Z2 Symmetry Research Articles

Inverse seesaw model with large SU(2)L multiplets and natural mass hierarchy

We propose an inverse seesaw model with large SU(2)L multiplet fields which realizes natural mass hierarchies among neutral fermions. Here, lighter neutral fermion mass matrices are induced via two suppression mechanisms; one is small vacuum expectation value of SU(2)L triplet required by rho parameter constraint and the other is generation of Majorana mass term of extra singlet fermions at one-loop level. To realize the loop masses, we impose Z2 symmetry which also guarantees stability of a dark matter candidate. Furthermore, we discuss anomalous magnetic moment and collider physics from interactions of large multiplet fields.

Antiferromagnetic self-ordering of a Fermi gas in a ring cavity

We explore the density and spin self-ordering of driven spin-1/2 collisionless fermionic atoms coupled to the electromagnetic fields of a ring resonator. The two spin states are two-photon Raman-coupled via a pair of degenerate counterpropagating cavity modes and two transverse pump fields. In this one-dimensional configuration the coupled atom-field system possesses a continuous U(1) translational symmetry and a discrete Z2 spin inversion symmetry. At half filling for sufficiently strong pump strengths, the combined U(1) × Z2 symmetry is spontaneously broken at the onset of a superradiant phase transition to a state with self-ordered density and spin structures. We predominately find an antiferromagnetic lattice order at the cavity wavelength. The self-ordered states exhibit unexpected positive momentum pair correlations between fermions with opposite spin. These strong cavity-mediated correlations vanish at higher pump strength.

Exploring fine-tuning of the Next-to-Minimal Composite Higgs Model

We perform a detailed study of the fine-tuning of the two-site, 4D, Next-to-Minimal Composite Higgs Model (NMCHM), based on the global symmetry breaking pattern SO(6) → SO(5). Using our previously-defined fine-tuning measure that correctly combines the effect of multiple sources of fine-tuning, we quantify the fine-tuning that is expected to result from future collider measurements of the Standard Model-like Higgs branching ratios, in addition to null searches for the new resonances in the model. We also perform a detailed comparison with the Minimal Composite Higgs Model, finding that there is in general little difference between the fine-tuning expected in the two scenarios, even after measurements at a high-luminosity, 1 TeV linear collider. Finally, we briefly consider the relationship between fine-tuning and the ability of the extra scalar in the NMCHM model to act as a dark matter candidate, finding that the realisation of a Z2 symmetry that stabilises the scalar is amongst the most natural solutions in the parameter space, regardless of future collider measurements.

Simple A4 models for dark matter stability with texture zeros

In a simple framework which naturally incorporates dark matter stability and neutrino phenomenology, we compute all the possible texture zeros which arise when the non-abelian flavor symmetry A4 is spontaneously broken to Z2. As a result, we obtain four textures with two vanishing matrix elements. Two of such textures predict a zero contribution to the neutrinoless double beta decay effective mass parameter at tree level, and as a one loop bound we get $m_{ee}<8\times 10^{-2}$ meV. These are compatible with the normal ordering for the neutrino masses and the allowed range for the lightest neutrino mass is between $m_{\nu_{min}}\sim3$ meV and $m_{\nu_{max}}\sim8$ meV. Additionally we obtain dark matter stability linked to the way the flavor symmetry is broken, leaving a residual Z2 symmetry

Active and sterile neutrino phenomenology with A4 based minimal extended seesaw

We study a model of neutrino within the framework of minimal extended seesaw (MES), which plays an important role in active and sterile neutrino phenomenology in (3+1) scheme. The A4 flavor symmetry is augmented by additional Z4×Z3 symmetry to constraint the Yukawa Lagrangian of the model. We use non-trivial Dirac mass matrix, with broken μ−τ symmetry, as the origin of leptonic mixing. Interestingly, such structure of mixing naturally leads to the non-zero reactor mixing angle θ13. Non-degenerate mass structure for right-handed neutrino MR is considered so that we can further extend our study to Leptogenesis. We have also considered three different cases for sterile neutrino mass, MS to check the viability of this model, within the allowed 3σ bound in this MES framework.

Radiative neutrino mass in an alternative U(1)B−L gauge symmetry

We propose a neutrino model in which neutrino masses are generated at one loop level and three right-handed fermions have non-trivial charges under U(1)B−L gauge symmetry in no conflict with anomaly cancellation. After the spontaneously symmetry breaking, a remnant Z2 symmetry is induced and plays an role in assuring the stability of dark matter candidate.

Emergent statistical bubble localization in aZ2lattice gauge theory

We introduce a clean cluster spin chain coupled to fully interacting spinless fermions, forming an unconstrained Z2 lattice gauge theory (LGT) which possesses dynamical proximity effect controlled by the entanglement structure of the initial state. We expand the machinery of interaction-driven localization to the realm of LGTs such that for any starting product state, the matter fields exhibits emergent statistical bubble localization, which is driven solely by the cluster interaction, having no topologically trivial non-interacting peer, and thus is of pure dynamical many-body effect. In this vein, our proposed setting provides possibly the minimal model dropping all the conventional assumptions regarding the existence of many-body localization. Through projective measurement of local constituting species, we also identify the coexistence of the disentangled nonergodic matter and thermalized gauge degrees of freedom which stands completely beyond the standard established phenomenology of quantum disentangled liquids. As a by product of self-localization of the proximate fermions, the spin subsystem hosts the long-lived topological edge zero modes, which are dynamically decoupled from the thermalized background Z2 charges of the bulk, and hence remains cold at arbitrary high-energy density. This provides a convenient platform for strong protection of the quantum bits of information which are embedded at the edges of completely ergodic sub-system; the phenomenon that in the absence of such proximity-induced self-localization could, at best, come about with a pre-thermal manner in translational invariant systems. Finally, by breaking local Z2 symmetry of the model, we argue that such admixture of particles no longer remains disentangled and the ergodic gauge degrees of freedom act as a "small bath" coupled to the localized components.

Factoring the strong CP problem

We present a new mechanism to solve the strong CP problem using N ≥ 2 axions, each dynamically relaxing part of the θ parameter. At high energies M ≫ ΛQCD the SU(3)c group becomes the diagonal subgroup of an SU(3)N gauge group, and the non-perturbative effects in each individual SU(3) factor generate a potential for the corresponding axion. The vacuum is naturally aligned to ensure overline{theta} = 0 at low energies, and the masses of these axions can be much larger than for the standard QCD axion. This mechanism avoids the introduction of a discrete Z2 symmetry and associated ‘mirror’ copies of the SM fermions, and also avoids the introduction and stabilization of new light colored states to modify the running of the QCD gauge coupling found in other heavy axion models. This strengthens the motivation for axion-like particles solving the strong CP problem at points beyond the standard QCD axion curve in the (ma, fa) plane.

Dark side of the seesaw

In an attempt to unfold (if any) a possible connection between two apparently uncorrelated sectors, namely neutrino and dark matter, we consider the type-I seesaw and a fermion singlet dark matter to start with. Our construction suggests that there exists a scalar field mediator between these two sectors whose vacuum expectation value not only generates the mass of the dark matter, but also takes part in the neutrino mass generation. While the choice of Z4 symmetry allows us to establish the framework, the vacuum expectation value of the mediator field breaks Z4 to a remnant Z2, that is responsible to keep dark matter stable. Therefore, the observed light neutrino masses and relic abundance constraint on the dark matter, allows us to predict the heavy seesaw scale as illustrated in this paper.The methodology to connect dark matter and neutrino sector, as introduced here, is a generic one and can be applied to other possible neutrino mass generation mechanism and different dark matter candidate(s).

{R}_{K^{left(*right)}} with leptoquarks and the origin of Yukawa couplings

We construct a model where the Yukawa couplings of the Standard Model (SM) fermions arise from the breaking of a Z2 symmetry and through mixing with a fourth family of vector-like fermions. By adding a scalar leptoquark, which is an electroweak triplet and odd under the Z2 symmetry, we obtain an explanation for {R}_{K^{left(*right)}} that is linked to the origin of the Yukawa couplings. The coupling of SM fermions to the leptoquark is mediated by the fourth family fermions, and is predicted to be related to CKM entries and mass ratios of SM fermions.

Reconciling B-meson decay anomalies with neutrino masses, dark matter and constraints from flavour violation

Motivated by an explanation of the {R}_{K^{left(*right)}} anomalies, we propose a Standard Model extension via two scalar SU(2)L triplet leptoquarks and three generations of triplet Majorana fermions. The gauge group is reinforced by a Z2 symmetry, ensuring the stability of the lightest Z2-odd particle, which is a potentially viable dark matter candidate. Neutrino mass generation occurs radiatively (at the three-loop level), and leads to important constraints on the leptoquark couplings to leptons. We consider very generic textures for the flavour structure of the h1 leptoquark Yukawa couplings, identifying classes which succeed in saturating the {R}_{K^{left(*right)}} anomalies. We subsequently carry a comprehensive analysis of the model’s contributions to numerous high-intensity observables such as meson oscillations and decays, as well as charged lepton flavour violating processes, which put severe constraints on the flavour structure of these leptoquark extensions. Our findings suggest that the most constraining observables are {K}^{+}to {pi}^{+}nu overline{nu} decays, and charged lepton flavour violating μ − e conversion in nuclei (among others). Nevertheless, for several classes of flavour textures and for wide mass regimes of the new mediators (within collider reach), this Standard Model extension successfully addresses neutrino mass generation, explains the current {R}_{K^{left(*right)}} tensions, and offers a viable dark matter candidate.

Dark matter for b \u2192 s\u03bc+\u03bc\u2212 anomaly in a gauged U(1)X model

We propose a new physics model which has a cold dark matter candidate and can explain the b → sμ+μ− anomaly at the same time. Our model includes a scalar quark tilde{q} and a scalar lepton tilde{ell} which are SU(2)L-doublet as well as a Dirac fermion N which is SU(2)L-singlet. The new particles are charged under a gauged U(1)X group which is spontaneously broken to a discrete Z2 symmetry by a dark scalar S. The remnant Z2 symmetry stabilizes the dark matter. Box diagrams with tilde{q} , tilde{ell} , and N running inside the loop can generate the correct Wilson coefficients C9μ = − C10μ to accommodate the b → sμ+μ− anomaly while avoiding constraints such as {B}_s-{overline{B}}_s mixing. The dark matter annihilation into a second generation lepton pair via t-channel tilde{ell} -exchanging process plays an important role in producing the current dark matter relic abundance of the universe, showing a strong interplay between the flavor and dark matter physics. We also discuss dark-gauge-interaction-dominated and Higgs-portal-dominated scenarios for dark matter physics.

Cosmological scenarios from multiquintessence

In this work we derive and analyse cosmological scenarios coming from multi-component scalar field models. We consider a direct sum of a sine-Gordon with a Z2 model, and also a combination of those with a BNRT model. Moreover, we work with a modified version of the BNRT model, which breaks the Z2 times Z2 symmetry of the original BNRT potential, coupled with the sine-Gordon and with the standard Z2 models. We show that our approach can be straightforwardly elevated to N fields. All the computations are made analytically and some parameters restriction is put forward in order to get in touch with complete and realistic cosmological scenarios.

Validity of the effective potential and the precision of Higgs field self-couplings

The global picture of the Higgs potential in the bottom-up approach is still unknown. A large deviation as big as O(1) fluctuations of the Higgs self couplings is still a viable option for the New Physics. An interesting New Physics scenario which can be linked to a large Higgs self coupling is the baryogenesis based on the strong first order phase transition. We revisit the strong first order phase transition in two classes of Beyond the Standard Models, namely the Higgs portal with the singlet scalar under the Standard Model gauge group with Z2 symmetry and the effective field theory approach with higher-dimensional operators. We numerically investigate a few important issues in the validity of the effective potential, caused by the breakdown of the high-temperature approximation, and in the criteria for the strong first order phase transition. We illustrate that these issues can lead to O(1) uncertainties in the precision of the Higgs self couplings, which are relevant when discussing sensitivity limits of different future colliders. We also find that the quartic coupling of the above two classes of scenarios compatible with the strong first order electroweak phase transition where the cubic coupling is not negligible, can achieve a $2\sigma$ sensitivity at the 100 TeV pp-collider. From this novel observation, we show that the correlation between the Higgs cubic coupling and the quartic coupling will be useful for differentiating various underlying New Physics scenarios and discuss its prospect for the future colliders. Throughout our numerical investigation, the contribution from Goldstone boson is not included.

Implications of Higgs discovery for the strong CP problem and unification

A Z2 symmetry that extends the weak interaction, SU(2)L → SU(2)L ×SU(2)′, and the Higgs sector, H(2) → H(2, 1) + H′(1, 2), yields a Standard Model quartic coupling that vanishes at scale v′ = 〈H′〉 ≫ 〈H〉. Near v′, theories either have a “prime” sector, or possess “Left-Right” (LR) symmetry with SU(2)′ = SU(2)R. If the Z2 symmetry incorporates spacetime parity, these theories can solve the strong CP problem. The LR theories have all quark and lepton masses arising from operators of dimension 5 or more, requiring Froggatt-Nielsen structures. Two-loop contributions to overline{theta} are estimated and typically lead to a neutron electric dipole moment of order 10−27e cm that can be observed in future experiments. Minimal models, with gauge group SU(3) × SU(2)L × SU(2)L × U(1)B−L, have precise gauge coupling unification for v′ = 1010±1 GeV, successfully correlating gauge unification with the observed Higgs mass of 125 GeV. With SU(3) × U(1)B−L embedded in SU(4), the central value of the unification scale is reduced from 1016−17 GeV to below 1016 GeV, improving the likelihood of proton decay discovery. Unified theories based on SO(10) × CP are constructed that have H + H′ in a 16 or 144 and generate higher-dimensional flavor operators, while maintaining perturbative gauge couplings.

Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry

This paper is concerned with the number of limit cycles bifurcating in three-dimensional quadratic vector fields with [Formula: see text] symmetry. The system under consideration has three fine focus points which are symmetric about the [Formula: see text]-axis. Center manifold theory and normal form theory are applied to prove the existence of 12 limit cycles with [Formula: see text]–[Formula: see text]–[Formula: see text] distribution in the neighborhood of three singular points. This is a new lower bound on the number of limit cycles in three-dimensional quadratic systems.

Cosmic acceleration and de Sitter expansion in hybrid mass varying neutrino model

A nonminimally coupled hybrid dark energy model is introduced. The dark energy evolution is triggered by mass varying neutrinos. Quintessence evolution begins from an initial point, with an insignificant dark energy density, and arrives at a final de Sitter attractor. While initially, for a Higgs-like potential, the non-minimal coupling keeps the system in a state with negligible dark energy density, finally the second quintessence conducts the evolution to a stable fixed point. These evolutions occur through successive Z2 symmetry breakings.

Charged lepton flavor violation and electric dipole moments in the inert Zee model

The inert Zee model is an extension of the Zee model for neutrino masses to allow for a solution to the dark matter problem that involves two vector-like fields, a doublet and a singlet of SU(2)L, and two scalars, also a doublet and a singlet of SU(2)L, all of them being odd under an exact Z2 symmetry. The introduction of the Z2 guarantees one-loop neutrino masses, forbids tree-level Higgs-mediated flavor changing neutral currents and ensures the stability of the dark matter candidate. Due to the natural breaking of lepton numbers in the inert Zee model and encouraged by the ambitious experimental program designed to look for charged lepton flavor violation signals and the electron electric dipole moment, we study the phenomenology of the processes leading to these kind of signals, and establish which are the most promising experimental perspectives on that matter.

Constraining a lighter exotic scalar via same-sign top

It was shown recently that, in two Higgs doublet models without Z2 symmetry, extra Yukawa couplings such as ρtc, ρtt can fuel enough CP violation for electroweak baryogenesis (EWBG). We revisit an old proposal where a pseudoscalar A0 has mass between tc¯ and tt¯ thresholds. With ρtt small, it evades gg→A0→h0(125)Z constraints, where approximate alignment also helps. We find this scenario with relatively light A0 is not yet ruled out, and cg→tA0→ttc¯ can probe sizable ρtc at the LHC, giving access to the second mechanism of EWBG provided by such models.

A Monte-Carlo Study on the Coupling of Magnetism and Ferroelectricity in the Hexagonal Multiferroic RMnO3

The ferroelectric phase transition in RMnO3 breaks both Z3 and Z2 symmetries, giving rise to 6 structural domains. Topological protected vortices are formed at the junctions of all 6 domains, and the ferroelectric phase transition is closely related to these Z6 vortices. In this work, Monte-Carlo studies on both the ferroelectric and magnetic transition have been performed on RMnO3 system. The magnetic simulation results on lattices with different structural domain distributions induced by external electric field and simulated quenching show different magnetic transition temperature T s , indicating that the coupling of magnetism and ferroelectricity is through the Z6 structural domain. At extreme case, lattice quenched from above the ferroelectric transition results in high vortex density, which can drive the system into spin glass.