity -- are typically necessary. However, the post-inflationary preheating dynamics of these same interactions could also trigger vacuum decay, thereby recreating the problem we sought t…
The current central experimental values of the parameters of the Standard Model give rise to a striking conclusion: metastability of the electroweak vacuum is favoured over absolute stability. A metastable vacuum for the Higgs boson implies that it is possible, and in fact inevitable, that a vacuum decay takes place with catastrophic consequences for the Universe. The metastability of the Higgs vacuum is especially significant for cosmology, because there are many mechanisms that could have triggered the decay of the electroweak vacuum in the early Universe. We present a comprehensive review o…
Electroweak metastability and Higgs inflation
本文研究标准模型希格斯势在电弱与普朗克尺度极小值间的势垒，发现足够大的非最小引力耦合可使原本亚稳态的希格斯势支持暴胀，且所需耦合更小、允许更大的顶夸克质量。
If the Higgs mass m_H is as low as suggested by present experimental information, the Standard Model ground state might not be absolutely stable. We present a detailed analysis of the lower bounds on m_H imposed by the requirement that the electroweak vacuum be sufficiently long-lived. We perform a complete one-loop calculation of the tunnelling probability at zero temperature, and we improve it by means of two-loop renormalization-group equations. We find that, for m_H=115 GeV, the Higgs potential develops an instability below the Planck scale for m_t>(166\pm 2) GeV, but the electroweak vacuu…
Higgs near-criticality at future colliders
本文分析了低尺度Majoron模型如何通过重费米子和扩展标量扇区实现电弱真空亚稳态，提出了多标量理论中亚稳态界限的推广和隧穿速率计算方法，并证明未来FCC对撞机可探测相关参数空间。
Bubble wall velocity during electroweak phase transition in the inert doublet model
本研究针对相变引力波谱、电弱重子生成等相关的泡壁速度问题，采用微物理方法结合最新手段，在惰性二重态模型中完成了泡壁速度的详细计算。
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…
Vacuum Metastability from Axion-Higgs Criticality
本研究提出轴子-希格斯临界性模型，以与希格斯耦合的类轴子粒子（ALP）替代传统类矢量费米子实现电弱真空自组织临界性，预言ALP质量在MeV到10 GeV量级，其参数空间可通过未来多类实验探测，为电弱等级问题提供新的研究范式与可观测信号。
The vacuum stability bounds on flavour-violating trilinear soft terms are revisited from the viewpoint that one should not ban a standard-model-like false vacuum as long as it is long-lived on a cosmological timescale. The vacuum transition rate is evaluated numerically by searching for the bounce configuration. Like stability, a metastability bound does not decouple even if sfermion masses grow. Apart from being more generous than stability, the new bounds are largely independent of Yukawa couplings except for the stop trilinears. With vacuum longevity imposed on otherwise arbitrary LR insert…
We study the strength of a first-order electroweak phase transition in the Inert Doublet Model (IDM), where particle dark matter (DM) is comprised of the lightest neutral inert Higgs boson. We improve over previous studies in the description and treatment of the finite-temperature effective potential and of the electroweak phase transition. We focus on a set of benchmark models inspired by the key mechanisms in the IDM leading to a viable dark matter particle candidate, and illustrate how to enhance the strength of the electroweak phase transition by adjusting the masses of the yet undiscovere…
The constraints imposed by the requirement that the scalar potential of supersymmetric theories does not have unbounded directions and charge or color breaking minima deeper than the usual electroweak breaking minimum (EWM) are significantly relaxed if one just allows for a metastable EWM but with a sufficiently long lifetime. For this to be acceptable one needs however to explain how the vacuum state reaches this metastable configuration in the first place. We discuss the implications for this issue of the inflaton induced scalar masses, of the supersymmetry breaking effects generated during …
Contributions of inert electroweak multiplets to Higgs properties
本文分析不与标准模型混合且无期望值的惰性电弱多重态对 HZγ（或暗光子）分支比和三 Higgs 耦合的影响，并纳入信号强度、斜参数与幺正性约束。
Gravity-improved metastability bounds for the Type-I Seesaw Mechanism
本研究首次在I型跷跷板机制中纳入引力效应，全面分析电弱真空亚稳性，发现引力可显著稳定真空并放宽约束，还提出了更普适的亚稳性边界表达形式及简化的RG分析新技术。
We made global fits of the inert Higgs doublet model (IDM) in the light of collider and dark matter search limits and the requirement for a strongly first-order electroweak phase transition (EWPT). These show that there are still IDM parameter spaces compatible with the observational constraints considered. In particular, the data and theoretical requirements imposed favour the hypothesis for the existence of a scalar dark matter candidate around 100 GeV. This is mostly due to the pull towards lower masses by the EWPT constraint. The impact of electroweak precision measurements, the dark matte…
The extension of the standard model's minimal Higgs sector with an inert $SU(2)_L$ scalar doublet can provide light dark matter candidate and simultaneously induce a strong phase transition for explaining Baryogenesis. There is however no symmetry reasons to prevent the extension using scalars with higher $SU(2)_L$ representations. By making random scans over the models' parameters, we show that in the light of electroweak physics constraints, strong first order electroweak phase transition and the possibility of having sub-TeV cold dark matter candidate the higher representations are rather d…
Higgs Criticality and the Metastability Bound: a target for future colliders
本文探讨TeV能标新物理可能导致的电弱真空失稳，提出真空亚稳态界作为Higgs质量上界，并总结相关可测假说，指出未来对撞机可在自然参数空间验证或排除该新物理。
We study the dynamics of electroweak phase transition in a simple extension of the Standard Model where the Higgs sector is extended by adding an $SU(2)_L$-triplet with hypercharge Y=2. By making random scans over the parameters of the model, we show that there are regions consistent with constraints from collider experiments and the requirement for a strong first-order electroweak phase transition which is needed for electroweak baryogenesis. Further, we also study the power spectrum of the gravitational waves which can be generated due to the first-order phase transitions. Moreover, the dete…
The inert higgs model is a minimal extension of the Standard Model that features a viable dark matter candidate, the so-called inert higgs ($H^0$). In this paper, we compute and analyze the dominant electroweak corrections to the direct detection cross section of dark matter within this model. These corrections arise from one-loop diagrams mediated by gauge bosons that, contrary to the tree-level result, do not depend on the unknown scalar coupling $λ$. We study in detail these contributions and show that they can modify in a significant way the prediction of the spin-independent direct detect…
The main virtue of the Inert Doublet Model (IDM) is that one of its spinless neutral bosons can play the role of Dark Matter. Assuming that the additional sources of CP violation are present in the form of higher dimensional operator(s) we reexamine the possibility that the model parameters for which the right number density of relic particles is predicted are compatible with the first order phase transition that could lead to electroweak baryogenesis. We find, taking into account recent indications from the LHC and the constraints from the electroweak precision data, that for a light DM (40-6…
We study the electroweak phase transition in the framework of scalar singlet-doublet mixed dark matter model, where the particle dark matter candidate is the lightest neutral Higgs that comprised of the CP-even component of inert doublet and a singlet scalar. The dark matter can be dominated by the inert doublet or singlet scalar depending on the mixing. We present several benchmark models to investigate the two situations after imposing several theoretical and experimental constraints. An additional singlet scalar and the inert doublet drive the electroweak phase transition to be strongly fir…
The inert doublet dark matter model has recently gained attention as a possible means of facilitating a strongly first order electroweak phase transition (EWPT), as needed for baryogenesis. We extend previous results by considering the regime where the DM is heavier than half the Higgs mass, and its relic density is determined by annihilation into W, Z and Higgs bosons. We find a large natural region of parameter space where the EWPT is strongly first order, while the lightest inert doublet state typically contributes only 0.1-3% of the total dark matter. Despite this small density, its intera…
Within the Standard Model, the current Higgs and top quark data favor metastability of the electroweak vacuum, although the uncertainties are still significant. The true vacuum is many orders of magnitude deeper than ours and the barrier separating the two is tiny compared to the depth of the well. This raises a cosmological question: how did the Higgs field get trapped in the shallow minimum and why did it stay there during inflation? The Higgs initial conditions before inflation must be fine--tuned to about one part in 10^8 in order for the Higgs field to end up in the right vacuum. In this …
The Scotogenic Model with Two Inert Doublets: Parameters Space and Electroweak Precision Tests
本文研究了包含两个惰性标量双态和三个单态Majorana费米子的斯科廷扩展模型，探讨了参数空间及电弱精密测试。分析发现标量sector中相长干涉导致Yukawa耦合增强，仅ΔT对带电质量分裂敏感，但60%参数空间因CMS W玻色子质量测量被排除。
The single Higgs doublet in the standard model (SM) may be the simplest way of introducing electroweak symmetry breaking, but SM extensions with more scalar doublets are not excluded. A special case of the two Higgs doublet models is the inert doublet model - a minimalistic version with interesting phenomenology. These proceedings reviews the inert doublet model's theoretical setup, constraints, collider prospects and its dark matter phenomenology.
The Standard Model of electroweak interactions has been recast as a gauge free theory where the fields present in the Lagrangian are made inert under $SU(2)_L \times U(1)_Y$ gauge transformations. Furthermore, the residual $U(1)_{em}$ gauge freedom of the dynamical fields are also removed to yield a completely gauge free theory. This formulation thus in turn resolves the issue of gauge dependency of the Standard Model effective potential which plays significant role in determining the instability scale of the electroweak vacuum.
We provide a comprehensive and up-to-date analysis of the prospects to realize Dark Matter (DM) in the Inert Doublet Model, while simultaneously enhancing the Electroweak Phase Transition (EWPhT) such as to allow for electroweak baryogenesis. Instead of focusing on certain aspects or mass hierarchies, we perform extensive, yet fine-grained, parameter space scans, where we analyze the nature of the EWPhT in both the light and the heavy DM regions, confronting it with the amount of DM potentially residing in the lightest inert-doublet state. Thereby, we point out a viable region where a non-triv…
We study the minimal type-III seesaw model in which we extend the SM by adding two $SU(2)_L$ triplet fermions with zero hypercharge to explain the origin of the non-zero neutrino masses. We show that the naturalness conditions and the limits from lepton flavor violating decays provide very stringent bounds on the model parameters along with the constraints from the stability/metastability of the electroweak vacuum. We perform a detailed analysis of the model parameter space including all the constraints for both normal as well as inverted hierarchies of the light neutrino masses. We find that …
We reconsider the strength of the electroweak phase transition (EWPT) in the inert doublet dark matter model, using a quantitatively accurate form for the one-loop finite temperature effective potential, taking into account relevant particle physics and dark matter constraints, focusing on a standard model Higgs mass near 126 GeV, and doing a full scan of the space of otherwise unconstrained couplings. We find that there is a significant (although fine-tuned) space of parameters for achieving an EWPT sufficiently strong for baryogenesis while satisfying the Xenon100 constraints from direct det…
The mechanism behind Electroweak Symmetry Breaking (EWSB) and the nature of dark matter (DM) are currently among the most important issues in high energy physics. Since a natural dark matter candidate is a weakly interacting massive particle or WIMP, with mass around the electroweak scale, it is clearly of interest to investigate the possibility that DM and EWSB are closely related. In the context of a very simple extension of the Standard Model, the Inert Doublet Model, we show that dark matter could play a crucial role in the breaking of the electroweak symmetry. In this model, dark matter i…
Current measurements of the Higgs boson mass and top Yukawa coupling suggest that the effective Higgs potential develops an instability below the Planck scale. If the energy scale of inflation is as high as the GUT scale, inflationary quantum fluctuations of the Higgs field can easily destabilize the standard electroweak vacuum and produce a lot of AdS domains. This destabilization during inflation can be avoided if a relatively large nonminimal Higgs-gravity or inflaton-Higgs coupling is introduced. Such couplings generate a large effective mass term for the Higgs, which can raise the effecti…
The measurements of the Higgs mass and top Yukawa coupling indicate that we live in a very special Universe, at the edge of the absolute stability of the electroweak vacuum. If fully stable, the Standard Model (SM) can be extended all the way up to the inflationary scale and the Higgs field, non-minimally coupled to gravity with strength $ξ$, can be responsible for inflation. We show that the successful Higgs inflation scenario can also take place if the SM vacuum is not absolutely stable. This conclusion is based on two effects that were overlooked previously. The first one is associated with…
We consider singlet extensions of the standard model, both in the fermion and the scalar sector, to account for the generation of neutrino mass at the TeV scale and the existence of dark matter respectively. For the neutrino sector we consider models with extra singlet fermions which can generate neutrino mass via the so called inverse or linear seesaw mechanism whereas a singlet scalar is introduced as the candidate for dark matter. We show that although these two sectors are disconnected at low energy, the coupling constants of both the sectors get correlated at high energy scale by the cons…
Electroweak phase transition with radiative symmetry breaking in Type-II seesaw with inert doublet
本文研究了扩展惰性双重态的 Type-II seesaw 模型中通过辐射效应触发电弱对称性破缺，利用两圈 $β$ 函数分析表明在特定参数下可实现一阶相变，并满足暗物质约束与真空稳定性。
Higgs vacuum metastability in $R+R^2$ gravity
本文研究Starobinsky暴胀中希格斯真空亚稳性的宇宙学后果，在R+R²引力框架下给出非最小耦合ξ的最新下界，并发现结果暗示反对永恒暴胀。
We update instability and metastability bounds of the Standard Model electroweak vacuum in view of the recent ATLAS and CMS Higgs results. For a Higgs mass in the range 124--126 GeV, and for the current central values of the top mass and strong coupling constant, the Higgs potential develops an instability around $10^{11}$ GeV, with a lifetime much longer than the age of the Universe. However, taking into account theoretical and experimental errors, stability up to the Planck scale cannot be excluded. Stability at finite temperature implies an upper bound on the reheat temperature after inflat…
If a Higgs field is conformally coupled to gravity, then it can give rise to the scale invariant density perturbations. We make use of this result in a realistic inert Higgs doublet model, where we have a pair of Higgs doublets conformally coupled to the gravity in the early universe. The perturbation of the inert Higgs is shown to be the scale invariant. This gives rise to the density perturbation observed through CMB by its couplings to the standard model Higgs and the subsequent decay. Loop corrections of this conformally coupled system gives rise to electroweak symmetry breaking. We constr…
We analyze the vacuum stability in the inert Higgs doublet extension of the Standard Model (SM), augmented by right-handed neutrinos (RHNs) to explain neutrino masses at tree level by the seesaw mechanism. We make a comparative study of the high- and low-scale seesaw scenarios and the effect of the Dirac neutrino Yukawa couplings on the stability of the Higgs potential. Bounds on the scalar quartic couplings and Dirac Yukawa couplings are obtained from vacuum stability and perturbativity considerations. The regions corresponding to stability, metastability and instability of the electroweak va…
We perform a global fit within the inert doublet model taking into account experimental observables from colliders, direct and indirect dark matter searches and theoretical constraints. In particular, we consider recent results from searches for dark matter annihilation-induced gamma-rays in dwarf spheroidal galaxies and relax the assumption that the inert doublet model should account for the entire dark matter in the Universe. We moreover study in how far the model is compatible with a possible dark matter explanation of the so-called Galactic center excess. We find two distinct parameter spa…
The inert doublet model is a well-motivated extension of the Standard Model that contains a dark matter candidate and modifies the dynamics of the electroweak symmetry breaking. In order to detail its phenomenology, we perform a comprehensive study of cosmic phase transitions and gravitational wave signals implied by the framework, accounting for the latest results of collider experiments. We require the neutral inert scalar to constitute, at least, a subdominant part of the observed dark matter abundance. While most of the phase transitions proceed through a single step, we identify regions o…
Our current measurements of the Standard Model parameters imply that the Higgs field resides in a metastable electroweak vacuum, where the vacuum can decay to a lower ground state, with cataclysmic repercussions for our Universe. According to our observations, no such event has happened in the observable universe, in spite of the various energetic processes that could have triggered it. This work serves as an overview of a method that uses the metastability of the false vacuum during cosmological inflation to provide constraints on the Higgs curvature coupling $ξ$. Considering also the effects…
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.
We study a dark matter model constructed by extending the standard model with an inert $\mathrm{SU}(2)_\mathrm{L}$ sextuplet scalar of hypercharge 1/2. The sextuplet components are split by the quartic couplings between the sextuplet and the Higgs doublet after electroweak symmetry breaking, resulting in a dark sector with one triply charged, two doubly charged, two singly charged, and two neutral scalars. The lighter neutral scalar boson acts as a dark matter particle. We investigate the constraints on this model from the $\text{monojet} + /\!\!\!\!E_\mathrm{T}$ and $\text{soft-dilepton} + \t…
Current data point toward metastability of the electroweak vacuum within the Standard Model. We study the possibility of stabilizing the Higgs potential in U(1) extensions thereof. A generic Z$'$ boson improves stability of the scalar potential in two ways: it increases the Higgs self--coupling, due to a positive contribution to the beta--function of the latter, and it decreases the top quark Yukawa coupling, which again has a stabilizing effect. We determine the range of U(1) charges which leads to a stable electroweak vacuum. In certain classes of models, such stabilization is possible even …
We examine the relic density of the light mass dark matter region in the inert doublet model (IDM) when the dominant process is due to co-annihilation between the lightest neutral scalars of the model. The full one-loop electroweak corrections are computed in an on-shell scheme and are found to be well approximated as an effective cross-section expressed in terms of $Z$-observables. The electroweak corrections to the subdominant process which consists of an annihilation into an on-shell $W$ and an off-shell $W$, that is calculated as a annihilation into a 3-body final state, is also performed.…
We propose a radiative seesaw model with an inert triplet scalar field in which Majorana neutrino masses are generated at the two loop level. There are fermionic or bosonic dark matter candidates in the model. We find that each candidate can satisfy the WMAP data when its mass is taken to be around the half of the mass of the standard model like Higgs boson. We also discuss phenomenology of the inert triplet scalar bosons, especially focusing on the doubly-charged scalar bosons at Large Hadron Collider in parameter regions constrained by the electroweak precision data and WMAP data. We study h…
The scalar potential of the Minimal Supersymmetric Standard Model (MSSM) admits the existence of vacua with non-vanishing expectation values of electrically and color charged fields. If such minima are deep enough, the physical electroweak vacuum is rendered unstable by quantum tunneling. By comparing the lifetime of the electroweak vacuum with the age of the universe, the MSSM parameter space can be constrained. Furthermore, the appearance of charge and color breaking minima associated with the stop sector is strongly correlated with the Higgs mass, which has been recently measured at the Lar…
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…
Is our vacuum global in a 331 model with three triplets?
该研究探讨了在包含三个三重态的331模型中，电弱真空是否为全局真空，并通过轨道空间方法分析了标量势能极小值和稳定性界限。
Strongly coupled inert scalar sector with radiative neutrino masses
本文提出含强耦合惰性 Higgs 二重态的三二重态标量模型，通过单圈与普适跷跷板机制产生中微子和带电费米子质量，并兼容多项实验约束及 95 GeV 双光子超出。
We study the vacuum behavior at one loop level in extended Higgs sectors with two doublets (2HDM), where $U(1)$ and $Z_{2}$ symmetries are considered to protect the $CP$ symmetry in the Higgs potential and to avoid Flavor Changing Neutral Currents at tree level in the Yukawa sector. In the Inert Higgs Model case, a detailed comparison is made between both models by using the energy evolution of couplings, which should satisfy energy scale dependent relations deduced for minima and stationary points of the Higgs potential at tree level. Besides, perturbative unitarity constraints at tree level …
In this work, we consider an extension of the Standard Model (SM) with an inert Higgs doublet and a real scalar singlet, in order to address problems around the origin of dark matter (DM). In this model, the lightest among the CP-odd and CP-even neutral inert components plays the role of a DM candidate, where the model parameters are subject to many theoretical and experimental constraints. These constraints include vacuum stability, perturbativity, LEP negative searches, electroweak precision tests, Higgs di-photon, Higgs invisible and Higgs undetermined decays, DM relic density and DM direct…
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 quadratic divergences of the Higgs mass may be cancelled either accidentally or by the exchange of some new particles. Alternatively its impact on naturalness may be weakened by raising the Higgs mass, which requires changing the Standard Model below its natural cut-off. We show in detail how this can be achieved, while preserving perturbativity and consistency with the electroweak precision tests, by extending the Standard Model to include a second Higgs doublet that has neither a vev nor couplings to quarks and leptons. This Inert Doublet Model yields a perturbative and completely natura…
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