Higgs Alignment Research Articles

Maximising CP Violation in naturally aligned Two-Higgs Doublet Models

The Two-Higgs Doublet Model (2HDM) is a well-motivated theoretical framework that provides additional sources of CP Violation (CPV) beyond the Standard Model (SM). After studying the vacuum topology of a general (convex) 2HDM potential, we unambiguously identify three origins of CPV: (i) Spontaneous CPV (SCPV), where the vacuum manifold has at least two degenerate CPV minima disconnected by domain walls, (ii) Explicit CPV (ECPV) with one single CPV ground state, and (iii) Mixed Spontaneous and Explicit CPV (MCPV), where the theory possesses more than one non-degenerate CPV local minimum. Most importantly, we define a novel complex parameter rCP whose norm and phase control the three different realisations of CPV, at least at the tree level. In all these scenarios, only two CPV phases can be made independent, as any third CPV parameter will always be constrained via the CP-odd tadpole condition. Since ECPV vanishes in 2HDMs where SM Higgs alignment is achieved naturally through accidental continuous symmetries, we analyse the possibility of maximising CPV through soft and explicit breaking of these symmetries. We derive upper limits on key CPV parameters that quantify the degree of SM misalignment from constraints due to the non-observation of an electron Electric Dipole Moment (EDM). Finally, we delineate the CP-violating parameter space of the so-constrained naturally aligned 2HDMs that can further be probed at the CERN Large Hadron Collider (LHC).

Multicomponent scalar dark matter with an extended Gauge sector

We consider an extension of the Standard Model of particle physics with an additional SU(2) gauge sector along with an additional scalar bidoublet and a non-linear sigma field. The neutral components of the bidoublet serve as dark matter candidates by virtue of the bidoublet being odd under a Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_2$$\\end{document} symmetry. Generic beyond Standard Model constraints like vacuum stability, invisible decay of Higgs, Higgs alignment limit and collider constraints on heavy gauge bosons restrict the parameter space of this model. In this multicomponent dark matter scenario, we investigate the interplay between the annihilation and co-annihilation channels originating from the new gauge sector as those contribute to the relic abundance. We also inspect the direct detection constraints on scattering cross-sections of the dark matter particles with the detector nucleons and present our observations.

Multiphoton signatures as a probe of CP violation in extended Higgs sectors

We propose a novel signature with four-photon final states to probe CP-violating (CPV) extended Higgs sectors via ff¯→Z*→H1H2→4γ processes with H1,2 being additional neutral Higgs bosons. We focus on the nearly Higgs alignment scenario, in which the discovered Higgs boson almost corresponds to a neutral scalar state belonging to the isospin doublet field with the vacuum expectation value v≃246 GeV. We show that the branching ratios of H1,2→γγ can simultaneously be sizable when CPV phases in the Higgs potential are of order one due to the enhancement of charged-Higgs boson loops. Such branching ratios can be especially significant when the fermiophobic scenario is taken into account. As a simple example, we consider the general two Higgs doublet model, and demonstrate that the cross section for the four-photon process can be 0.1 fb at LHC with the masses of H1,2 to be a few 100 GeV in the Higgs alignment limit under the constraints from electric dipole moments (EDMs) and LHC Run-II data. We also illustrate that the searches for EDMs and diphoton resonances at high-luminosity LHC play complementary roles to explore CPV extended Higgs sectors. Published by the American Physical Society 2024

Gildener-Weinberg two-Higgs-doublet model at two loops

The Gildener-Weinberg two-Higgs doublet model provides a naturally light and aligned Higgs boson, $H=H(125)$. It has been studied in the one-loop approximation of its effective potential, ${V}_{1}$. An important consequence is that the masses of the model's beyond the Standard Model (BSM) Higgs bosons (${H}^{\ensuremath{'}},A,{H}^{\ifmmode\pm\else\textpm\fi{}}$) are bounded by the sum rule ${({M}_{{H}^{\ensuremath{'}}}^{4}+{M}_{A}^{4}+2{M}_{{H}^{\ifmmode\pm\else\textpm\fi{}}}^{4})}^{1/4}=540\text{ }\text{ }\mathrm{GeV}$. Although they are well within reach of the LHC, searches for them have been stymied by large QCD backgrounds. Another consequence is that $H$ is highly aligned, i.e., $H--{H}^{\ensuremath{'}}$ mixing is small and $H$ has only Standard Model couplings. A corollary of this alignment is that commonly pursued discovery modes such as ${H}^{\ensuremath{'}}$, $A\ensuremath{\leftrightarrow}{W}^{+}{W}^{\ensuremath{-}}$, $ZZ$, $HZ$, and ${H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\leftrightarrow}{W}^{\ifmmode\pm\else\textpm\fi{}}Z,{W}^{\ifmmode\pm\else\textpm\fi{}}H$ are beyond the reach of LHC experiments. To assess the accuracy of the sum rule and Higgs alignment, we study this model in two loops. This calculation is complicated by having many new contributions. We present two formulations of it to calculate the $H--{H}^{\ensuremath{'}}$ mass matrix, its eigenvectors ${H}_{1}$, ${H}_{2}$, and the mass ${M}_{{H}_{2}}$ while fixing ${M}_{{H}_{1}}=125\text{ }\text{ }\mathrm{GeV}$. They give similar results and are in accord with the one-loop results. Requiring ${M}_{A}={M}_{{H}^{\ifmmode\pm\else\textpm\fi{}}}$, we find $180\text{ }\text{ }\mathrm{GeV}\ensuremath{\lesssim}{M}_{A,{H}^{\ifmmode\pm\else\textpm\fi{}}}\ensuremath{\lesssim}380--425\text{ }\text{ }\mathrm{GeV}$ and $550--700\text{ }\text{ }\mathrm{GeV}\ensuremath{\gtrsim}{M}_{{H}_{2}}\ensuremath{\gtrsim}125\text{ }\text{ }\mathrm{GeV}$, with ${M}_{{H}_{2}}$ decreasing as ${M}_{A,{H}^{\ifmmode\pm\else\textpm\fi{}}}$ increase. The corrections to $H$ alignment are below $\mathcal{O}(1%)$. So, the BSM searches above will remain fruitless. Finding the BSM Higgses requires improved sensitivity to their low masses. We discuss three possible searches for this.

Chasing the two-Higgs doublet model in the di-Higgs boson production

We investigate the di-Higgs production at the Large Hadron Collider in the two-Higgs doublet model (2HDM). In particular, we study the production of an extra neutral Higgs boson $\phi$ in association with the Standard Model (SM) Higgs boson $h$ in the Higgs alignment limit. We analyze two scenarios where the additional Higgs $\phi$ is CP-even or -odd state with a large top-Yukawa interaction. The leading contribution of this production comes from the top-quark loop-induced gluon-fusion channel $gg \to h\phi$. The measurement of the $h\phi$ production can probe the quartic couplings in the Higgs potential as well as the top-Yukawa couplings. Imposing both theoretical constraints (from the perturbative unitarity and the vacuum stability bounds) and experimental bounds (from the SM Higgs and flavor physics measurements) on the 2HDM parameter space, we calculate the production cross-section of $gg \to h\phi$. Furthermore, we scrutinize these processes in the parameter spaces where the CMS di-tau and di-photon excesses around 100$\,$GeV, and/or the muon $g-2$ anomaly can be accommodated.

P-even,CP-violating signals in scalar-mediated processes

Most studies of Higgs sector CP violation focus on the detection of CP-violating neutral Higgs-fermion Yukawa couplings, which yield P-odd, CP-violating phenomena. There is some literature on purely bosonic signatures of Higgs sector CP violation, where the simultaneous observation of three processes (suitably chosen) constitutes a signal of P-even CP violation. However, in the examples previously analyzed, some of the processes are strongly suppressed in the approximate Higgs alignment limit (corresponding to the existence of a Standard Model like Higgs boson as suggested by LHC data), in which case the proposed CP-violating signals are difficult to observe in practice. In this paper, we extend the existing literature by examining processes that do not vanish in the Higgs alignment limit and whose simultaneous observation would provide unambiguous evidence for scalar-mediated P-even CP violation. We assess the discovery potential of such signals at various future multi-TeV lepton (and $\gamma\gamma$) colliders. The potential for detecting loop-induced P-even, CP-violating phenomena is also considered.

Higgs alignment and novel CP -violating observables in two-Higgs-doublet models

Null results from searches for new physics at the Large Hadron Collider (LHC) tend to enforce the belief that new particles must be much heavier than the weak scale. We undertake a systematic study of the interplay between Higgs alignment and $CP$-violation in complex two-Higgs-doublet models, which enables us to construct a $CP$-violating scenario where new Higgs bosons are close to the weak scale after including stringent constraints from the electric dipole moment and measurements at the LHC. In addition, we propose a novel potential signal of $CP$-violation in the Higgs-to-Higgs decays, ${h}_{3}\ensuremath{\rightarrow}{h}_{2}{h}_{1}$, where ${h}_{3}$, ${h}_{2}$, and ${h}_{1}$ are the heaviest, second heaviest and the Standard Model-like neutral Higgs bosons, respectively. The decay could manifest itself in triple boson final states in ${h}_{1}{h}_{1}{h}_{1}$ and ${h}_{1}{h}_{1}Z$, which are quite distinct and provide unique venues for new measurements at the LHC.

Higgs alignment and the top quark

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, $\ensuremath{\lesssim}\mathcal{O}(1%)$, and probably experimentally inaccessible.

Exceptional regions of the 2HDM parameter space

The exceptional region of the parameter space (ERPS) of the two Higgs doublet model (2HDM) is defined to be the parameter regime where the scalar potential takes on a very special form. In the standard parameterization of the 2HDM scalar potential with squared mass parameters $m_{11}^2$, $m_{22}^2$, $m_{12}^2$, and dimensionless couplings, $\lambda_1$, $\lambda_2$, $\ldots,\lambda_7$, the ERPS corresponds to $\lambda_1=\lambda_2$, $\lambda_7=-\lambda_6$, $m_{11}^2=m_{22}^2$ and $m_{12}^2=0$, corresponding to a scalar potential with an enhanced generalized CP symmetry called GCP2. Many special features persist if $\lambda_1=\lambda_2$ and $\lambda_7=-\lambda_6$ are retained while allowing for $m_{11}^2\neq m_{22}^2$ and/or $m_{12}^2\neq 0$, corresponding to a scalar potential with a softly-broken GCP2 symmetry, which we designate as the ERPS4. In this paper, we examine many of the special features of the ERPS4, as well as even more specialized cases within the ERPS4 framework in which additional constraints on the scalar potential parameters are imposed. By surveying the landscape of the ERPS4, we complete the classification of 2HDM scalar potentials that exhibit an exact Higgs alignment (where the tree-level couplings of one neutral scalar coincide with those of the Standard Model Higgs boson), due to a residual symmetry that is unbroken in the vacuum. One surprising aspect of the ERPS4 is the possibility that the scalar sector is CP-conserving despite the presence of a complex parameter of the scalar potential whose complex phase cannot be removed by separate rephasings of the two scalar doublet fields. The significance of the ERPS4 regime for custodial symmetry is also discussed, and the cases where a custodial symmetric 2HDM scalar potential preserves an exact Higgs alignment are elucidated.

A natural mechanism for approximate Higgs alignment in the 2HDM

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.

Higgs alignment of visible and dark gauge groups

We discuss a dark family of lepton-like particles with their own “private” gauge bosons वμ and धμ under a local SU’(2) × U’(1) symmetry. The product of dark and visible gauge groups SU’(2) × U’(1) × SUw(2) × UY(1) is broken dynamically to the diagonal (vector-like) subgroup SU(2) × U(1) through the coupling of two fields (math) to the Higgs field and the dark lepton-like particles. This defines a new Higgs portal, where the “dark leptons” can contribute to the dark matter and interact with Standard Model matter through Higgs exchange.

R-symmetry for Higgs alignment without decoupling

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=1 supersymmetry breaking sectors. This absence of symmetry does not spoil alignment at the minimum of the potential. We show how the (small) misalignment induced by higher order corrections can be described as the appearance of non-singlet representations of SU(2)_R in the quartic potential.

Heavy Higgs boson decays in the alignment limit of the 2HDM

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 H1, 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, H2 and H3, in the alignment limit of the 2HDM are also elucidated. It is shown that the couplings of H2 and H3 in the alignment limit are tightly constrained and correlated. For example, in the exact alignment limit at tree level, for bosonic final states BR(H2,3 → W+W−, ZZ, H1Z) = 0 and BR(H± → W±H1) = 0, whereas for fermionic final states Γ(H2 → ff¯)/Γ(H3 → ff¯) ∼ M2/M3 (where Mα is the mass of Hα). 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 BR(H2,3 → H1H1) = 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.

Higgs alignment from extended supersymmetry

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 on the scale of superpartners. We contrast the results of the minimal Dirac gaugino model, where alignment is automatic, with the hMSSM and the MRSSM, where it is not, also providing an hMSSM-inspired analysis for the new models.

The impact of two-loop effects on the scenario of MSSM Higgs alignment without decoupling

In multi-Higgs models, the properties of one neutral scalar state approximate those of the Standard Model (SM) Higgs boson in a limit where the corresponding scalar field is roughly aligned in field space with the scalar doublet vacuum expectation value. In a scenario of alignment without decoupling, a SM-like Higgs boson can be accompanied by additional scalar states whose masses are of a similar order of magnitude. In the Minimal Supersymmetric Standard Model (MSSM), alignment without decoupling can be achieved due to an accidental cancellation of tree-level and radiative loop-level effects. In this paper we assess the impact of the leading two-loop mathcal{O}(alpha _s h_t^2) corrections on the Higgs alignment condition in the MSSM. These corrections are sizable and important in the relevant regions of parameter space and furthermore give rise to solutions of the alignment condition that are not present in the approximate one-loop description. We provide a comprehensive numerical comparison of the alignment condition obtained in the approximate one-loop and two-loop approximations, and discuss its implications for phenomenologically viable regions of the MSSM parameter space.

Natural quasi-alignment with two Higgs doublets and RGE stability

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 renormalisation group equations 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 this stable solution can be obtained by imposing on the Lagrangian a \(Z_3 \times Z^\prime _3\) flavour symmetry. Quark masses of the lighter quark generations are generated through the breaking of this discrete symmetry, and, at this stage, scalar-mediated flavour-changing neutral-currents arise, but they are naturally suppressed by the smallness of the light quark masses. In this way, we relate Higgs alignment to the hierarchy of the quark masses through a discrete family symmetry.