We provide a complete description of perturbative unitarity bounds on the gauge-scalar sectors of models with extra $SU(2)$ doublet, neutral singlet, and charged singlet scalars. Such additions are very frequent in models beyond the Standard Model, and, in particular, they are almost universal in models explaining the dark matter problem. We propose a specific classification and minimal set of scattering matrices containing all the relevant information. We also developed a Mathematica implementation of our results, BounDS, and we use it to fully study a number of simple cases, comparing with the literature, when available. The Mathematica notebook BounDS is provided via a public GitHub repository.
Unitarity constraints for Yukawa couplings are considered in the Two Higgs Doublet Model type III, by using a general expansion in partial waves for fermionic scattering processes. Constraints over general Flavor Changing Neutral Currents are found from that systematic, such bounds compete with those coming from Lagrangian perturbativity requirement but are weaker than those imposed from phenomenological processes and precision tests. Nevertheless, for bounds based on unitarity the number of assumptions is the lowest among phenomenological and theoretical limits. Indeed, these new theoretical …
We investigate unitarity bounds in the most general two Higgs doublet model without a discrete $Z_2$ symmetry nor CP conservation. S-wave amplitudes for two-body elastic scatterings of Nambu-Goldstone bosons and physical Higgs bosons are calculated at high energies for all possible initial and final states (14 neutral, 8 singly-charged and 3 doubly-charged states). We obtain analytic formulae for the block-diagonalized scattering matrix by the classification of the two body scattering states using the conserved quantum numbers at high energies. Imposing the condition of perturbative unitarity …
Motivated by the discovery of a new scalar field and amelioration of the electroweak vacuum stability ascribed to a singlet scalar field embedded in the standard model (SM), we examine the implication of the perturbative unitarity in the SM with a singlet scalar field. Taking into account the full contributions to the scattering amplitudes, we derive unitarity conditions on the scattering matrix which can be translated into bounds on the masses of the scalar fields. In the case that the singlet scalar field develops vacuum expectation value (VEV), we get the upper bound on the singlet scalar m…
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…
We compute all of the one-loop corrections that are enhanced, $O(λ_i λ_j / 16 π^2)$, in the limit $s \gg |λ_i | v^2 \gg M_{W}^2$, $s \gg m_{12}^2$ to all the $2 \to 2$ longitudinal vector boson and Higgs boson scattering amplitudes in the $CP$-conserving two-Higgs doublet model with a softly broken $\mathbb{Z}_2$ symmetry. In the two simplified scenarios we study, the typical bound we find is $|λ_i(s)| \lessapprox 4$.
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…
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…
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…
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 …
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.
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…
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 …
If the scalar sector of the Standard Model is non-minimal, one might expect multiple generations of the hypercharge-1/2 scalar doublet analogous to the generational structure of the fermions. In this work, we examine the structure of a Higgs sector consisting of N Higgs doublets (where N \geq 2). It is particularly convenient to work in the so-called charged Higgs basis, in which the neutral Higgs vacuum expectation value resides entirely in the first Higgs doublet, and the charged components of remaining N-1 Higgs doublets are mass-eigenstate fields. We elucidate the interactions of the gauge…
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…
Two-Higgs-Doublet-Models (THDMs) are among the simplest extensions of the standard model and are intensively studied in the literature. Using on-shell parameters such as the masses of the additional scalars as input, corresponds often to large quartic couplings in the underlying Lagrangian. Therefore, it is important to check if these couplings are for instance in agreement with perturbative unitarity. The common approach for doing this check is to consider the two-particle scattering matrix of scalars in the large centre-of-mass energy limit where only point interactions contribute. We show t…
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…
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.
We consider a Z_2-symmetric Two Higgs Doublet Model (2HDM), where the vacuum expectation values of both doublets are non-vanishing. Unitarity constraints for the SM-like 2HDM are analyzed for the mass of the lightest Higgs boson in the range [115,127] GeV. New stringent bounds on tanβ, 0.17<tanβ<6.10, are derived. A discussion of the source of these constraints is provided.
We study bounds from perturbative unitarity in a Composite 2-Higgs Doublet Model (C2HDM) based on the spontaneous breakdown of a global symmetry $SO(6)\to SO(4)\times SO(2)$ at the compositeness scale $f$. The eight pseudo Nambu-Goldstone Bosons (pNGBs) emerging from such a dynamics are identified as two isospin doublet Higgs fields. We calculate the $S$-wave amplitude for all possible 2-to-2-body elastic (pseudo)scalar boson scatterings at energy scales $\sqrt{s}$ reachable at the Large Hadron Collider (LHC) and beyond it, including the longitudinal components of weak gauge boson states as th…
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…
We study the perturbative unitarity bound given by dimension six derivative interactions consisting of Higgs doublets. These operators emerge from kinetic terms of composite Higgs models or integrating out heavy particles that interact with Higgs doublets. They lead to new phenomena beyond the Standard Model. One of characteristic contributions by derivative interactions appear in vector boson scattering processes. Longitudinal modes of massive vector bosons can be regarded as Nambu Goldstone bosons eaten by each vector field with the equivalence theorem. Since their effects become larger and …
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 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 explore the possibility of a beyond the standard model scalar ($ϕ$) as a possible explanation of the diphoton resonance at 750~GeV invariant mass reported by the ATLAS and CMS collaborations at the large hadron collider (LHC). We first present in a model-independent way the scalar-gluon-gluon and scalar-photon-photon effective couplings needed for obtaining the required diphoton cross-section at the LHC for different total widths. We investigate here two new-physics possibilities that can generate these effective couplings, namely, (i) the 2-Higgs-doublet model (2HDM) in the alignment limit…
We study the renormalizable singlet-doublet fermionic extension of the Standard Model. In this model, the new vector-like fermions couple to the gauge bosons and to the Higgs via new Yukawa couplings, that allow for nontrivial mixing in the new sector, providing a stable, neutral dark matter candidate. Approximate analytic formulae are given for the mass spectrum around the blind spots, where the dark matter candidate coupling to $h$ or $Z$ vanishes. We calculate the two particle scattering amplitudes in the model, impose the perturbative unitarity constraints and establish bounds on the Yukaw…
Non-unitarity of CKM matrix from the vector singlet quark mixing and neutron electric dipole moment
在标准模型（SM）中，夸克电偶极矩（EDM）的最低阶贡献发生在三圈水平。我们发现，在扩展夸克扇区的模型中，CKM矩阵的非么正性通常会在两个回路水平上产生夸克EDM，除了外部夸克质量外，它没有类似GIM的抑制因子。感生中子EDM的数量级为10^{-29} e cm，如果像SM中发生的那样通过长距离物理进一步增强，则可以很好地在下一代实验的范围内。
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.
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 investigate the general two Higgs doublet model imposing both the unitarity conditions and the bounded-from-below conditions. Both types of conditions restrict the ranges of the parameters of the scalar potential. We study the model in the Higgs basis, i.e. in the basis for the scalar doublets where only one doublet has vacuum expectation value. We use the experimental bounds on the oblique parameter T, to produce scalar particles with masses and cubic and quartic couplings of the Higgs in agreement with the phenomenology. The numerical calculations show that the cubic coupling may be up to…
We study the one-loop corrections to the $Zb\bar{b}$ vertex in extensions of the Standard Model with arbitrary numbers of scalar doublets, neutral scalar singlets, and charged scalar singlets. Starting with a general parameterization of theories with neutral and singly-charged scalar particles, we derive the conditions that, in a renormalizable model, must be obeyed by the couplings in order for the divergent contributions to cancel. Then, we show that those conditions are indeed obeyed by the models that we are interested in, and we write down the full finite expression for the vertex in thos…
We examine an extension of the Standard Model that addresses the dark matter puzzle and generates Dirac neutrinos masses through the radiative seesaw mechanism. The new field content includes a scalar field that plays an important role in setting the relic abundance of dark matter. We analyze the phenomenology in the light of direct, indirect, and collider searches of dark matter. In this framework, the dark matter candidate is a Dirac particle that is a mixture of new singlet-doublet fields with mass $m_{χ_1^0}\lesssim 1.1\,\text{TeV}$. We find that the allowed parameter space of this model i…
We present the next-to-leading-order calculation of the partial decay widths of light CP-even Higgs bosons decaying into four fermions in the Two-Higgs-Doublet Model and a Singlet Extension of the Standard Model. Different renormalization schemes are applied in the calculation, which is implemented into the analysis tool PROPHECY4F. Some sample results on the Higgs->4fermions decay widths illustrate how the corrections reduce the dependence on the renormalization scale and the choice of the scheme.
In light of recent data from direct detection experiments and the Large Hadron Collider, we explore models of dark matter in which an SU(2) doublet is mixed with a Standard Model singlet. We impose a thermal history. If the new particles are fermions, this model is already constrained due to null results from XENON100. We comment on remaining regions of parameter space and assess prospects for future discovery. We do the same for the model where the new particles are scalars, which at present is less constrained. Much of the remaining parameter space for both models will be probed by the next …
We present a detailed study of a combined singlet-doublet scalar and singlet-doublet fermion model for dark matter. These models have only been studied separately in the past. We show that their combination allows for the radiative generation of neutrino masses, but that it also implies the existence of lepton-flavour violating (LFV) processes. We first analyse the dark matter, neutrino mass and LFV aspects separately. We then perform two random scans for scalar dark matter imposing Higgs mass, relic density and neutrino mass constraints, one over the full parameter space, the other over regio…
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 revisit the singlet-doublet dark matter model with a special emphasis on the effect of CP violation on the dark matter phenomenology. The CP violation in the dark sector induces a pseudoscalar interaction of a fermionic dark matter candidate with the SM Higgs boson. The pseudoscalar interaction helps the dark matter candidate evade the strong constraints from the dark matter direct detection experiments. We show that the model can explain the measured value of the dark matter density even if dark matter direct detection experiments do not observe any signal. We also show that the electron e…
Confinement indicates an asymptotic quark state not observable except its energy is zero. Unitarity indicates that the total probability of a definite state of quark system to transit to any final state is exactly one. This talk reviews some important conclusions/predictions from the basic properties like unitarity of the combination model, as addressed by the title. We also in the Postscript section address the bottom quark energy loss. In the discussions around the dinner table in the Rencontre, the author combined the large transverse momentum J/Psi suppression and the contribution to J/Psi…
The non-unitarity of the effective leptonic mixing matrix at low energies is a generic signal of extensions of the Standard Model (SM) with extra fermionic singlet particles, i.e. sterile or right-handed neutrinos, to account for the observed neutrino masses. The low energy effects of such extensions can be described in a model-independent way by the Minimal Unitarity Violation (MUV) scheme, an effective field theory extension of the SM. We perform a global fit of the MUV scheme parameters to the present experimental data, which yields the up-to-date constraints on leptonic non-unitarity. Furt…
In this talk, we report unitarity constraints and phenomenological studies at the Large Hadron Collider for the extra Higgs bosons of a Composite 2-Higgs Doublet Model.
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 propose a minimal extension of the standard model (SM) by including a scalar triplet with hypercharge 2 and two vector-like leptons: one doublet and a singlet, to explain simulatenously the non-zero neutrino mass and dark matter (DM) content of the Universe. The DM emerges out as a mixture of the neutral component of vector-like lepton doublet and singlet, being odd under a discrete $Z_2$ symmetry. After electroweak symmetry breaking the triplet scalar gets an induced vev, which give Majorana masses not only to the light neutrinos but also to the DM. Due to the Majorana mass of DM, the $Z$ …
We study parameters of an extension of the Standard Model. The neutrino sector is enlarged by one right-handed singlet field, allowing for the seesaw mechanism type-I, and the Higgs sector contains one additional doublet, which contributes to light neutrino masses through one-loop radiative corrections. Employing an approximation for the effective light neutrino mass matrix we express the masses of the light neutrinos analytically, allowing us to parametrize the Yukawa couplings to neutrinos by the experimental measurements on the neutrino sector and only two free parameters. We focus on a CP-…
In a bid to simultaneous explanation of dark matter (DM) and tiny but non-zero masses of left-handed neutrinos, we propose a minimal extension of the Standard Model (SM) by a vector-like fermion doublet and three right handed (RH) singlet neutrinos. 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 additional $\mathcal{Z}_2$ symmetry. As a result, the DM emerges to be a dominantly Majorana particle and escapes from $Z$-mediated direct search constraints to mark a significant difference from singlet-doublet Di…
