A natural mechanism for approximate Higgs alignment in the 2HDM
Patrick Draper, Andreas Ekstedt, Howard E. Haber
备注：
55 pages, 8 figures, 3 tables, and 3 appendices; version 2 adds references, corrects typographical errors and adds one figure; version 3 updates references
The 2HDM possesses a neutral scalar interaction eigenstate whose tree-level properties coincide with the Standard Model (SM) Higgs boson. In light of the LHC Higgs data which suggests that the observed Higgs boson is SM-like, it follows that the mixing of the SM Higgs interaction eigenstate with the other neutral scalar interaction eigenstates of the 2HDM should be suppressed, corresponding to the so-called Higgs alignment limit. The exact Higgs alignment limit can arise naturally due to a global symmetry of the scalar potential. If this symmetry is softly broken, then the Higgs alignment limit becomes approximate (although still potentially consistent with the current LHC Higgs data). In this paper, we obtain the approximate Higgs alignment suggested by the LHC Higgs data as a consequence of a softly broken global symmetry of the Higgs Lagrangian. However, this can only be accomplished if the Yukawa sector of the theory is extended. We propose an extended 2HDM with vector-like top quark partners, where explicit mass terms in the top sector provide the source of the soft symmetry breaking of a generalized CP symmetry. In this way, we can realize approximate Higgs alignment without a significant fine-tuning of the model parameters. We then explore the implications of the current LHC bounds on vector-like top quark partners for the success of our proposed scenario.
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…
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…
We introduce a 3-Higgs Doublet Model (3HDM) with two Inert (or dark) scalar doublets and an active Higgs one, hence termed I(2+1)HDM, in the presence of a discrete $Z_3$ symmetry acting upon the three doublet fields. We show that such a construct yields a Dark Matter (DM) sector with two mass-degenerate states of opposite CP parity, both of which contribute to DM dynamics, which we call \textit{Hermaphrodite DM}, distinguishable from a (single) complex DM candidate. We show that the relic density contributions of both states are equal, saturating the observed relic density compliant with (in)d…
We present the complete set of continuous maximal symmetries that the potential of an $n$-Higgs Doublet Model ($n$HDM) should satisfy for natural Standard Model (SM) alignment. As a result, no large mass scales or fine-tuning is required for such alignment, which still persists even if these symmetries were broken softly by bilinear mass terms. In particular, the Maximal Symmetric $n$HDM (MS-$n$HDM) can provide both natural SM alignment and quartic coupling unification up to the Planck scale. Most remarkably, we show that the MS-2HDM is a very predictive extension of the SM governed by two onl…
The potential of $n$-Higgs Doublet Models ($n$HDMs) contains a large number of SU(2)$_L$-preserving accidental symmetries as subgroups of the symplectic group Sp(2$n)$. To classify these, we introduce prime invariants and irreducible representations in bilinear field space that enable us to explicitly construct accidentally symmetric $n$HDM potentials. We showcase the classifications of symmetries and present the relationship among the theoretical parameters of the scalar potential for; (i) the Two Higgs Doublet Model (2HDM) and (ii) the Three Higgs Doublet Model (3HDM). We recover the maximum…
Maximally Symmetric $n$-Higgs Doublet Models (MS-$n$HDMs)define very economic settings that enable sharp Higgs-sector predictions beyond the Standard Model (SM) potentially testable at high-energy colliders. The scalar potential of a MS-$n$HDM obeys an $\mathrm{Sp(2}n)$ symmetry, which is softly broken by bilinear scalar masses and explicitly by hypercharge and Yukawa couplings through renormalisation-group effects. The $\mathrm{Sp(2}n)$ also ensures natural SM alignment and allows for quartic coupling unification up to the Planck scale. As typical examples, we consider maximally symmetric rea…
We explore the possibility that the discrepancy in the observed anomalous magnetic moment of the muon $Δa _μ$ and the predicted relic abundance of Dark Matter by Planck data, can be explained in a lepto-philic 2-HDM augmented by a real SM singlet scalar of mass $\sim$ 10-80 GeV. We constrain the model from the observed Higgs Decay width at LHC, LEP searches for low mass exotic scalars and anomalous magnetic moment of an electron $Δa_e$. This constrained light singlet scalar serves as a portal for the fermionic Dark Matter, which contributes to the required relic density of the universe. A larg…
A $ Z_3 $ symmetric 3-Higgs Doublet Model (3HDM) with two inert doublets and one active doublet (that plays the role of the Higgs doublet), the so-called I(2+1)HDM, is studied. We discuss the behaviour of this 3HDM realisation when one allows for a $ Z_3 $ soft breaking term. Such a symmetry enables the presence of a two-component Dark Matter (DM) scenario in the form of "Hermaphrodite DM", where the two inert candidates have opposite CP parity and are protected by this discrete symmetry from decaying into Standard Model (SM) particles. Furthermore, the two DM states are potentially distinguis…
We perform a comprehensive study of The Higgs potential of the two Higgs doublet model extended by a real triplet scalar field $Δ$. This model, dubbed $2\mathcal{HDM+T}$, has a rich Higgs spectrum consisting of three CP-even Higgs $h_{1,2,3}$, one CP-odd $A_0$ and two pairs of charged Higgs $H^\pm_{1,2}$. First, we determine the perturbative unitarity constraints and a set of non trivial conditions for the boundedness from below (BFB). Then we derive the Veltman conditions by considering the quadratic divergencies of Higgs boson self energies in $2\mathcal{HDM+T}$. We find that the parameter s…
We calculate an $s$-wave amplitude matrix for all the possible 2--to--2 body scalar boson elastic scatterings in models with three scalar doublets, including contributions from the longitudinal component of weak gauge bosons via the Equivalence Theorem Approximation. Specifically, we concentrate on the two cases with two[one] active plus one[two] inert doublet fields, referred to as I(1+2)HDM[I(2+1)HDM], under CP conservation. We obtain three analytically irreducible sub-matrices with the $3\times 3$ form and eighteen eigenvalues for the amplitude matrix as an independent set, where the same f…
The $Z_3$ soft breaking in the I(2+1)HDM and its cosmological probes
Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla（普埃布拉自治理工医科大学理学院）；Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla（普埃布拉自治理工大学电子科学学院）；Dual CP Institute of High Energy Physics（高能物理双CP研究所）；Facultad de Ciencias, Universidad de Colima（科利马大学理学院）；School of Physics and Astronomy, University of Southampton（南安普顿大学物理与天文学院）；Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文系）；Division of Liberal-Arts, Kogakuin University（工机大学文理学部）；Department of Natural Science, International Christian University（国际基督教大学自然科学系）
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The exact alignment of the Yukawa structures on multi-Higgs doublet models provides cancellation of tree-level flavour changing couplings of neutral scalar fields. We show that family symmetries can provide a suitable justification for the Yukawa alignment.
We derive the complete set of continuous maximal symmetries for Standard Model (SM) alignment that may occur in the tree-level scalar potential of multi-Higgs Doublet Models, with $n > 2$ Higgs doublets. Our results generalize the symmetries of SM alignment, without decoupling of large mass scales or fine-tuning, previously obtained in the context of two-Higgs Doublet Models.
We study an extension of the Standard Model (SM) in which two copies of the SM Higgs doublet are added to the scalar sector. These extra doublets do not develop a vacuum expectation value, hence, they are \textit{inert}. This essentially leads to a 3-Higgs Doublet Model (3HDM) with 2 inert and 1 active scalar doublets, which we denote as I(2+1)HDM. We allow for CP-violation in the \textit{inert} sector, where the lightest \textit{inert} state is protected from decaying to SM particles through the conservation of a $Z_2$ symmetry, so that it is a Dark Matter (DM) candidate. For this scenario, w…
The current LHC Higgs data provide strong constraints on possible deviations of the couplings of the observed 125 GeV Higgs boson from the Standard Model (SM) expectations. Therefore, it now becomes compelling that any extended Higgs sector must comply with the so-called SM alignment limit. In the context of the Two Higgs Doublet Model (2HDM), this alignment is often associated with either decoupling of the heavy Higgs sector or accidental cancellations in the 2HDM potential. Here we present a new solution realizing natural alignment based on symmetries, without decoupling or fine-tuning. In p…
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We explain how an $SU(2)_R$ R-symmetry allows alignment of the vacuum expectation value and the mass eigenstates in the Higgs bosons squared-mass matrix. More important, we discuss how our parametrization of the breaking of this global symmetry allows to quantitatively apprehend the diverse sources of misalignment, which are kept, by supersymmetry, small.
The most general two-Higgs doublet model (2HDM) includes potentially large sources of flavor changing neutral currents (FCNCs) that must be suppressed in order to achieve a phenomenologically viable model. The flavor alignment ansatz postulates that all Yukawa coupling matrices are diagonal when expressed in the basis of mass-eigenstate fermion fields, in which case tree-level Higgs mediated FCNCs are eliminated. In this work, we explore models with the flavor alignment condition imposed at a very high energy scale, which results in the generation of Higgs-mediated FCNCs via renormalization gr…
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In the two Higgs doublet model, natural flavour conservation can be achieved through the use of a discrete Z2 symmetry. A less restrictive condition is the requirement of alignment in the Yukawa sector. So far, alignment has been an anzatz, not rooted in a specific model. In this letter we present a model for alignment, which starts with 2+N Higgs doublets, with natural flavour conservation imposed by a discrete symmetry. Only two of these scalars couple to the fermions, the other N scalars are in a hidden sector. Assuming that the two scalar doublets coupled to fermions are heavy, their decou…
We consider the effective type-II Two-Higgs doublet model originating from Dirac gaugino models with extended supersymmetry in the gauge sector, which is automatically aligned in the simplest realisations. We show that raising the scale at which the extended supersymmetry is manifest and including quantum corrections actually improves the alignment. Using an effective field theory approach including new threshold corrections and two-loop RGEs, plus two-loop corrections to the Higgs mass in the low-energy theory, we study the implications from the Higgs mass and other experimental constraints o…
Extended electroweak scalar sectors containing several doublet multiplets require flavour-aligned Yukawa matrices to prevent the appearance at tree level of unwanted flavour- changing neutral-current transitions. We analyse the misalignment induced by one-loop quantum corrections and explore possible generalizations of the alignment condition and their compatibility with current experimental constraints. The hypothesis of flavour alignment at a high scale turns out to be consistent with all known phenomenological tests.
The Standard Model (SM)-like couplings of the observed Higgs boson impose strong constraints on the structure of any extended Higgs sector. We consider the theoretical properties and the phenomenological implications of a generic two Higgs doublet model (2HDM). This model constitutes a simple and attractive extension of the SM that is consistent with the observation of the SM-like Higgs boson and precision electroweak observables, while providing a potential new source of CP-violation. In this paper we focus on the so-called Higgs alignment limit of the generic 2HDM, where the neutral scalar f…
We study the alignment of Yukawa couplings in the framework of general two Higgs doublet models (2HDMs) considering a scenario in which the lightest neutral Higgs boson is purely CP even while the two heavier neutral Higgs bosons are allowed to mix in the presence of nontrivial CP-violating phases in the Higgs potential. Identifying the lightest neutral Higgs boson as the 125 GeV one discovered at the LHC, we find that the alignment of Yukawa couplings without decoupling could be easily achieved in the type-I 2HDM with no much conflict with the current LHC Higgs precision data. Otherwise, we o…
In multi-Higgs-doublet models the alignment in flavour space of the relevant Yukawa matrices guarantees the absence of tree-level flavour-changing couplings of the neutral scalar fields. We analyze the consequences of this condition within the two-Higgs-doublet model and show that it leads to a generic Yukawa structure which contains as particular cases all known specific implementations of the model based on Z_2 symmetries. All possible freedom in the Yukawa sector gets parametrized in terms of three complex couplings. In spite of having flavour conservation in the neutral scalar couplings, t…
In multi-Higgs-doublet models, the alignment in flavour space of all Yukawa matrices coupling to a given right-handed fermion guarantees the absence of tree-level flavour-changing neutral couplings, while introducing new sources of CP violation. With N Higgs doublets (and no right-handed neutrinos) the Yukawa Lagrangian is characterized by the fermion masses, the CKM quark mixing matrix and 3(N-1) complex couplings. Quantum corrections break the alignment, generating a minimal-flavour-violation structure with flavour-blind phases. The aligned multi-Higgs-doublet models lead to a rich and viabl…
In the alignment limit of a multi-doublet Higgs sector, one of the Higgs mass eigenstates aligns in field space with the direction of the scalar field vacuum expectation values, and its couplings approach those of the Standard Model (SM) Higgs boson. We consider CP-conserving Two-Higgs-Doublet Models (2HDMs) of Type I and Type II near the alignment limit in which the heavier of the two CP-even Higgs bosons, $H$, is the SM-like state observed with a mass of 125 GeV, and the couplings of $H$ to gauge bosons approach those of the SM. We review the theoretical structure and analyze the phenomenolo…
In the alignment limit of a multi-doublet Higgs sector, one of the Higgs mass eigenstates aligns with the direction of the scalar field vacuum expectation values, and its couplings approach those of the Standard Model (SM) Higgs boson. We consider CP-conserving Two-Higgs-Doublet Models (2HDMs) of Type I and Type II near the alignment limit in which the lighter of the two CP-even Higgs bosons, $h$, is the SM-like state observed at 125 GeV. In particular, we focus on the 2HDM parameter regime where the coupling of $h$ to gauge bosons approaches that of the SM. We review the theoretical structure…
The most general two Higgs doublet model contains new sources of flavour violation that are usually in conflict with the experimental constraints. One possibility to suppress the exotic contribution to the flavour changing neutral currents consists on imposing the alignment of the Yukawa couplings. This condition presumably holds at a high-energy scale and is spoiled by the radiative corrections. We compute in this letter the size of the radiatively induced flavour violating Higgs couplings at the electroweak scale. These also yield the absolute lower bound on the size of the exotic contributi…
We examine the $h\to μτ$ and muon g-2 in the exact alignment limit of two-Higgs-doublet model. In this case, the couplings of the SM-like Higgs to the SM particles are the same as the Higgs couplings in the SM at the tree level, and the tree-level lepton-flavor-violating coupling $hμτ$ is absent. We assume the lepton-flavor-violating $μτ$ excess observed by CMS to be respectively from the other neutral Higgses, $H$ and $A$, which almost degenerates with the SM-like Higgs at the 125 GeV. After imposing the relevant theoretical constraints and experimental constraints from the precision electrow…
We study the charged Higgs couplings to fermions in the "democratic" three-Higgs-doublet model, in which one doublet couples to down-type quarks, one to up-type quarks, and one to charged leptons. Flavor-changing neutral Higgs couplings are absent because the Glashow-Weinberg-Paschos condition for natural flavor conservation is in effect. We show that this model reproduces the coupling structure of the charged Higgs boson in the recently-proposed Yukawa-aligned two-Higgs-doublet model, with two subtle constraints that arise from the unitarity of the charged Higgs mixing matrix. Adding a fourth…
We write down the renormalization-group equations for the Yukawa-coupling matrices in a general multi-Higgs-doublet model. We then assume that the matrices of the Yukawa couplings of the various Higgs doublets to right-handed fermions of fixed quantum numbers are all proportional to each other. We demonstrate that, in the case of the two-Higgs-doublet model, this proportionality is preserved by the renormalization-group running only in the cases of the standard type-I, II, X, and Y models. We furthermore show that a similar result holds even when there are more than two Higgs doublets: the Yuk…
We study the conditions required to make the 2HDM scalar potential stable up to the Planck scale. The lightest CP-even scalar is assumed to have been found at the LHC and the {\em alignment limit} is imposed in view of the LHC Higgs data. We find that ensuring stability up to scales $\gtrsim 10^{10}$~GeV necessitates the introduction of a soft breaking parameter in the theory. Even then, some interesting correlations between the nonstandard masses and the soft breaking parameter need to be satisfied. Consequently, a 2HDM becomes completely determined by only two nonstandard parameters, namely,…
We show that a non-abelian global $SU(2)_R$ acting on the quartic part of the two Higgs Doublet Model leads, at tree-level, to an automatic alignment without decoupling. An example of phenomenologically viable model with this feature is the the low energy effective field theory of the Minimal Dirac Gaugino Supersymmetric Model in the limit where the adjoint scalars are decoupled. We discuss here how the $SU(2)_R$ can be identified with the R-symmetry of the $N=2$ supersymmetry in the gauge and Higgs sectors. We also review how the radiative corrections lead to a very small misalignment.
In the context of two Higgs doublet models, we study the conditions required in order to have stable quasi-alignment in flavour space. We show that stability under the RGE imposes strong constraints on the flavour structure of the Yukawa couplings associated to each one of the Higgs doublets. In particular, we find a novel solution, where all Yukawa couplings are proportional to the so-called democratic matrix. This solution is rather unique, since it is the only stable solution which is a good starting point for reproducing the observed pattern of quark masses and mixing. We also show that th…
We consider a 4-Higgs-doublet model in which each Higgs doublet gives mass to one of the fermion sets $\{ m_t\}$, $\{ m_b,m_τ,m_c \}$, $\{ m_μ,m_s \}$, and $\{ m_d,m_u,m_e \}$. The sets have the feature that within each of them the masses are similar. Our model explains the mass hierarchies of the sets by hierarchies of the vacuum expectation values of the Higgs doublets associated to them. All Yukawa couplings are therefore of order one. Neutrino masses are generated by a type-I seesaw mechanism with PeV-scale singlet neutrinos. To avoid the appearance of tree-level flavor changing neutral cu…
We study in detail the little-Higgs model proposed by Low, Skiba and Smith with an SU(6)/Sp(6) group structure. The effective theory at the TeV scale is a two-Higgs doublet model (2HDM) with additional heavy vector-like fermions and vector-bosons. We identify a set of independent input parameters and develop expressions for masses and couplings in terms of these. We perform a random scan of the parameter space and find points that satisfy constraints, including the recent 8 TeV LHC Higgs measurements, namely, the Higgs mass, Higgs couplings to the top, bottom, $τ$, $W^\pm$ and $Z$, top-quark m…
A three Higgs-doublet model admitting an $S_3$-symmetry can predict the observed pattern of the quark masses and their mixings. However the same symmetry also introduces potential flavour-changing neutral currents at the tree level. We assume in this work that the scalar potential contains appropriate \emph{soft} $S_3$-breaking terms in order to keep the choices of the scalar masses flexible. We identify the parameters in the Yukawa Lagrangian in the quark sector responsible for such FCNCs and constrain them using data from some of the flavour physics observables like meson-decays and meson-mi…
In a two-Higgs-doublet model (2HDM), at the vicinity of the alignment limit, the extra contributions to the couplings of the SM-like Higgs with other particles can be subdominant to the same coming from the six dimensional operators. In this context, we revisit the alignment limit itself. It is investigated to what extent these operators can mask the actual alignment in a 2HDM. The bosonic operators which rescale the Higgs kinetic terms can lead to substantial change in the parameter space of the model. We find that some other bosonic operators, which are severely constrained from the electrow…
For the general Two-Higgs-Doublet model, we present conditions for having spontaneous CP violation, in terms of physical masses and couplings. These relations involve the charged-Higgs mass, its cubic couplings with neutral scalars and quartic coupling, and become particularly simple in the alignment limit. In the simplified model with softly broken $Z_2$ symmetry, some deviation from alignment is required for spontaneous CP violation to be present.
In models with an extended Higgs sector there exists an alignment limit, in which the lightest CP-even Higgs boson mimics the Standard Model Higgs. The alignment limit is commonly associated with the decoupling limit, where all non-standard scalars are significantly heavier than the $Z$ boson. However, alignment can occur irrespective of the mass scale of the rest of the Higgs sector. In this work we discuss the general conditions that lead to "alignment without decoupling", therefore allowing for the existence of additional non-standard Higgs bosons at the weak scale. The values of $\tanβ$ fo…
The two-Higgs doublet model (2HDM) provides an excellent benchmark to study physics beyond the Standard Model (SM). In this work we discuss how the behaviour of the model at high energy scales causes it to have a scalar with properties very similar to those of the SM -- which means the 2HDM can be seen to naturally favor a decoupling or alignment limit. For a type II 2HDM, we show that requiring the model to be theoretically valid up to a scale of 1 TeV, by studying the renormalization group equations (RGE) of the parameters of the model, causes a significant reduction in the allowed magnitude…
There is a surprising connection between the top quark and Higgs alignment in Gildener-Weinberg multi-Higgs doublet models. Were it not for the top quark and its large mass, the coupling of the 125 GeV Higgs boson $H$ to gauge bosons and fermions would be indistinguishable from those of the Standard Model Higgs. The top quark's coupling to a single Higgs doublet breaks this perfect alignment in higher orders of the Coleman-Weinberg loop expansion of the effective potential. But the effect is still small, $< {\cal{O}}(1\%)$, and probably experimentally inaccessible.
We examine some of the theoretical and phenomenological implications of the Higgs boson discovery and discuss what these imply for future Higgs studies at the LHC and future colliders. In particular, one of the outstanding unanswered questions is whether additional scalars beyond the observed Higgs boson are present in the spectrum of fundamental particles. Any theory of a non-minimal Higgs sector must possess a scalar state whose properties are approximately those of the Standard Model Higgs boson. This can be achieved in the so-called alignment limit of the extended scalar sector. Examples o…
As the LHC Higgs data persistently suggest the couplings of the observed 125 GeV Higgs boson to be consistent with the Standard Model (SM) expectations, any extended Higgs sector must lead to the so-called SM alignment limit, where one of the Higgs bosons behaves exactly like that of the SM. In the context of the Two Higgs Doublet Model (2HDM), this alignment is often associated with either decoupling of the heavy Higgs sector or accidental cancellations in the 2HDM potential. We present a novel symmetry justification for `natural' alignment without necessarily decoupling or fine-tuning. We sh…
The properties of the Higgs boson discovered at the Large Hadron Collider are very well described by the Standard Model (SM). Thus, any theory that invokes an extended Higgs sector must explain why the neutral scalar observed at the LHC so closely resembles the SM Higgs boson. In this talk, I review the Higgs alignment limit, in which one neutral scalar state of the Higgs sector is SM-like. An approximate Higgs alignment can be achieved "naturally" either via decoupling or via an approximate symmetry. Using the two-Higgs doublet model as a prototype for an extended Higgs sector, I examine the …
It has been observed that an automatic alignment without decoupling is predicted at tree-level in a Two-Higgs Doublet Model (2HDM) with extended supersymmetry in the gauge and Higgs sectors. Moreover, it was found that radiative corrections preserve this alignment to a very good precision. We show that it is the non-abelian global $SU(2)_R$ R-symmetry that is at the origin of this alignment. This differs from previously considered Higgs family symmetries as it is present only in the quartic part of the Higgs potential. It can not be imposed to the quadratic part which has to be generated by $N…
