Z2 Symmetry Research Articles

Dark matter as the trigger of flavor changing neutral current decays of the top quark

We suggest a simplified model that simultaneously addresses the dark matter problem and gives rise to top-quark flavor changing neutral current (FCNC) interactions at the one-loop order. The model consists of two extra SU(2)L gauge singlets: a colored mediator of spin zero (S) and a right-handed fermion (χ); both are odd under an Z2 symmetry. The right-handed fermion plays the role of the dark matter candidate. In this model, the presence of the two dark sector particles generates one-loop induced FCNC decays of the top quark into light quarks and bosons such as the gluon, the photon, the Z boson, or the Higgs boson. As a case study, we analyze the top-quark FCNC decays into light quarks (u or c) and Z or Higgs bosons. We then study the reliable solutions to the dark matter problem by estimating the regions in the parameter space that are consistent with the measurement of the dark matter relic density. We also revisit the bounds from the searches of dark matter in events with at least one high-pT jet and large missing transverse energy at the Large Hadron Collider (LHC). We then define four benchmark points that are consistent with the existing constraints from collider experiments and cosmology. We finally estimate, for these benchmark scenarios, the rates of a broad range of channels that can be used to probe the connection between the top FCNC transitions and dark matter, both at the HL-LHC and at a future 100 TeV collider. Published by the American Physical Society 2024

Irreducible cosmological backgrounds of a real scalar with a broken symmetry

We explore the irreducible cosmological implications of a singlet real scalar field. Our focus is on theories with an approximate and spontaneously broken Z2 symmetry where quasistable domain walls can form at early times. This seemingly simple framework bears a wealth of phenomenological implications that can be tackled by means of different cosmological and astrophysical probes. We elucidate the connection between domain wall dynamics and the production of dark matter and gravitational waves. In particular, we identify three main benchmark scenarios. The gravitational wave signal observed by pulsar timing arrays can be generated by the domain walls if the mass of the singlet is ms∼PeV. For lower masses, but with ms≳10 GeV, scalars produced in the annihilation of the domain walls can be dark matter with a distinctive feature in their power spectrum. Finally, the thermal bath provides an unavoidable source of unstable scalars via the freeze-in mechanism whose subsequent decays can be tested by their imprints on cosmological and terrestrial observables. Published by the American Physical Society 2024

Relic abundance of dark matter with [formula omitted](54) flavor symmetry

In this work we discuss the neutrino phenomenology in a Δ(54) discrete flavor symmetry and evaluate the relic abundance of dark matter (DM) and active neutrino-DM mixing angle considering various cosmological constraints. We introduced two Standard Model Higgs particles along with vector-like fermions and a new particle (S) which is a gauge singlet in the Standard Model. This modification leads to a mass matrix that diverges from the tribimaximal neutrino mixing pattern resulting in a non-zero reactor angle (θ13). We also incorporated a Z2⊗Z3⊗Z4 symmetry for the specific interactions in our model. The additional particle S is a sterile neutrino which is considered to be a probable dark matter candidate with mass in keV range.

Fermion masses and mixings and g − 2 muon anomaly in a Q6 flavored 2HDM

We propose an extended 2HDM with Q6×Z4×Z2 symmetry that can successfully accommodate the SM fermion mass and mixing hierarchy. The tiny masses of the active neutrinos are generated from a type-I seesaw mechanism mediated by very heavy right-handed Majorana neutrinos. The model gives a natural explanation of the charged lepton mass hierarchy. Besides that, the experimental values of the physical observables of the neutrino sector: the neutrino mass squared splittings, the leptonic mixing angles and the leptonic Dirac CP violating phase, are also successfully reproduced for both normal and inverted neutrino mass hierarchies. We find a feasible range of values for the leptonic Dirac CP phase to be in the ranges δCP∈(305.90,348.70)∘ for normal ordering and δCP∈(308.00,348.00)∘ for inverted ordering, which is consistent with the 3σ experimentally allowed limits. The sum of neutrino masses is obtained as ∑mi∈(58.03,60.51) meV for normal ordering and ∑mi∈(98.07,101.40) meV for inverted ordering which are well consistent with all the recent limits. In addition, the obtained ranges for the effective neutrino masses are 〈mee〉∈(3.80,4.38) meV, mβ∈(8.53,9.34)meV for normal ordering and 〈mee〉∈(47.85,49.58) meV, mβ∈(48.39,50.09)meV for inverted ordering which are in agreement with the recent experimental bounds. For the quark sector, the derived results are also in agreement with the recent data on the quark masses and mixing angles. The model under consideration can also accommodate the muon anomalous magnetic moment.

Revisiting for maximal flavor violating Zeμ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {Z}_{e\\mu}^{\\prime } $$\\end{document} and its phenomenology constraints

Lepton flavor violation (LFV), observed conclusively in neutrino oscillations, remains a pivotal area of investigation due to its absence in the Standard Model (SM). Beyond the Standard Model (BSM) physics explores charged lepton flavor violation (CLFV), particularly through new particle candidates such as the Z′. This article focuses on maximal LFV interactions facilitated by the Z′ boson, specifically targeting its off-diagonal interactions with the first and second generations of charged and neutral leptons. In our ultraviolet (UV) model for the origin of the Z′, inspired by the work of [R.Foot et al., Phys.Rev. D50 (1994) 4571-4580], we utilize the discrete Z2 symmetry to investigate the maximal LFV mediated by the Z′ between the muon (μ) and electron (e) arising from the additional scalars. This symmetry prohibits flavor-conserving interactions between Z′ and μ+μ−, e+e−. In conjunction with collider, (g – 2)μ, (g – 2)e, inverse μ decay, Muonium-to-Antimuonium conversion and LFV decay constraints, we provide forecasts for anticipated limits derived from processes such as νμN → νeμ+e−N in neutrino trident experiments like the DUNE search at the first time. These limits highlight the prospective scope and significance of LFV investigations within these experimental frameworks. Within the mass range of 0.01 GeV to 10 GeV, the most stringent limit arises from Bμ→e+X+γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{B}\\left(\\mu \ o e+X+\\gamma \\right) $$\\end{document} when MZ′<mμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {M}_{Z^{\\prime }}<{m}_{\\mu } $$\\end{document}, while ∆ae provides effective constraints as MZ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {M}_{Z^{\\prime }} $$\\end{document} approaches 10 GeV. Looking ahead, the proposed Muonium-to-Antimuonium Conversion Experiment (MACE) is expected to impose the most stringent constraints on Muonium-to-Antimuonium oscillation, improving sensitivity by about one order of magnitude against ∆ae.

The breaking of μ − τ reflection symmetry in a B − L extended 3HDM with (Z2 × Z4)⋊Z2 (II) symmetry

We propose a new neutrino mass matrix texture satisfying the μ−τ reflection symmetry in a B−L model with three Higgs doublets based on non-Abelian discrete symmetry (Z2×Z4)⋊Z2(II). The Dirac and Majorana mass matrices, which is motivated in the framework of the Type I seesaw mechanism in association with (Z2×Z4)⋊Z2(II) symmetry, hint for a realistic lepton mixing pattern where the co-bimaximal mixing pattern is broken by the charged-lepton contribution. The hierarchy of lepton masses is naturally achieved and the constraints on the effective neutrino mass are consistent with the recent experimental limits.

Common origin of dark matter and leptogenesis in U(1)B−L

In this paper, we investigate the common parameter space of dark matter and leptogenesis in the U(1)B−L symmetry. This model involves a complex scalar ϕ, sterile neutrinos N, and Majorana dark matter χ, where only dark matter χ is charged under the Z2 symmetry. Masses of N and χ are generated via the Yukawa interactions to ϕ after breaking of the U(1)B−L symmetry. TeV scale sterile neutrinos N are responsible for the generation of baryon asymmetry through the resonance leptogenesis mechanism. The new particles in the U(1)B−L have a significant impact on the dilution of N, thus on leptogenesis. Meanwhile, the annihilation processes of dark matter χ are almost identical to that of N, which indicates that both leptogenesis and dark matter are closely related to satisfying the observed results simultaneously. Under various theoretical and experimental constraints, the viable common parameter space of dark matter and leptogenesis is obtained for both global and local U(1)B−L symmetry.

New renormalization scheme in the two Higgs doublet models

We propose a new renormalization scheme in the two Higgs doublet models with a softly-broken Z2 symmetry and CP-conservation in the Higgs sector. In this scheme, counterterms for mixing angles of the Higgs bosons are determined by using the decay rates of the discovered Higgs boson h, i.e., h→τ+τ− and h→ZZ⁎→Zℓ+ℓ− at next leading order (NLO) instead of using the renormalized two-point functions which are adopted in the previous scheme. We require that the decay rates at NLO are determined to be the corresponding predictions at NLO in the Standard Model (SM) times square of the scaling factor which describes the deviation of h couplings at tree level from the SM value. The mixing angles then maintain the meaning of the “alignmentness”, i.e., how the properties of h are close to the SM predictions, while they lose such meaning in the previous scheme. We compare the predictions of the decay rates at NLO given in the new scheme and those in the previous scheme.

Coscattering in the extended singlet-scalar Higgs portal

We study the coscattering mechanism in a simple Higgs portal which add two real singlet scalars to the Standard Model. In this scenario, the lighter scalar is stabilized by a single 𝒵2 symmetry and acts as the dark matter relic, whose freeze-out is driven by conversion processes. The heavier scalar becomes an unstable state which participate actively in the coscattering. We find viable parameter regions fulfilling the measured relic abundance, while evading direct detection and big-bang nucleosynthesis bounds. In addition, we discuss collider prospects for the heavier scalar as a long-lived particle at present and future detectors.

Neutrino masses in the mirror twin Higgs with spontaneous ℤ2 breaking

We introduce a mirror twin Higgs model with spontaneous ℤ2 symmetry breaking that ameliorates the constraints in twin Higgs cosmology and, at the same time, generates the Standard Model neutrino masses. The model features an SU(2) triplet with hypercharge 1 alongside its twin counterpart. Spontaneous breaking of both ℤ2 and electroweak symmetry occurs in the scalar sector. The Standard Model neutrinos acquire small masses through the type-II seesaw mechanism. In contrast, their twin counterparts acquire large masses, effectively addressing the dark radiation problem in mirror twin Higgs scenarios. We study the impact of the model on the Neff. constraints, as well as on collider phenomenology.

Unveiling desert region in inert doublet model assisted by Peccei-Quinn symmetry

The Inert Higgs Doublet model (IDM), assisted by Peccei-Quinn (PQ) symmetry, offers a simple but natural framework of a dark sector that accommodates Weakly Interacting Massive Particle (WIMP) and axion as dark matter components. Spontaneous breaking of U(1)PQ symmetry, which was originally proposed as an elegant solution to the strong charge-parity (CP) problem, also ensures the stability of WIMP through a residual ℤ2 symmetry. Interestingly, additional fields necessitated by PQ symmetry further enrich the dark sector. These include a scalar field proprietor for axion DM and a vector-like quark (VLQ) that acts as a portal for the dark sector through Yukawa interactions. Moreover, this combination of the axion and WIMP components satisfies the observed DM relic density and reopens the phenomenologically exciting region of the IDM parameter space where the WIMP mass falls between 100 - 550 GeV. We investigate the model-independent pair production of VLQs exploring this region at the Large Hadron Collider (LHC), incorporating the effects of next-to-leading order (NLO) QCD corrections. After production, each VLQ decays into a top or bottom quark accompanied by an inert scalar, a consequence of the residual ℤ2 symmetry. Utilising relevant observables with a leptonic search channel and employing multivariate analysis, we demonstrate the ability of this analysis to exclude a significant portion of the parameter space with an integrated luminosity of 300 fb−1.

Discrete Z4 Symmetry in Quantum Gravity

We consider the discrete Z4 symmetry i^, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation, i^, the emerging tetrads are multiplied by the imaginary unit, i^eμa=−ieμa. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid 3He-B. The order parameter in 3He-B is also the bilinear combination of the fermionic operators. This order parameter is the analog of the tetrad field, but it has complex values. The i^-symmetry operation changes the phase of the complex order parameter by π/2, which corresponds to the Z4 discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this Z4 symmetry, in which the i^-operation changes sign of the scalar curvature, i^R=−R, and thus the Einstein–Hilbert action violates the i^-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling K=1/16πG plays the role of the order parameter, which changes sign under i^-transformation.

Two-Higgs-doublet model effective field theory

We construct the general two-Higgs doublet model effective field theory where the effects of additional new physics are parametrized by operators up to mass dimension-six. We further transform this effective theory to the Higgs basis and provide matching of the Wilson coefficients between the two descriptions. We illustrate the advantages of the Higgs basis which include the separation of operators that modify standard model couplings and masses from operators that contribute to scattering processes only, transparent correlations between scattering processes resulting from the same operator, and derivation of correlations between different operators in specific UV completions. For completeness, we also construct specific versions corresponding to four types of two-Higgs-doublet models: type-I, -II, -X, and -Y, distinguished by Z2 symmetries which restrict the couplings of the Higgs doublets to standard model fermions. Furthermore, we derive general vacuum and stability conditions of the scalar potential in the presence of higher-dimensional terms. Published by the American Physical Society 2024

Early dark energy and scalarization in a scalar-tensor model

We present a model in which the Gauss-Bonnet invariant holds the quintessence at a fixed point, respecting an initial Z2 symmetry in the radiation-dominated era. This results in an early dark energy that becomes significant around the matter-radiation equality era. However, due to Z2 symmetry breaking, scalarization occurs, leading to a rapid reduction in the early dark energy density. The model then quickly behaves like the ΛCDM model. This scenario may also explain the reduction of sound horizon and aligns with the assumption that the gravitational wave speed is infinitesimally close to the speed of light.

Topological structures, dark matter and gravitational waves in E6

We discuss the appearance of topological structures from the spontaneous breaking of E6 to the Standard Model via its maximal subgroup SO(10) × U(1)ψ. They include dumbbells, metastable strings, as well as domain walls bounded by necklaces. We provide a novel scenario for producing metastable strings based on the symmetry breaking U(1)ψ ⟶ ℤ8 ⟶ ℤ4. The metastable string arises from the merger of ℤ8 strings that bound a domain wall. An unbroken gauge ℤ2 symmetry from SO(10) breaking yields viable stable dark matter candidates as well as topologically stable strings. We discuss the gravitational wave emission from two varieties of cosmic strings, namely the superheavy metastable ones and the intermediate scale topologically stable cosmic strings.

Probing Inert Triplet Model at a multi-TeV muon collider via vector boson fusion with forward muon tagging

This study investigates the potential of a multi-TeV Muon Collider (MuC) for probing the Inert Triplet Model (ITM), which introduces a triplet scalar field with hypercharge Y = 0 to the Standard Model. The ITM stands out as a compelling Beyond the Standard Model scenario, featuring a neutral triplet T0 and charged triplets T±. Notably, T0 is posited as a dark matter (DM) candidate, being odd under a Z2 symmetry. Rigorous evaluations against theoretical, collider, and DM experimental constraints corner the triplet scalar mass to a narrow TeV-scale region, within which three benchmark points are identified, with T± masses of 1.21 TeV, 1.68 TeV, and 3.86 TeV, for the collider study. The ITM’s unique TTVV four-point vertex, differing from fermionic DM models, facilitates efficient pair production through Vector Boson Fusion (VBF). This characteristic positions the MuC as an ideal platform for exploring the ITM, particularly due to the enhanced VBF cross-sections at high collision energies. To address the challenge of the soft decay products of T± resulting from the narrow mass gap between T± and T0, we propose using Disappearing Charged Tracks (DCTs) from T± and Forward muons as key signatures. We provide event counts for these signatures at MuC energies of 6 TeV and 10 TeV, with respective luminosities of 4 ab−1 and 10 ab−1. Despite the challenge of beam-induced backgrounds contaminating the signal, we demonstrate that our proposed final states enable the MuC to achieve a 5σ discovery for the identified benchmark points, particularly highlighting the effectiveness of the final state with one DCT and one Forward muon.

Scalar dark matter explanation of the excess in the Belle II B+→ K++ invisible measurement

Recently Belle II reported the first measurement of B+ → K+ + invisible(inv), which is 2.7σ above the standard model (SM) prediction. If confirmed, this calls for new physics beyond SM. In the SM, the invisible particles are neutrino-anti-neutrino pairs. There are more possibilities when going beyond the SM. In this work, we focus on decays to dark matter (DM) and show that the B → K + inv excess from Belle II and DM relic density can be simultaneously explained in a simple extension of the SM. The model introduces a real scalar singlet ϕ acting as a DM candidate, and two heavy vector-like quarks Q, D with the same quantum numbers as the SM left-handed quark doublet and right-handed down-type quark singlet, respectively. All these new particles are odd under a ℤ2 symmetry while the SM particles are even. The model can successfully explain the Belle II anomaly and DM relic density for TeV-scale heavy quarks with hierarchical Yukawa couplings involving b and s quarks. At the same time, it can easily satisfy other flavour physics constraints. Direct detection searches utilizing the Migdal effect constrain some of the parameter space.

Electroweak phase transition with a double well done doubly well

We revisit the electroweak phase transition in the scalar singlet extension of the standard model with a ℤ2 symmetry. In significant parts of the parameter space the phase transition occurs in two steps — including canonical benchmarks used in experimental projections for gravitational waves. Domain walls produced in the first step of the transition seed the final step to the electroweak vacuum, an effect which is typically neglected but leads to an exponentially enhanced tunnelling rate. We improve previous results obtained for the seeded transition, which made use of the thin-wall or high temperature approximations, by using the mountain pass algorithm that was recently proposed as a useful tool for seeded processes. We then determine the predictions of the seeded transition for the latent heat, bubble size and characteristic time scale of the transition. Differences compared to homogeneous transitions are most pronounced when there are relatively few domain walls per hubble patch, potentially leading to an enhanced gravitational wave signal. We also provide a derivation of the percolation criteria for a generic seeded transition, which applies to the domain wall seeds we consider as well as to strings and monopoles.

A closer look in the mirror: reflections on the matter/dark matter coincidence

We argue that the striking similarity between the cosmic abundances of baryons and dark matter, despite their very different astrophysical behavior, strongly motivates the scenario in which dark matter resides within a rich dark sector parallel in structure to that of the standard model. The near cosmic coincidence is then explained by an approximate ℤ2 exchange symmetry between the two sectors, where dark matter consists of stable dark neutrons, with matter and dark matter asymmetries arising via parallel WIMP baryogenesis mechanisms. Taking a top-down perspective, we point out that an adequate ℤ2 symmetry necessitates solving the electroweak hierarchy problem in each sector, without our committing to a specific implementation. A higher-dimensional realization in the far UV is presented, in which the hierarchical couplings of the two sectors and the requisite ℤ2-breaking structure arise naturally from extra-dimensional localization and gauge symmetries. We trace the cosmic history, paying attention to potential pitfalls not fully considered in previous literature. Residual ℤ2-breaking can very plausibly give rise to the asymmetric reheating of the two sectors, needed to keep the cosmological abundance of relativistic dark particles below tight bounds. We show that, despite the need to keep inter-sector couplings highly suppressed after asymmetric reheating, there can naturally be order-one couplings mediated by TeV scale particles which can allow experimental probes of the dark sector at high energy colliders. Massive mediators can also induce dark matter direct detection signals, but likely at or below the neutrino floor.

Electric-magnetic duality and Z2 symmetry enriched Abelian lattice gauge theory

Kitaev’s quantum double model is a lattice realization of Dijkgraaf–Witten topological quantum field theory. Its topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory. We investigate the Z2 symmetry enriched generalization of the model for the Abelian group in a categorical framework and present an explicit Hamiltonian construction. This model provides a lattice realization of the Z2 symmetry of the topological phase. We discuss in detail the categorical symmetry of the phase, for which the electric-magnetic (EM) duality symmetry is a special case. The aspects of symmetry defects are investigated using the G-crossed unitary braided fusion category. By determining the corresponding anyon condensation, the gapped boundaries and boundary-bulk duality are also investigated. In the last part, an explicit lattice realization of EM duality is discussed.