Search

We explore the phenomenology of Weinberg's $Z_2\times Z_2$ symmetric three-Higgs-doublet potential, allowing for spontaneous violation of CP due to complex vacuum expectation values. An overview of all possible ways of satisfying the stationary-point conditions is given, with one, two or three non-vanishing vacuum expectation values, together with conditions for CP conservation in terms of basis invariants. All possible ways of satisfying the conditions for CP conservation are given. Scans of allowed parameter regions are given, together with measures of CP violation, in terms of the invariants. The light states identified in an earlier paper are further explored in terms of their CP-violating couplings. Loop-induced CP violation in $WWZ$ couplings, as well as charge-asymmetric scattering are also commented on., Comment: 45 pages, 19 figures

The Two Higgs Doublet Model invariant under the gauge group SU(2)xU(1) is known to have six additional global discrete or continuous symmetries of its scalar sector. We have discovered regions of parameter space of the model which are basis and renormalization group invariant to all orders of perturbation theory in the scalar and gauge sectors, but correspond to none of the hitherto considered symmetries. We therefore identify seven new symmetries of the model and discuss their phenomenology. Soft symmetry breaking is required for some of these models so that electroweak symmetry breaking can occur. We show that, at least at the two-loop level, it is possible to extend some of these symmetries to include fermions., Comment: 46 pages, minor changes, references added

CP violation plays a very important role in nature with implications both for Particle Physics and for Cosmology. Accounting for the observed matter anti-matter asymmetry of the Universe requires the existence of new sources of CP violation beyond the Standard Model. In models with an extended scalar sector CP violation can emerge either explicitly, i.e., at the Lagrangian level, or spontaneously. In the context of multi-Higgs extensions of the Standard Model imposing the existence of a scalar basis where all couplings are real is a sufficient condition for CP to be explicitly conserved. We discuss a three-Higgs-doublet model with an underlying $S_3$ symmetry, allowing in principle for complex couplings. In this framework it is possible to have either spontaneous or explicit CP violation in the scalar sector, depending on the regions of parameter space corresponding to the different possible vacua of the $S_3$ symmetric potential. We list all possible vacuum structures allowing for CP violation in the scalar sector specifying whether it can be explicit or spontaneous. It is by now established that CP is violated in the flavour sector and that the Cabibbo-Kobayashi-Maskawa matrix is complex. In order to understand what are the possible sources of CP violation in the Yukawa sector we analyse the implications of the different available choices of representations for the quarks under the $S_3$ group. This classification is based strictly on the exact $S_3$-symmetric scalar potential with no soft symmetry breaking terms. The scalar sector of one such model was explored numerically. After applying the theoretical and the most important experimental constraints the available parameter space is shown to be able to give rise to light neutral scalars at the $\mathcal{O}(\text{MeV})$ scale., Comment: 42 pages, 2 figures, V2: version consistent with JHEP

Models with an extended scalar electroweak sector are well motivated. Such models could accommodate a dark matter candidate if there is an additional scalar representation with a vanishing vacuum expectation value and, in addition, there are no couplings between fermions and the dark matter candidate. The most natural way to have these conditions implemented is to consider models where an underlying symmetry is imposed. Governed by this, we consider a three-Higgs-doublet model with an $S_3$ symmetry. Within this framework there are different implementations which could possibly accommodate a dark matter candidate. The family of $S_3$-symmetric three-Higgs-doublet implementations arises due to different vacua and, as a result, different minimisation conditions. In this framework the dark matter candidate falls into the class of weakly interacting massive particles. The dark matter candidate is associated with an $\mathbb{Z}_2$ symmetry which survives spontaneous symmetry breaking and is a remnant of the $S_3$ symmetry. We explore two cases, they share many aspects of the Type-I two-Higgs-doublet model plus an inert SU(2) doublet. The main difference between these two cases is the presence of an irremovable phase, which leads to CP violation in one of the implementations. The two candidate cases differ from other previously studied models with three scalar doublets by the fact that they do not allow for heavy dark matter candidates, $\mathcal{O}(500)\text{ GeV}$. Valid dark matter regions were identified as $m_\mathrm{DM} \in [52.5,\,89]~\text{GeV}$ for a model without CP violation and $m_\mathrm{DM} \in [6.5,\,44.5]~\text{GeV}$ for a model with CP violation. In the present work we refine the parameter space by applying additional checks to our previous work coming from LHC data and from indirect detection data., Comment: 8 pages, 5 figures, to be published in the Proceedings of DISCRETE 2022: 8th Symposium on Prospects in the Physics of Discrete Symmetries, 7-11 November, 2022, Baden-Baden, Germany

The $\mathbb Z_2\times \mathbb Z_2$-symmetric 3HDM potential, sometimes called Weinberg's 3HDM potential, can accommodate both explicit and spontaneous CP violation as well as natural flavour conservation and is hence relevant for studies of CP violation coming from a realistic extended Higgs sector. The model has an interesting regime, controlled by a single parameter, where it acquires an approximate global $U(1) \times U(1)$ symmetry which causes CP violating effects to be small and two pseudo-Goldstone bosons to be present in the scalar spectrum. From parameter space scans, we find that, in a realistic implementation featuring an SM-like Higgs boson, this model predominantely leads to the existence of light additional Higgs bosons with a mass lower than the SM-like Higgs boson.

Soft breaking of a symmetry requires an invariance of the dimension-4 part of the Lagrangian and non-trivial variation of the lower-dimensional part. However, in general, separation between the dim-4 and lower-dimensional Lagrangian is not invariant with respect to basis transformations of fields. Therefore, a natural question of the physical meaning of soft symmetry breaking arises. This problem is addressed here in the framework of two-Higgs-Doublet Models (2HDM). It has been shown, within these models, that in spite of the ambiguity corresponding to the separation between dim-4 and the lower-dimension Lagrangian, implications of the soft symmetry breaking could be formulated in terms of observables, i.e., they are physical and measurable. There are six global symmetries that can be imposed on the scalar sector of the generic 2HDM. Necessary and sufficient tree-level conditions for soft breaking of all of them have been formulated in terms of observables., Comment: 40 pages, 1 figure, matches published version

We study the potential of Weinberg's $\mathbb{Z}_2\times\mathbb{Z}_2$-symmetric three-Higgs-doublet model (3HDM). The potential is designed to accommodate CP violation in the scalar sector within a gauge theory, while at the same time allowing for natural flavour conservation. This framework allows for both explicit and spontaneous CP violation. CP can be explicitly violated when the coefficients of the potential are taken to be complex. With coefficients chosen to be real, CP can be spontaneously violated via complex vacuum expectation values (vevs). In the absence of the terms leading to the possibility of CP violation, either explicit or induced by complex vevs, the potential has two global U(1) symmetries. In this case, spontaneous symmetry breaking would in general give rise to massless states. In a realistic implementation, those terms must be included, thus preventing the existence of Goldstone bosons. A scan over parameters, imposing the existence of a neutral state at 125 GeV that is nearly CP-even shows that, in the absence of fine-tuning, the scalar spectrum contains one or two states with masses below 125 GeV that have a significant CP-odd component. These light states would have a low production rate via the Bjorken process and could thus have escaped detection at LEP. At the LHC the situation is less clear. While we do not here aim for a full phenomenological study of the light states, we point out that the $\gamma\gamma$ decay channel would be challenging to measure because of suppressed couplings to $WW$., Comment: Minor changes, some references added. Matches Phys. Rev. D version

Models with an extended scalar electroweak sector can have vanishing vacuum expectation values in a basis where an underlying symmetry is imposed. Such extensions are very well motivated. If a symmetry prevents couplings between fermions and additional scalars, such scalars could become viable dark matter candidates if some additional criteria are satisfied. We catalogue $S_3$-symmetric three-Higgs-doublet models, also allowing for softly broken $S_3$-symmetric scalar potential terms, based on whether a specific model could possibly accommodate a dark matter candidate. The variety of the $S_3$-symmetric family models arises due to different possibilities to arrange vacuum expectation values. Such models can have vacua with one or two vanishing vacuum expectation values. In our study we assume that the dark matter candidate is stabilised by the $\mathbb{Z}_2$ symmetry. The $\mathbb{Z}_2$ symmetry is a remnant of $S_3$ symmetry which survived spontaneous symmetry breaking, and not superimposed over $S_3$. We explore two models; with an without CP violation. These models have a single dark and two active scalar sectors. The active sectors behave in many aspects like a Type-I two-Higgs-doublet model. The dark matter candidate masses, in two cases, are different from the known (previously studied) models with three scalar doublets. After investigating the models in detail, identifying parameters compatible with both theoretical and experimental constraints, we found that the dark matter candidate mass could be within the range of $[52.5,\,89]~\text{GeV}$ or $[6.5,\,44.5]~\text{GeV}$ for a model with CP violation., Comment: 6 pages, 3 figures, to be published in the Proceedings of DISCRETE 2020-2021: 7th Symposium on Prospects in the Physics of Discrete Symmetries, 29th November - 3rd December 2021, Bergen, Norway; v2: Minor changes

In spite of the success of the Standard Model of Particle Physics, there are some theoretical predictions which are not yet fully established experimentally as well as some experimental observations which cannot be fitted within its theoretical framework, thus requiring physics beyond the Standard Model. One of these is a hypothetical non-luminous form of matter - dark matter. Models with an extended scalar electroweak sector yield plausible dark matter candidates. In this paper we study a specific model, C-III-a, from a family of $S_3$-symmetric three-Higgs-doublet models. The model consists of two active SU(2) doublets and an inert one. The latter is inert due to a $\mathbb{Z}_2$ symmetry that survives the breaking of $S_3$, and would accommodate a dark matter particle. We explore the model numerically, based on theoretical and experimental constraints. After applying a number of successive checks over the parameter space we found a viable dark matter mass region in the range $[6.5;\,44.5]~\text{GeV}$. This region is drastically different from the Higgs-like dark matter states that have been proposed: the well-known Inert Doublet Model and models with three scalar doublets, with one or two inert doublets. Furthermore, the C-III-a model allows for spontaneous CP violation., Comment: 40 pages, 12 figures. v2: PRD version, minor clarifications. arXiv admin note: text overlap with arXiv:2108.07026

Models with two or more scalar doublets with discrete or global symmetries can have vacua with vanishing vacuum expectation values in the bases where symmetries are imposed. If a suitable symmetry stabilises such vacua, these models may lead to interesting dark matter candidates, provided that the symmetry prevents couplings among the dark matter candidates and the fermions. We analyse three-Higgs-doublet models with an underlying $S_3$ symmetry. These models have many distinct vacua with one or two vanishing vacuum expectation values which can be stabilised by a remnant of the $S_3$ symmetry which survived spontaneous symmetry breaking. We discuss all possible vacua in the context of $S_3$-symmetric three-Higgs-doublet models, allowing also for softly broken $S_3$, and explore one of the vacuum configurations in detail. In the case we explore, only one of the three Higgs doublets is inert. The other two are active, and therefore the active sector, in many aspects, behaves like a two-Higgs-doublet model. The way the fermions couple to the scalar sector is constrained by the $S_3$ symmetry and is such that the flavour structure of the model is solely governed by the $V_\text{CKM}$ matrix which, in our framework, is not constrained by the $S_3$ symmetry. This is a key requirement for models with minimal flavour violation. In our model there is no CP violation in the scalar sector. We study this model in detail giving the masses and couplings and identifying the range of parameters that are compatible with theoretical and experimental constraints, both from accelerator physics and from astrophysics., Comment: 50 pages, 14 figures, V2: typos fixed, some plots changed, V3: minor text edits, V4: version consistent with JHEP

Symmetries of the Two-Higgs-Doublet Model (2HDM) potential that can be extended to the whole Lagrangian, i.e. the CP-symmetries CP1, CP2, CP3 and the Higgs-family symmetries Z2, U(1) and SO(3) are discussed. Sufficient and necessary conditions in terms of constraints on masses and physical couplings for the potential to respect each of these symmetries are found. Each symmetry can be realized through several alternative cases, each case being a set of relations among physical parameters. We will show that some of those relations are invariant under the renormalization group, but others are not. The cases corresponding to each symmetry group are illustrated by analyzing the interplay between the potential and the vacuum expectation values., Comment: 58 pages, 7 figures. JHEP version. References added, clarifications and minor changes made

In this paper we analyse in detail an $S_3$-symmetric three-Higgs-doublet model with a specific vacuum configuration. This analysis allows us to illustrate important features of models with several Higgs doublets, such as the possibility of having spontaneous CP violation. We start with a real potential and pick a particularly interesting complex vacuum configuration, which does not violate CP before adding soft breaking terms to the potential. We study the r\^ ole played by different soft symmetry breaking terms. These are essential for our choice of vacuum in order to remove unwanted massless scalars which arise from the spontaneous breaking of an accidental continuous symmetry. We list scalar sector and scalar-gauge sector-couplings for the particular case we consider in detail in this work. Results presented in this paper will be useful for model building, in particular for implementations of models with $S_3$ symmetry and spontaneous CP violation, extensions of the fermionic sector with realistic Yukawa couplings and for Dark Matter studies., Comment: 33 pages. v2: PRD version, Minor clarifications. References added. Title compliant with APS style

Symmetries play a very important r\^ole in Particle Physics. In extended scalar sectors, the existence of symmetries may permit the models to comply with the experimental constraints in a natural way, and at the same time reduce the number of free parameters. There is a strong interplay among internal symmetries of the scalar potential, its CP properties and mass degeneracies of the physical scalars. Some of these aspects were discussed in this talk., Comment: 8 pages, to be published in the Proceedings of DISCRETE2018: 6th Symposium on Prospects in the Physics of Discrete Symmetries, 26-30 Nov 2018. Vienna, Austria

We discuss the three different classes of CP-symmetries that can be realized in a two-Higgs-doublet model, CP1, CP2 and CP3. We express conditions for realizing these symmetries in terms of masses and couplings of the model, thereby providing a way of verifying which, if any, of these symmetries is realized by nature., Comment: Contribution to the conference proceedings of DISCRETE 18

We explore some aspects of models with two and three SU(2) scalar doublets that lead to mass degeneracies among some of the physical scalars. In Higgs sectors with two scalar doublets, the exact degeneracy of scalar masses, without an artificial fine-tuning of the scalar potential parameters, is possible only in the case of the inert doublet model (IDM), where the scalar potential respects a global U(1) symmetry that is not broken by the vacuum. In the case of three doublets, we introduce and analyze the replicated inert doublet model, which possesses two inert doublets of scalars. We then generalize this model to obtain a scalar potential, first proposed by Ivanov and Silva, with a CP4 symmetry that guarantees the existence of pairwise degenerate scalar states among two pairs of neutral scalars and two pairs of charged scalars. Here, CP4 is a generalized CP symmetry with the property that $({\rm CP}4)^n$ is the identity operator only for integer $n$ values that are multiples of 4. The form of the CP4-symmetric scalar potential is simplest when expressed in the Higgs basis, where the neutral scalar field vacuum expectation value resides entirely in one of the scalar doublet fields. The symmetries of the model permit a term in the scalar potential with a complex coefficient that cannot be removed by any redefinition of the scalar fields within the class of Higgs bases (in which case, we say that no real Higgs basis exists). A striking feature of the CP4-symmetric model is that it preserves CP even in the absence of a real Higgs basis, as illustrated by the cancellation of the contributions to the CP violating form factors of the effective ZZZ and ZWW vertices., Comment: 52 pages, 2 figures, second revised version with new material, as published by JHEP

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 field~$H_1$, with the tree-level couplings of the SM Higgs boson, is a mass eigenstate that is aligned in field space with the direction of the Higgs vacuum expectation value. The properties of the two other heavier neutral Higgs scalars, $H_2$ and $H_3$, in the alignment limit of the 2HDM are also elucidated. It is shown that the couplings of $H_2$ and $H_3$ in the alignment limit are tightly constrained and correlated. For example, in the exact alignment limit at tree level, for bosonic final states $\text{BR}(H_{2,3} \to W^+W^-, ZZ, H_1 Z) = 0$ and $\text{BR}(H^\pm \to W^\pm H_1) = 0$, whereas for fermionic final states $\Gamma(H_2 \to f\bar f)/\Gamma(H_3 \to f\bar f) \sim M_2/M_3$ (where $M_\alpha$ is the mass of $H_\alpha$). In some cases, the results of the alignment limit differ depending on whether or not alignment is achieved via the decoupling of heavy scalar states. In particular, in the exact alignment limit without decoupling $\text{BR}(H_{2,3}\to H_1 H_1)=0$, whereas these branching ratios are nonzero in the decoupling regime. Observables that could be used to test the alignment scenario at the LHC are defined and discussed. The couplings of the Higgs bosons away from their exact alignment values are determined to leading order, and some consequences are elucidated., Comment: 44 pages, 1 figure; v2: references added; v3: major clarifications; v4: JHEP version

We discuss how one can identify CP violation (and conservation) in multi-Higgs-doublet potentials. After a brief review of CP violation in the 2HDM, we refer to the fact that for NHDM with $N \geq 3$ the well known methods useful in the case $N = 2$ have not been generalized in order to provide a set of well defined necessary and sufficient conditions for CP conservation. We then present a simple method, proposed by the authors, to be used in such cases. Two non-trivial examples based on an $S_3$-symmetric three-doublet model are analyzed by means of this new method., Comment: 10 pages. Talk given at Corfu Summer Institute 2017, School and Workshops on Elementary Particle Physics and Gravity, September 2017. To appear in conference proceedings

We discuss the importance of basis invariants in the general 2HDM and how these relates to masses and couplings. We also present a simple, yet powerful technique to translate parameters of the potential into combinations of masses and couplings of the theory and apply this to CP odd invariants., Comment: 14 pages. Talk given at Corfu Summer Institute 2017, School and Workshops on Elementary Particle Physics and Gravity, September 2017. To appear in conference proceedings

The talk summarises work done by the authors consisting of a detailed study of the possible vacua in models with three Higgs doublets with $S_3$ symmetry and without explicit CP violation. Different vacua require special regions of the parameter space which were analysed in our work. We establish the possibility of spontaneous CP violation in this framework and we also show which complex vacua conserve CP. In our work we discussed constraints from vacuum stability. The results presented here are relevant for model building., Comment: 11 pages, no figures. Prepared for the proceedings of DISCRETE2016: the Fifth Symposium on Prospects in the Physics of Discrete Symmetries, 28 November-3 December 2016, University of Warsaw, Poland, to appear in the Journal of Physics: Conference Series (JPCS)

For models with several Higgs doublets we present an alternative method to the one proposed by Branco, Gerard and Grimus, in 1984, to check whether or not CP is spontaneously violated in the Higgs potential. The previous method is powerful and rigorous. It requires the identification of a matrix $U$ corresponding to a symmetry of the Lagrangian and verifying a simple relation involving the vacuum expectation values. The nonexistence of such a matrix signals spontaneous CP violation. However, as the number of Higgs doublets increases, finding such a matrix $U$ may not be straightforward and it may turn out to be easier to analyse the potential by going to the so-called Higgs basis. The transformation to the Higgs basis is straightforward once the vacuum expectation values are known. The method proposed in this work is also powerful and rigorous and can be particularly useful to analyse models with more than two Higgs doublets and with continuous symmetries., Comment: 9 pages, no figures. v2: minor changes, matching JHEP version

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., Comment: 22 pages

Models with an extended scalar sector may in principle provide new sources of CP violation originating in the scalar potential. One of the simplest ways to implement this idea is to have CP violation in a two-Higgs-doublet model. Here, it leads to CP violation in trilinear weak gauge boson couplings. We discuss how these couplings are becoming constrained in the alignment limit. In a model with three Higgs doublets, subject to an $S_3$ symmetry, several complex vacua are possible. Some of these, but not all, may lead to spontaneous CP violation., Comment: 8 pages, Proceedings of the Corfu Summer Institute 2015 "Summer School and Workshop on the Standard Model and Beyond", 1-11 September 2015 Corfu, Greece

We discuss possibilities of measuring CP violation in the Two-Higgs-Doublet Model by studying effects of one-loop generated $ZZZ$ and $ZWW$ vertices. We discuss a set of CP-sensitive asymmetries for $ZZ$ and $W^+W^-$ production at linear $e^+e^-$-colliders, that directly depends on the weak-basis invariant Im $J_2$ that parametrises the strength of CP violation. Given the restrictions on this model that follow from the LHC measurements, the predicted effects are small. Pursuing such measurements is however very important, as an observed signal might point to a richer scalar sector., Comment: 28 pages, v2: Signs in Eqs. (3.4) and (A.4) corrected, confirming result of arXiv:1710.05563. Fig. 2 corrected

We present a detailed study of the vacua of the $S_3$-symmetric three-Higgs-doublet potential, specifying the region of parameters where these minimisation solutions occur. We work with a CP conserving scalar potential and analyse the possible real and complex vacua with emphasis on the cases in which the CP symmetry can be spontaneously broken. Results are presented both in the reducible-representation framework of Derman, and in the irreducible-representation framework. Mappings between these are given. Some of these implementations can in principle accommodate dark matter and for that purpose it is important to identify the residual symmetries of the potential after spontaneous symmetry breakdown. We are also concerned with constraints from vacuum stability., Comment: 37 pages. v2: Minor changes in the references, matches published version. v3: Table 6 corrected: two additional cases conserve CP. Related discussion adapted. Version consistent with JHEP Erratum

We review CP properties of the Two-Higgs-Doublet model. In particular, we show that spontaneous CP violation occurs in the parameter space on the border between regions allowing explicit CP violation and those where there is another minimum, deeper than the one corresponding to v=246 GeV. We discuss weak-basis invariants which describe CP violation and express them through measurable quantities like coupling constants and masses. Also, we discuss how CP violation is constrained by the LHC Higgs data. Finally, we identify effective operators that could be adopted to measure CP-invariants., Comment: 9 pages, Proceedings of the Corfu Summer Institute 2014 "School and Workshops on Elementary Particle Physics and Gravity", 3-21 September 2014 Corfu, Greece. v2: References added

In Two-Higgs-Doublet models, the conditions for CP violation can be expressed in terms of invariants under U(2) rotations among the two SU(2) Higgs doublet fields. In order to design a strategy for measuring the invariants we express them in terms of observables, i.e., masses and couplings of scalar bosons. We find amplitudes directly sensitive to the invariants. Observation of the Standard-Model-like Higgs boson at the LHC severely constrains the models. In particular, in the model with Z_2 symmetry imposed on dimension-4 terms (in order to eliminate tree-level flavour-changing neutral currents), CP violation is strongly suppressed. On the other hand, the most general Two-Higgs-Doublet model (without Z_2 symmetry) would still allow for CP violation to be present in the model, without being in conflict with the LHC data. Consequently, also flavour-changing neutral currents would in general be expected. We briefly sketch a strategy for measuring the remaining CP violation., Comment: 26 pages, 7 figures. Version published in JHEP

We have investigated a Two-Higgs-Doublet Model (2HDM), focusing on CP violation. Various scenarios with spontaneous and explicit breaking of CP have been considered. Some features of CP violation related to a choice of the basis for the two Higgs doublets have been discussed and clarified. Regions in the physical parameter space corresponding to spontaneous and explicit CP violation have been located and discussed. The possibility to determine parameters of the scalar potential with no reference to Yukawa couplings has been considered and an unavoidable ambiguity has been found. The issue of disentangling spontaneous and explicit CP violation has been investigated., Comment: 32 pages, 5 figures. Minor changes. Version to appear in JHEP

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 at the LHC., Comment: Contribution to PoS Proceedings, The XXth International Workshop High Energy Physics and Quantum Field Theory, September 24 - October 1, 2011, Sochi, Russia

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., Comment: 39 pages, several figures. v2: Extraneous figures removed, name corrected. v3: version to appear in JHEP

We explore an extension of the Inert Doublet Model which allows also for CP violation in the Higgs sector. This necessitates two non-inert doublets. The lightest neutral scalar of the inert doublet is a candidate for dark matter. Scanning over parameters we preserve the abundance of the dark matter in agreement with the WMAP data. We also impose all relevant collider and theoretical constraints to determine the allowed parameter space for which both the dark matter is appropriate and CP is violated. In addition we find regions where the cut-off of the model originating from naturality arguments can be substantially lifted compared to its Standard Model value, reaching 2-3 TeV., Comment: 38 pages, 8 figures, LaTeX. v2: PRD version (some clarifications, two new figures)

We present general expressions for the oblique parameters S, T, U, V, W, and X in the SU(2)xU(1) electroweak model with an arbitrary number of scalar SU(2) doublets, with hypercharge 1/2, and an arbitrary number of scalar SU(2) singlets., Comment: 18 pages, 5 figures

We derive a general expression for Delta rho (or, equivalently, for the oblique parameter T) in the SU(2) x U(1) electroweak model with an arbitrary number of scalar SU(2) doublets, with hypercharge +-1/2, and an arbitrary number of scalar SU(2) singlets. The experimental bound on Delta rho constitutes a strong constraint on the masses and mixings of the scalar particles in that model., Comment: 19 pages, 2 figures, part of the introduction rewritten, small changes in the bibliography, one reference added

We review recent work on constraining the parameter space of the Two-Higgs-Doublet Model by theoretical and experimental results. Some characteristics of the model, in particular the distribution of masses in the surviving parameter space, are discussed., Comment: 4 pages, Latex, 3 eps-figures included, Talk given at 2007 International Linear Collider Workshop (LCWS07 and ILC07), Hamburg, Germany, 30 May - 3 Jun 2007

We confront the Two-Higgs-Doublet Model with a variety of experimental constraints as well as theoretical consistency conditions. The most constraining data are the \bar B\to X_s\gamma decay rate (at low values of M_{H^\pm}), and \Delta\rho (at both low and high M_{H^\pm}). We also take into account the B\bar B oscillation rate and R_b, or the width \Gamma(Z\to b\bar b) (both of which restrict the model at low values of \tan\beta), and the B^-\to\tau\nu_\tau decay rate, which restricts the model at high \tan\beta and low M_{H^\pm}. Furthermore, the LEP2 non-discovery of a light, neutral Higgs boson is considered, as well as the muon anomalous magnetic moment. Since perturbative unitarity excludes high values of \tan\beta, the model turns out to be very constrained. We outline the remaining allowed regions in the \tan\beta-M_{H^\pm} plane for different values of the masses of the two lightest neutral Higgs bosons, and describe some of their properties., Comment: 17 pages, 17 figures

The Two-Higgs-Doublet Model is considered, in its CP-non-conserving version. It is shown quantitatively how vacuum stability and tree-level unitarity in the Higgs-Higgs-scattering sector constrain the parameter space of the model. In particular, at high values of tanbeta, the model violates unitarity, unless some of the Higgs bosons are heavy. In the regime of large CP violation in the neutral-Higgs-t-quark sector, which requires tanbeta lsim 1, the Yukawa coupling parameter space (determined by the neutral-Higgs-sector rotation matrix) is reasonably unconstrained. On the other hand, the corresponding neutral-Higgs-b-quark sector allows for large CP violation at tanbeta gg 1. However, here the model is more constrained: Significant CP violation is correlated with a considerable splitting among the two heavier Higgs bosons., Comment: 9 pages, Contribution to "FANS2006", to be published in " Nonlinear Phenomena in Complex Systems"

It is important to provide guidance on whether CP violation may be measurable in top-quark production at the Large Hadron Collider. The present work extends an earlier analysis of the non-supersymmetric Two-Higgs-Doublet Model in this respect, by allowing a more general potential. Also, a more comprehensive study of theoretical and experimental constraints on the model is presented. Vacuum stability, unitarity, direct searches and electroweak precision measurements severely constrain the model. We explore, at low \tan\beta, the allowed regions in the multidimensional parameter space that give a viable physical model. This exploration is focused on the parameter space of the neutral sector rotation matrix, which is closely related to the Yukawa couplings of interest. In most of the remaining allowed regions, the model violates CP. We present a quantitative discussion of a particular CP-violating observable. This would be measurable in semileptonically decaying top and antitop quarks produced at the LHC, provided the number of available events is of the order of a million., Comment: 45 pages, 10 figures, some in (essential) colour. Figures 2, 6 and 7 are bitmapped, better quality available on request. Version to appear in Nucl. Phys. B

Results are presented for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-, two- and three-dimensional series. The sums of these series can be evaluated with the help of various integral representations for hypergeometric functions, and expressed in terms of $\zeta(2)$, $\zeta(3)$, the Catalan constant $G$ and ${\rm Cl}_2(\pi/3)$ where ${\rm Cl}_2(\theta)$ is Clausen's function., Comment: 10 pages, LaTeX, 2 figures; presented at ICCAM-2000

We present results for infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-, two- and three-dimensional series. All these series can be expressed in terms of zeta(2) and zeta(3)., Comment: 17 pages, LaTeX, uses elsart.cls

We review the production of scalar Higgs-like particles in high-energy electron-electron collisions, via the fusion of electroweak gauge bosons. The emphasis is on how to distinguish a CP-even from a CP-odd Higgs particle. Among the more significant differences, we find that in the CP-odd case, the Higgs spectrum is much harder, and the dependence of the total cross section on the product of the polarizations of the two beams is much stronger, than in the CP-even case. We also briefly discuss parity violation, and the production of charged Higgs bosons., Comment: 31 pages, LaTeX, including 13 figures, uses epsf

We present results for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-dimensional and two-dimensional series. Most of these series can be expressed in terms of zeta(2), zeta(3), the Catalan constant G and Cl{2}(pi/3) where Cl{2}(theta) is Clausen's function., Comment: AMS-LaTeX v1.2, 24 pages

The sensitivity of various angular and energy distributions to the CP of a Higgs candidate are considered for the process $e^-e^- -> e^-e^-h$, where h is either a scalar or a pseudoscalar Higgs. This process may differ from the corresponding production at an $e^+e^-$ collider in the availability of both beams being polarized. Beam polarization enhances the sensitivity of the azimuthal distribution., Comment: 5 pages, Latex, 3 figures included, uses psfig.sty. Talk given at the XIth International Workshop on Quantum Field Theory and High Energy Physics, St. Petersburg, Russia, September 1996. To appear in the Proceedings