Z2 Symmetry Research Articles

First-order phase transitions in Twin Higgs models

We revisit phase transitions in Twin Higgs (TH) models. We show that strong first-order phase transitions (FOPTs) can occur provided that appropriate source of ℤ2 symmetry breaking between the twin and Standard Model (SM) sectors is present. We found FOPTs in two classes of models. First: with hard ℤ2 breaking in the scalar potential allowing for FOPT. Second: with ℤ2 broken by enhanced Yukawa couplings of twin leptons. We also considered supersymmetric UV completion of the second scenario with light sleptons. The signal of gravitational waves produced during these phase transitions is typically small but can be close to the reach of AEDGE and Einstein Telescope in the case of the FOPT induced by light twin sleptons. Our results open a way to generate SM baryon asymmetry in TH models.

The scalar singlet extension of the Standard Model: gravitational waves versus baryogenesis

We study the possible gravitational wave signal and the viability of baryogenesis arising from the electroweak phase transition in an extension of the Standard Model (SM) by a scalar singlet field without a ℤ2 symmetry. We first analyze the velocity of the expanding true-vacuum bubbles during the phase transition, confirming our previous finding in the unbroken ℤ2 symmetry scenario, where the bubble wall velocity can be computed from first principles only for weak transitions with strength parameters α ≲ 0.05, and the Chapman-Jouguet velocity defines the maximum velocity for which the wall is stopped by the friction from the plasma. We further provide an analytical approximation to the wall velocity in the general scalar singlet scenario without ℤ2 symmetry and test it against the results of a detailed calculation, finding good agreement. We show that in the singlet scenario with a spontaneously broken ℤ2 symmetry, the phase transition is always weak and we see no hope for baryogenesis. In contrast, in the case with explicit ℤ2 breaking there is a region of the parameter space producing a promising baryon yield in the presence of CP violating interactions via an effective operator involving the singlet scalar and the SM top quarks. Yet, we find that this region yields unobservable gravitational waves. Finally, we show that the promising region for baryogenesis in this model may be fully tested by direct searches for singlet-like scalars in di-boson final states at the HL-LHC, combined with present and future measurements of the electron electric dipole moment.

How arbitrary are perturbative calculations of the electroweak phase transition?

We investigate the extent to which perturbative calculations of the electroweak phase transition are arbitrary and uncertain, owing to their gauge, renormalisation scale and scheme dependence, as well as treatments of the Goldstone catastrophe and daisy diagrams. Using the complete parameter space of the Standard Model extended by a real scalar singlet with a ℤ2 symmetry as a test, we explore the properties of the electroweak phase transition in general Rξ and covariant gauges, OS and overline{textrm{MS}} renormalisation schemes, and for common treatments of the Goldstone catastrophe and daisy diagrams. Reassuringly, we find that different renormalisation schemes and different treatments of the Goldstone catastrophe and daisy diagrams typically lead to only modest changes in predictions for the critical temperature and strength of the phase transition. On the other hand, the gauge and renormalisation scale dependence may be significant, and often impact the existence of the phase transition altogether.

Bootstrapping the a-anomaly in 4d QFTs

We study gapped 4d quantum field theories (QFTs) obtained from a relevant deformation of a UV conformal field theory (CFT). For simplicity, we assume the existence of a ℤ2 symmetry and a single ℤ2-odd stable particle and no ℤ2-even particles at low energies. Using unitarity, crossing and the assumption of maximal analyticity we compute numerically a lower bound on the value of the a-anomaly of the UV CFT as a function of various non-perturbative parameters describing the two-to-two scattering amplitude of the particle.

Nonperturbative bounds on scattering of massive scalar particles in d ≥ 2

We study two-to-two scattering amplitudes of a scalar particle of mass m. For simplicity, we assume the presence of ℤ2 symmetry and that the particle is ℤ2 odd. We consider two classes of amplitudes: the fully nonperturbative ones and effective field theory (EFT) ones with a cut-off scale M. Using the primal numerical method which allows us to impose full non-linear unitarity, we construct novel bounds on various observables in 2 ≤ d ≤ 4 space-time dimensions for both classes of amplitudes. We show that our bounds are much stronger than the ones obtained by using linearized unitarity or positivity only. We discuss applications of our bounds to constraining EFTs. Finally, we compare our bounds to the amplitude in ϕ4 theory computed perturbatively at weak coupling, and find that they saturate the bounds.

Asymmetric mediator in scotogenic model

The scotogenic model is the Standard Model (SM) with Z2 symmetry and the addition of Z2 odd right-handed Majorana neutrinos and SU(2)L doublet scalar fields. We have extended the original scotogenic model by an additional Z2 odd singlet scalar field that plays a role in dark matter. In our model, the asymmetries of the lepton and Z2 odd doublet scalar are simultaneously produced through CP-violating right-handed neutrino decays. While the former is converted into baryon asymmetry through the sphaleron process, the latter is relaid to the DM density through the decay of SU(2)L doublet scalar that is named “asymmetric mediator”. In this way, we provide an extended scotogenic model that predicts the energy densities of baryon and dark matter being in the same order of magnitude, and also explains the low-energy neutrino masses and mixing angles.

A closed clockwork theory: ℤ2 parity and more

We develop a new class of clockwork theories with an augmented structure of the near-neighbour interactions along a one-dimensional closed chain. Such a topology leads to new and attractive features in addition to generating light states with hierarchical couplings via the usual clockwork mechanism. For one, there emerges a ℤ2 symmetry under the exchange of fields resulting in a physical spectrum consisting of states, respectively even and odd under the exchange parity with a two-fold degeneracy at each level. The lightest odd particle, being absolutely stable, could be envisaged as a potential dark matter candidate. The theory can also be obtained as a deconstruction of a five-dimensional theory embedded in a geometry generated by a linear dilaton theory on a S1/ℤ2 orbifold with three equidistant 3-branes. Analogous to the discrete picture, the ℤ2 symmetry in the bulk theory necessitates the existence of a KK spectrum of even and odd states, with doubly degenerate modes at each KK level when subject to certain boundary conditions.

Radiative corrections to decay branching ratios of the CP-odd Higgs boson in two Higgs doublet models

We calculate radiative corrections to decay rates of CP-odd Higgs boson A for various decay modes in the four types of two Higgs doublet models with the softly broken discrete Z2 symmetry. The decay branching ratios are evaluated at the next-to-leading order for electroweak corrections and the next-to-next-to-leading order for QCD corrections. We comprehensively study the impact of the electroweak corrections on the decay rates and the branching ratios. We find that the radiative corrections can sizably modify the branching ratios, especially for the A→Zh decay mode in the nearly alignment scenario, where coupling constants of the SM-like Higgs boson h are close to those in the standard model. We also show correlations between the branching ratios of A and the scaling factor of the SM-like Higgs boson coupling including higher-order corrections. In addition, we show characteristic predictions on the decay pattern depending on the types of Yukawa interaction, by which we can discriminate the types of Yukawa interaction in future collider experiments.

One-loop matching of scotogenic model onto standard model effective field theory up to dimension 7

The scotogenic neutrino seesaw model is a minimal extension of the standard model with three ℤ2-odd right-handed singlet fermions N and one ℤ2-odd Higgs doublet η that can accommodate the tiny neutrino mass and provide a dark matter candidate in a unified picture. Due to lack of experimental signatures for electroweak scale new physics, it is appealing to assume these new particles are well above the electroweak scale and take the effective field theory approach to study their effects on low energy observables. In this work we apply the recently developed functional matching formalism to the one-loop matching of the model onto the standard model effective field theory up to dimension seven for the case when all new states N and η are heavy to be integrated out. This is a realistic example which has no tree-level matching due to the ℤ2 symmetry. Using the matching results, we analyze their phenomenological implications for several physical processes, including the lepton number violating effect, the CDF W mass excess, and the lepton flavor violating decays like μ → eγ and μ → 3e.

WIMP and FIMP dark matter in singlet-triplet fermionic model

We present an extension of the SM involving three triplet fermions, one triplet scalar and one singlet fermion, which can explain both neutrino masses and dark matter. One triplet of fermions and the singlet are odd under a Z2 symmetry, thus the model features two possible dark matter candidates. The two remaining Z2-even triplet fermions can reproduce the neutrino masses and oscillation parameters consistent with observations. We consider the case where the singlet has feeble couplings while the triplet is weakly interacting and investigate the different possibilities for reproducing the observed dark matter relic density. This includes production of the triplet WIMP from freeze-out and from decay of the singlet as well as freeze-in production of the singlet from decay of particles that belong to the thermal bath or are thermally decoupled. While freeze-in production is usually dominated by decay processes, we also show cases where the annihilation of bath particles give substantial contribution to the final relic density. This occurs when the new scalars are below the TeV scale, thus in the reach of the LHC. The next-to-lightest odd particle can be long-lived and can alter the successful BBN predictions for the abundance of light elements, these constraints are relevant in both the scenarios where the singlet or the triplet are the long-lived particle. In the case where the triplet is the DM, the model is subject to constraints from ongoing direct, indirect and collider experiments. When the singlet is the DM, the triplet which is the next-to-lightest odd particle can be long-lived and can be probed at the proposed MATHUSLA detector. Finally we also address the detection prospects of triplet fermions and scalars at the LHC.

W-boson mass anomaly from scale invariant 2HDM

The recently reported measurement of the W-boson mass by CDF-II collaboration is significantly heavier than that of the Standard Model prediction. We study this anomaly in the scale invariant Two-Higgs-Doublet-Model (SI-2HDM) with a Z2 symmetry to avoid the flavor-changing-neutral-current (FCNC). In this scenario the Higgs particle is the classically massless scalon in the SI-2HDM gaining its mass by radiative corrections, hence being naturally light. Moreover, because of the scale symmetry the model is more predictive respect to the generic 2HDM. We show that the oblique parameters depending on the masses of the charged and CP-even (CP-odd) neutral scalar components of the SI-2HDM denoted respectively by MH± and Mh (MA), are large enough to accommodate the W-boson mass anomaly in the model. There are as well viable regions in the mass spectrum of the SI-2HDM that evade the experimental bounds from colliders on the charged Higgs and neutral scalars.

Pseudo-Nambu-Goldstone inflation with twin waterfalls

We propose a pseudo-Nambu-Goldstone inflation where twin waterfall fields coupled to the inflaton are responsible for the graceful exit from inflation by a waterfall transition. In this scenario, the Z2 symmetry for the waterfall fields and the inflaton protects the inflaton potential against dangerous quantum corrections coming from the waterfall couplings. We show that there is a wide range of natural model parameters and initial conditions for a successful inflation and discuss the reheating process by the perturbative decay of the waterfall field with a Z2 invariant Higgs portal. We also present a microscopic model for the inflaton couplings to the twin waterfall fields in the context of a dark QCD with light and heavy quarks.

Z2 non-restoration and composite Higgs: singlet-assisted baryogenesis w/o topological defects

Simple scalar-singlet extensions of the Standard Model with a (spontaneously broken) Z2 symmetry allow for a strong first order electroweak phase transition, as sought in order to realize electroweak baryogenesis. However they generically also lead to the emergence of phenomenologically problematic domain walls. Here we present a framework with a real scalar singlet that features a different thermal history that avoids this problem by never restoring the Z2 symmetry in the early universe. This is accomplished by considering D > 4 operators that emerge on general grounds, understanding the model as the low energy tail of a more complete theory, like for example in composite Higgs scenarios. Sticking to the latter framework, we present a concrete SO(6)/SO(5) composite realization of the idea. To this end, we additionally provide a complete classification of the structure of the Higgs potential (and the Yukawa couplings) in SO(6)/SO(5) models with fermions in the 1, 6, 15 or 20′ of SO(6).

Active-Sterile Neutrino Masses and Mixings in A4 Minimal Extended Seesaw Mechanism

Assuming the existence of an eV scale sterile neutrino, we develop a 3 + 1 neutrino mass model using A4 × Z4 × Z2 symmetry group. Three Higgs fields \(H, H^{\prime }\) and \(H^{\prime \prime }\) are considered to give a desired neutrino mass matrix which generates non-zero 𝜃13 and also successfully provides the active-sterile neutrino data in normal hierarchy. We also study the results of kinematic measurements of β −decay (mβ) and neutrinoless double beta decay (mββ) from the model. These results are consistent with latest experimental bounds and found to be in the ranges 0.0784 eV < mβ < 0.3034 eV and 0.0034 eV < mββ < 0.0667 eV respectively.

Critical dynamics of relativistic diffusion

We study the dynamics of self-interacting scalar fields with Z2 symmetry governed by a relativistic Israel-Stuart type diffusion equation in the vicinity of a critical point. We calculate spectral functions of the order parameter in mean-field approximation as well as using first-principles classical-statistical lattice simulations in real-time. We observe that the spectral functions are well-described by single Breit-Wigner shapes. Away from criticality, the dispersion matches the expectations from the mean-field approach. At the critical point, the spectral functions largely keep their Breit-Wigner shape, albeit with non-trivial power-law dispersion relations. We extract the characteristic time-scales as well as the dynamic critical exponent z, verifying the existence of a dynamic scaling regime. In addition, we derive the universal scaling functions implied by the Breit-Wigner shape with critical power-law dispersion and show that they match the data. Considering equations of motion for a system coupled to a heat bath as well as an isolated system, we perform this study for two different dynamic universality classes, both in two and three spatial dimensions.

Type III neutrino seesaw, freeze-in long-lived dark matter, and the W mass shift

In the framework of seesaw neutrino masses from heavy fermion triplets (Σ+,Σ0,Σ−), the addition of a light fermion singlet N and a heavy scalar triplet (ρ+,ρ0,ρ−) has some important consequences. The new particles are assumed to be odd under a new Z2 symmetry which is only broken softly, both explicitly and spontaneously. With N−Σ0 mixing, freeze-in long-lived dark matter through Higgs decay becomes possible. At the same time, the W mass is shifted slightly upward, as suggested by a recent precision measurement.

Next-to-leading order corrections to decays of the heavier CP-even Higgs boson in the two Higgs doublet model

We investigate the impact of electroweak (EW), scalar and QCD corrections to the full set of decay branching ratios of an additional CP-even Higgs boson (H) in the two Higgs doublet model with a softly broken Z2 symmetry. We employ the improved gauge independent on-shell scheme in the renormalized vertices. We particularly focus on the scenario near the alignment limit in which couplings of the discovered 125 GeV Higgs boson (h) coincide with those of the standard model while the Hhh coupling vanishes at tree level. The renormalized decay rate for H→hh can significantly be changed from the prediction at tree level due to non-decoupling loop effects of additional Higgs bosons, even in the near alignment case. We find that the radiative corrections to the branching ratio of H→hh can be a few ten percent level in the case with the masses of additional Higgs bosons being degenerate under the constraints of perturbative unitarity, vacuum stability and the EW precision data. Further sizable corrections can be obtained for the case with a mass difference among the additional Higgs bosons.

Searching for Charged Higgs Bosons via e+e−→ H+H−→ overline{c}boverline{c}b at Linear Colliders

We study a search for the charged Higgs boson via e+e−→ H+H−→ overline{c}boverline{c}b at the 500 GeV ILC. In a general two Higgs doublet model without Z2 symmetry, extra Yukawa couplings ρtt and ρtc can drive baryogenesis, but searches at the HL-LHC may still go empty-handed if the couplings are relatively weak. Taking {m}_{H^{+}} ≃ mH ≃ mA ≃ 200 GeV, with ρtt, ρtc ∼ 0.1 and no h(125)-H mixing, H+ → coverline{b} decay is dominant, and the overline{c}boverline{c}b final state is likely overwhelmed by QCD background at the LHC. We show that the electroweak production of H+H− at the ILC is discoverable with integrated luminosity of 1 ab−1. Furthermore, we show that {m}_{H^{+}} can be extracted by requiring the two pairs of b and light jets be roughly equal in mass, without assuming the mass value. Thus, ILC can probe low mass Higgs bosons in multijet final states to complement HL-LHC in the future.

Conditions of general Z2 symmetry and TM1,2 mixing for the minimal type-I seesaw mechanism in an arbitrary basis

In this paper, using a formula for the minimal type-I seesaw mechanism by LDLT (or generalized Cholesky) decomposition, conditions of general Z2-invariance for the neutrino mass matrix m are obtained in an arbitrary basis. The conditions are found to be (M22ai+−M12bi+)(M22aj−−M12bj−)=−det⁡Mbi+bj− for the Z2-symmetric and -antisymmetric part of a Yukawa matrix Yij±≡(Y±TY)ij/2≡(aj±,bj±) and the right-handed neutrino mass matrix Mij. In other words, the symmetric and antisymmetric part of bi must be proportional to those of the quantity a˜i≡ai−M12M22bi. They are equivalent to the condition that m is block diagonalized by eigenvectors of the generator T.These results are applied to three Z2 symmetries, the μ−τ symmetry, the TM1 mixing, and the magic symmetry which predicts the TM2 mixing. For the case of TM1,2, the symmetry conditions become M222a˜1TBMa˜2TBM=−det⁡Mb1TBMb2TBM and M222a˜1,2TBMa˜3TBM=−det⁡Mb1,2TBMb3TBM with components a˜iTBM and biTBM in the TBM basis v1,2,3. In particular, for the TM2 mixing, the magic (anti-)symmetric Yukawa matrix with S2Y=±Y is phenomenologically excluded because it predicts m2=0 or m1,m3=0. In the case where Yukawa is not (anti-)symmetric, the mass singular values are displayed without a root sign.

Dark matter and neutrinos in Left-Right Mirror Model with Z2 symmetry

We discussed the feasibility of including dark matter in the Left-Right Mirror Model with an additional discrete Z2 symmetry. The Z2 symmetry helps to prevent any decay of the possible dark matter candidate, that is, guarantees the stability of the dark matter. The dark matter candidate is proposed as the lightest mirror neutrino. This Z2 discrete symmetry not only guarantees the stability of the dark matter but also controls the free parameters of the model such that they are significantly reduced. Then, mass spectrum of neutrinos is also discussed in two possible scenarios obtained by assigning charge under Z2 symmetry. For one of the scenarios we obtain the relic density for the dark matter candidate and the spin independent scattering cross section between dark matter and proton (neutron).