arXiv subjects

A. Kunčinas

Publications and source records attributed to A. Kunčinas.

8 recordsLinked to original sources

arXiv2026

GOOFy-compatible 3HDMs and beyond

Beyond conventional Higgs-family and general CP transformations, one may also consider a broader class of non-standard "GOOFy" transformations, in which the scalar fields and their conjugates are assigned related but inequivalent transformations. Although these transformations are not symmetries of a full Lagrangian in the conventional sense, some nevertheless stabilise the scalar potential. Their impact on the quadratic sector has not yet been systematically classified. We develop a sign-orbit technique to determine the bilinear structures compatible with these transformations. Applied to three-Higgs-doublet models, and formulated so as to extend to larger multi-Higgs sectors, the method shows that a non-vanishing GOOFy-compatible quadratic sector exists only when two independent conditions are met: the underlying group admits a non-trivial sign character, and that character is realised within the tensor product of the scalar representation and its conjugate. As a key consequence, we demonstrate that the renormalisation-group stability of the $r_0 \to -r_0$ manifold in isolation is not a generic feature of multi-Higgs potentials, but rather a direct consequence of special algebraic properties of $SU(2)$. These results provide a classification of the admissible GOOFy quadratic structures and their invariant bilinear subspaces, highlighting the algebraic obstructions to their renormalisation-group stability.

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arXiv2026

Systematic analysis of 3HDM symmetries

Symmetries play a crucial role in shaping the structure and predictions of multi-Higgs-doublet models. In three-Higgs-doublet models considerable effort has been put into classifying possible symmetry groups and the conditions for their realisation, yet the completeness of existing classifications remains an open question. In this work, we revisit the problem of identifying realisable symmetries by re-examining conventional Higgs family and general CP transformations from an alternative perspective. Our analysis identifies certain limitations in previous approaches and introduces a clearer, more systematic framework for model builders. We expand our classification by investigating more generalised symmetry structures - the recently identified GOOFy transformations, which act non-trivially on the Higgs doublets and their conjugates. Our analysis consolidates known results, uncovers previously overlooked structures, and expands the set of symmetries in three-Higgs-doublet models, offering both a clearer theoretical foundation and a practical reference for symmetry-based model building.

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arXiv2024

$U(1)$-charged Dark Matter in three-Higgs-doublet models

We explore three-Higgs-doublet models that may accommodate scalar Dark Matter where the stability is based on an unbroken $U(1)$-based symmetry, rather than the familiar $\mathbb{Z}_2$ symmetry. Our aim is to classify all possible ways of embedding a $U(1)$ symmetry in a three-Higgs-doublet model. The different possibilities are presented and compared. All these models contain mass-degenerate pairs of Dark Matter candidates due to a $U(1)$ symmetry unbroken (conserved) by the vacuum. Most of these models preserve CP. In the CP-conserving case the pairs can be seen as one being even and the other being odd under CP or as having opposite charges under $U(1)$. Not all symmetries presented here were identified before in the literature, which points to the fact that there are still many open questions in three-Higgs-doublet models. We also perform a numerical exploration of the $U(1) \otimes U(1)$-symmetric 3HDM, this is the most general phase-invariant (real) three-Higgs-doublet model. The model contains a multi-component Dark Matter sector, with two independent mass scales. After imposing relevant experimental constraints we find that there are possible solutions throughout a broad Dark Matter mass range, 45-2000 GeV, the latter being a scan cutoff.

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arXiv2023

Complex $S_3$-symmetric 3HDM

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.

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arXiv2023

Revisiting two dark matter candidates in $S_3$-symmetric three-Higgs-doublet models

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.

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arXiv2022

Dark matter in a CP-violating three-Higgs-doublet model with $S_3$ symmetry

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.

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arXiv2022

Two dark matter candidates in three-Higgs-doublet models with $S_3$ symmetry

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.

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arXiv2022

Dark matter in three-Higgs-doublet models with $S_3$ symmetry

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.

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