Electroweak Symmetry Breaking Research Articles

Effects of the axion through the Higgs portal on primordial gravitational waves during the electroweak breaking

We investigate the effects of short axion kination eras on the energy spectrum of the primordial gravitational waves corresponding to modes that reenter the Hubble horizon at the postelectroweak symmetry breaking epoch well within the radiation domination era. Our main assumption is the existence of an extremely weakly coupled hidden sector between the Higgs and the axion, materialized by higher order nonrenormalizable dimension six and dimension eight operators, active at a scale $M$ of the order 20--100 TeV. This new physics scale $M$, which is way higher than the electroweak scale, is motivated by the lack of new particle observations in the large hadron collider to date beyond the electroweak scale. Once the electroweak symmetry breaking occurs at $T\ensuremath{\sim}100\text{ }\text{ }\mathrm{GeV}$, the axion potential acquires a new minimum due to the new terms generated by the electroweak breaking, and the axion oscillations at the origin are destabilized. In effect after some considerable amount of time, the axion rolls swiftly to its new minimum, experiencing a short kination epoch, where its energy density redshifts as ${\ensuremath{\rho}}_{a}\ensuremath{\sim}{a}^{\ensuremath{-}6}$. After it reaches the new minimum, since the latter is energetically less favorable that the Higgs minimum, it decays to the Higgs minimum and the Universe is described again by the Higgs minimum. The axion returns to the origin and commences again oscillations initiated by quantum fluctuations, redshifts as dark matter, and the same procedure is repeated perpetually. These short axion kination eras may disturb the background total equation of state parameter during the radiation domination era, changing it from that of radiation $w=1/3$ to some value closer to the kination value $w=1$. We examined the effect of a value $w=1/2$ on the energy density of the primordial gravitational waves. As we show, the energy spectrum of the gravitational waves mainly depends on how many times the short axion kination epochs occur, on the inflationary theory, on the actual value of the background equation of state parameter during the short kination eras, and finally on the reheating temperature. Our findings indicate a characteristic shape in the energy spectrum that can be observed in future gravitational wave experiments. We however disregarded the contribution of the electroweak phase transition on the gravitational waves for simplicity and transparency of our results.

Bottom quark and tau lepton masses in a toy textrm{SU}(6) model

We study a toy textrm{SU}(6) model with the symmetry breaking pattern of the extended 331 symmetry of textrm{SU}(3)_c otimes textrm{SU}(3)_W otimes textrm{U}(1)_X. A “fermion-Higgs mismatching” symmetry breaking pattern is proposed for more realistic model building. Within such symmetry breaking pattern, only one Higgs doublet develops vacuum expectation value for the spontaneous electroweak symmetry breaking, and gives tree-level top quark mass. A natural VEV splittings in the 331 breaking Higgs fields gives tree-level masses to both bottom quark and tau lepton. The 125,textrm{GeV} SM-like Higgs boson discovered at the LHC can have Yukawa couplings to bottom quark and tau lepton as in the SM prediction, and this suggests the 331 symmetry breaking scale to be sim {{{mathcal {O}}}}(10),textrm{TeV}.

Collective dynamics and the Anderson-Higgs mechanism in a bona fide holographic superconductor

The holographic superconductor is one of the most popular models in the context of applied holography. Despite what its name suggests, it does not describe a superconductor. On the contrary, the low temperature phase of its dual field theory is a superfluid with a spontaneously broken U(1) global symmetry. As already observed in the previous literature, a bona fide holographic superconductor can be constructed using mixed boundary conditions for the bulk gauge field. By exploiting this prescription, we study the near-equilibrium collective dynamics in the Higgs phase and reveal the characteristic features of the Anderson-Higgs mechanism. We show that second sound disappears from the spectrum and the gauge field acquires a finite energy gap of the order of the plasma frequency. We observe an overdamped to underdamped crossover for the Higgs mode which acquires a finite energy gap below ≈ Tc/2, with Tc the superconducting critical temperature. Interestingly, the energy gap of the Higgs mode at low temperature is significantly smaller than 2∆, with ∆ the superconducting energy gap. Finally, we interpret our results using Ginzburg-Landau theory and we confirm the validity of previously derived perturbative analytic expressions.

Hierarchies of Higgs Field and Theoretical Calculation of Higgs Particle Mass

A concept of isotime spin for Higgs particle and fermions is proposed in this paper. The Higgs field may be the time field, and the electroweak phase transition corresponds to the time phase transition. By describing the self-similar transformation process of the time phase transition, it is proved that the structural details of the time phase transition fully meet the requirements of the Higgs mechanism. Theoretical formulas of the Higgs mass, the mass and isotime spins of fermions are derived. The exact critical temperature of the electroweak phase transition is calculated, by using the solution for critical point and the experimental value of the Higgs particle mass. We discuss the behavior of the free Higgs particle and the saturation state of the time field containing I-bosons, point out that there is no parallel universes because weak force destroys the self-similar transformation of the time field, and the probability of the time field energy as a type of dark energy.

Vacuum stability and radiative symmetry breaking of the scale-invariant singlet extension of type II seesaw model

The questions of the origin of electroweak symmetry breaking and neutrino mass are two major puzzles in particle physics. Neutrino mass generation requires new physics beyond the Standard Model and also suggests reconsideration of physics of symmetry breaking. The aim of this paper is to study radiative symmetry breaking in the singlet scalar extension of type II seesaw neutrino mass model. We derive bounded-from-below conditions for the scalar potential of the model in full generality for the first time. The Gildener–Weinberg approach is utilised in minimising the multiscalar potential. Upon imposing the bounded-from-below and perturbativity conditions, as well as experimental constraints from colliders, we find the parameter space of scalar quartic couplings that can radiatively realise electroweak symmetry breaking at one-loop level. To satisfy all the constraints, the masses of the heavy triplet-like Higgs bosons must be nearly degenerate. The evolution of the Higgs doublet quartic coupling lambda _{H} can be prevented from being negative up to the Planck scale.

Type‐III Superconductivity

Superconductivity remains one of most fascinating quantum phenomena existing on a macroscopic scale. Its rich phenomenology is usually described by the Ginzburg-Landau (GL) theory in terms of the order parameter, representing the macroscopic wave function of the superconducting condensate. The GL theory addresses one of the prime superconducting properties, screening of the electromagnetic field because it becomes massive within a superconductor, the famous Anderson-Higgs mechanism. Here the authors describe another widely-spread type of superconductivity where the Anderson-Higgs mechanism does not work and must be replaced by the Deser-Jackiw-Templeton topological mass generation and, correspondingly, the GL effective field theory must be replaced by an effective topological gauge theory. These superconductors are inherently inhomogeneous granular superconductors, where electronic granularity is either fundamental or emerging. It is shown that the corresponding superconducting transition is a 3D generalization of the 2D Berezinskii-Kosterlitz-Thouless vortex binding-unbinding transition. The binding-unbinding of the line-like vortices in 3D results in the Vogel-Fulcher-Tamman scaling of the resistance near the superconducting transition. The authorsreport experimental data fully confirming the VFT behavior of the resistance.

Mass gap in U(1) Higgs–Yukawa model on a unit lattice

A non-perturbative proof of the mass generation of fermions via the Higgs mechanism is given. This is done by showing an exponential decay of the two point fermionic correlation function in a weakly coupled U(1) Higgs–Yukawa theory on a unit lattice in d = 4. This decay implies that the Higgs boson, the photon, and the fermion all have a non-zero physical mass, and the theory is said to have a mass gap.

Some new observations for the Georgi-Machacek scenario with triplet Higgs scalars

The Georgi-Machacek model, introducing a complex and a real scalar triplet as additional components of the electroweak symmetry breaking sector, enables substantial triplet contributions to the weak gauge boson masses, subject to the equality of the complex and the real triplet vacuum expectation values (vev) via a custodial SU(2) symmetry. We present an updated set of constraints on this scenario, from collider data (including those from 137/139~fb$^{-1}$ of luminosity at the Large Hadron Collider), available data on the 125-GeV scalar, indirect limits and also theoretical restrictions from vacuum stability and unitarity. It is found that some bounds get relaxed, and the phenomenological potential of the scenario is more diverse, if the doubly charged scalar in the spectrum can decay not only into two like-sign $W$'s but also into one or two singly charged scalars. Other interesting features are noticed in a general approach, such as substantial $\gamma\gamma$ and $Z\gamma$ branching ratios of the additional custodial singlet scalar, and appreciable strength of the trilinear interaction of a charged scalar, the $W$ and the $Z$. Finally,, we take into account the possibility of custodial SU(2) breaking, resulting in inequality of the real and the complex scalar vevs which too in principle may allow large triplet contribution to weak boson masses. Illustrative numerical results on the modified limits and predictions are presented, once more taking into account all the constraints mentioned above.

Explaining the CDF-II W-boson mass anomaly in the Georgi–Machacek extension models

Original Georgi–Machacek model can preserve the custodial symmetry at tree level after the electroweak symmetry breaking. Unless additional SU(2)_c custodial symmetry breaking effects are significant, the new physics contributions to Delta m_W are always very small. Our numerical results show that ordinary GM model can contribute to Delta m_W a maximal amount 0.0012 GeV, which can not explain the new CDF-II anomaly on W boson mass. We propose firstly to introduce small misalignment among the triplet VEVs to increase Delta m_W, which can give large new physics contributions to Delta m_W. Such slightly misaligned triplet VEVs from custodial symmetry preserving scalar potential can still be allowed. Our numerical results indicate that the resulting Delta m_W can easily reach the 1sigma range of CDF-II m_W data and the splitting among the triplet VEVs Delta v(equiv v_xi -v_chi ) can be as small as 0.8 GeV for v_chi lesssim 15 GeV. We also propose to introduce an additional custodial symmetry breaking source by extending the GM model with a low scale RH neutrino sector, which can adopt the leptogenesis mechanism and allow moderately large coupling strength h_{ij} even for triplet VEVs of order GeV. With low scale RH neutrino mass scale of order 10^2–10^4 TeV, the new physics contribution to Delta m_W can reach 0.03 GeV and is much larger than that of ordinary GM model. Combining both custodial SU(2)_c symmetry breaking effects, the small misalignment among the triplet VEVs and the moderately large h_{ij} couplings allowed with RH neutrino sector, the value of Delta m_W can still easily reach the 1sigma range of CDF-II m_W data, with a minimum splitting (among the triplet VEVs) approximately 0.7 GeV for v_chi lesssim 15 GeV.

Hilbert series, the Higgs mechanism, and HEFT

We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest at the level of the Hilbert series, as expected for the partition function of an S-matrix that is subject to the Goldstone equivalence theorem. In addition to massive vectors, we detail how other massive, spinning particles can be studied with Hilbert series; in particular, we spell out the ingredients for massive gravity in general spacetime dimensions. Further methodology is introduced to enable Hilbert series to capture the effect of spurion fields acquiring vevs. We apply the techniques to the Higgs Effective Field Theory (HEFT), providing a systematic enumeration of its operator basis. This is achieved both from a direct and a custodial symmetry spurion-based approach; we compare and contrast the two approaches, and our results to those appearing in previous literature.

The trilinear Higgs self-couplings at mathcal {O}(alpha _t^2) in the CP-violating NMSSM

In supersymmetric theories the Higgs boson masses are derived quantities where higher-order corrections have to be included in order to match the measured Higgs mass value at the precision of current experiments. Closely related through the Higgs potential are the Higgs self-interactions. In addition, the measurement of the trilinear Higgs self-coupling provides the first step towards the reconstruction of the Higgs potential and the experimental verification of the Higgs mechanism sui generis. In this paper, we advance our prediction of the trilinear Higgs self-couplings in the CP-violating Next-to-Minimal Supersymmetric extension of the SM (NMSSM). We provide the mathcal{O}(alpha _t^2) corrections in the gaugeless limit at vanishing external momenta. The higher-order corrections turn out to be larger than the corresponding mass corrections but show the expected perturbative convergence. The inclusion of the loop-corrected effective trilinear Higgs self-coupling in gluon fusion into Higgs pairs and the estimate of the theoretical uncertainty due to missing higher-order corrections indicate that the missing electroweak higher-order corrections may be significant.

Construction of entangled many-body states via the Higgs mechanism

We provide a guiding principle to generate entanglement of quantum many-body states by applying key ideas of the Higgs mechanism to systems without gauge structures. Unitary operators associated with the Higgs mechanism are constructed, named as mean-operators, and employed to prepare entangled many-body states out of a trivial state. We uncover a symmetry-protectedtopological state with two Ising symmetries on a square lattice and find entangled states with different symmetries and lattices. Plausible applications to quantum simulators such as Rydberg atoms and trapped ions, are also discussed, interpreting the mean-operators as the Ising coupling gates.

Observation of electroweak production of two jets and a Z-boson pair

Electroweak symmetry breaking explains the origin of the masses of elementary particles through their interactions with the Higgs field. Besides the measurements of the Higgs boson properties, the study of the scattering of massive vector bosons with spin 1 allows the nature of electroweak symmetry breaking to be probed. Among all processes related to vector-boson scattering, the electroweak production of two jets and a Z-boson pair is a rare and important one. Here we report the observation of this process from proton–proton collision data corresponding to an integrated luminosity of 139 fb−1 recorded at a centre-of-mass energy of 13 TeV with the ATLAS detector at the Large Hadron Collider. We consider two different final states originating from the decays of the Z-boson pair: one containing four charged leptons and another containing two charged leptons and two neutrinos. The hypothesis of no electroweak production is rejected with a statistical significance of 5.7σ, and the measured cross-section for electroweak production is consistent with the Standard Model prediction. In addition, we report cross-sections for inclusive production of a Z-boson pair and two jets for the two final states.

Twin Supersymmetric Dark Matter in Light of the First LZ Results

We review the status of dark matter (DM) candidates in supersymmetric Twin Higgs models in light of the first results of the LUX-ZEPLIN (LZ) experiment. We found that, for twin bino-dominated DM, the new results strengthened the lower bound on the higgsino mass. However, a large part of the parameter space consistent with natural electroweak symmetry breaking is still allowed. In the case of twin-stau DM, the new results imply that, if the thermal abundance of the twin-stau LSP fits the observed density of DM, the twin stau cannot have a large left-handed component anymore.

5D thermal field theory, Einstein field equations and spontaneous symmetry breaking

It has been shown previously, that the spatial thermal variation of a thermal medium can be recast as a variation in the Euclidean metric. It is now extended to temporal variations in temperature, for a non-relativistic thermal bath, which remains in local thermal equilibrium. This is achieved by examining the thermal field theory in a five-dimensional (5D) space–time–temperature. The bulk thermodynamic quantity, namely the energy density, is calculated for a neutral scalar field with a time-dependent Hamiltonian. Furthermore, the concept of recasting thermal variations as a variation in the metric is extended to thermal systems in a gravitational field. The Einstein field equations, in the 5D space–time–temperature, is determined. It is shown that, if the scalar Lagrangian is non-minimally coupled with gravity, the resulting Ricci scalar can lead to spontaneous symmetry breaking, leading to the Higgs mechanism. In essence, the asymmetry in the distribution of temperature in space–time can translate to spontaneous symmetry breaking of particle fields, in a very strong gravitational field.

The stability and the lifetime of the scalar boson star

In this paper, we introduce the formalism to examine the impact of the dark scalar sector to the conformal and the electroweak symmetries breaking in the sense of formation of the scalar boson star (BS). The BS is presented by the local scalar field containing the Higgs boson field and the scalar dilaton field in the conformal field theory. We study in detail the modification of the Higgs quartic coupling away from its Standard Model (SM) value within the influence of the dark sector. We show that the repulsive self-interactions and the flatness degree in the dark scalar sector can prevent an instability and the destruction of the BS. We have estimated the rate of the deviation from the SM with production of leptonic pairs due to decays of dilatons and dark photons emerged because of the BS instability. The lifetime, the maximal mass and the density of the BS, the average minimal distance between the stars are estimated. The effects of new physics should be visible at the HL-LHC, FCC-hh accompanied by the current LHC and the cosmological data.

The Complex Field Theory and Mass Formation—An Alternative Model to Higgs Mechanism

The electromagnetic force, strong nuclear force, weak nuclear force, and gravitational force are the four fundamental forces of nature. The Standard Model (SM) succeeded in combining the first three forces to describe the most basic building blocks of matter and govern the universe. Despite the model’s great success in resolving many issues in particle physics but still has several setbacks and limitations. The model failed to incorporate the fourth force of gravity. It infers that all fermions and bosons are massless contrary to experimental facts. In addition, the model addresses neither the 95% of the universe’s energy of Dark Matter (DM) and Dark Energy (DE) nor the universe’s expansion. The Complex Field Theory (CFT) identifies DM and DE as complex fields of complex masses and charges that encompasses the whole universe, and pervade all matter. This presumption resolves the issue of failing to detect DM and DE for the last five decades. The theory also presents a model for the universe’s expansion and presumes that every material object carries a fraction of this complex field proportional to its mass. These premises clearly explain the physical nature of the gravitational force and its complex field and pave the way for gravity into the SM. On the other hand, to solve the issue of massless bosons and fermions in the SM, Higgs mechanism introduces a pure and abstractive theoretical model of unimaginable four potentials to generate fictitious bosons as mass donors to fermions and W± and Z bosons. The CFT in this paper introduces, for the first time, a physical explanation to the mystery of the mass formation of particles rather than Higgs’ pure mathematical derivations. The analyses lead to uncovering the mystery of electron-positron production near heavy nuclei and never in a vacuum. In addition, it puts a constraint on Einstein’s mass-energy equation that energy can never be converted to mass without the presence of dense dark matter and cannot be true in a vacuum. Furthermore, CFT provides different perspectives and resolves real-world physics concepts such as the nuclear force, Casimir force, Lamb’s shift, and the anomalous magnetic moment to be published elsewhere.

Anderson-Higgs Mass of Magnons in Superconductor-Ferromagnet-Superconductor Systems

The dynamic interplay of superconductivity and magnetism is promising for developing quantum magnonics and spintronics. Recent experiments have reported significant, enigmatic shifts of ferromagnetic resonance frequency in layered SFS structures. The author explains that the origin of this effect is spontaneous generation of magnon mass due to the celebrated Anderson-Higgs mechanism, a cornerstone of the Standard Model of particle physics. Upon cooling below the superconducting critical temperature, the magnons acquire a frequency gap and change their propagation direction. This effect enables the creation of magnon resonators, crystals, parametric amplifiers, and other useful devices.

Spontaneous conformal symmetry breaking and quantum quadratic gravity

We investigate several quantum phenomena related to quadratic gravity after rewriting the general fourth-order action in a more convenient form that is second order in derivatives and produces only first-class constraints in phase space. We find that a Higgs mechanism may occur in the conformally invariant subset of the general quadratic action if the theory is conformally coupled to a scalar field that acquires a nonzero vacuum expectation value and spontaneously breaks the conformal symmetry. Then, in the broken phase, the originally massless spin-2 ghost may absorb both the scalar and vector fields to become massive. We also perform a Becchi-Rouet-Stora-Tyutin quantization of second-order quadratic gravity in the covariant operator formalism and discuss conditions under which unitarity of the full interacting quantum theory may be established.

CT or P problem and symmetric gapped fermion solution

An analogous ``strong $CP$ problem'' is identified in a toy model in two-dimensional spacetime: a general $1+1\mathrm{d}$ Abelian U(1) anomaly free chiral fermion and chiral gauge theory with a generic theta instanton term $\frac{\ensuremath{\theta}}{2\ensuremath{\pi}}\ensuremath{\int}F$. The theta term alone violates the charge-conjugation-time-reversal $CT$ and the parity $P$ discrete symmetries. The analogous puzzle here is the $CT$ or $P$ problem in $1+1\mathrm{d}$: Why can the $\overline{\ensuremath{\theta}}$ angle (including the effect of $\ensuremath{\theta}$ and the complex phase of a mass matrix) be zero or small for a natural reason? We show that this $CT$ or $P$ problem can be solved by a symmetric mass generation mechanism (SMG, namely generating a mass or energy gap while preserving an anomaly free symmetry). This $1+1\mathrm{d}$ toy model mimics several features of the $3+1\mathrm{d}$ Standard Model: chiral matter content, confinement, and Anderson-Higgs mass by Yukawa-Higgs term. One solution replaces some chiral fermion's Higgs-induced mean-field mass with SMG-induced non-mean-field mass. Another solution enriches this toy model by introducing several new physics beyond the Standard Model: a parity-reflection $PR$ discrete symmetry maps between the chiral and mirror fermions as fermion doubling localized on two domain walls at high energy, and SMG dynamically generates mass to the mirror fermion while still preserving the anomaly free chiral symmetry at an intermediate energy scale, much before the Higgs mechanism generates mass to the chiral fermion at lower energy. Without loss of generality, an arguably simplest $1+1\mathrm{d}$ U(1) symmetric anomaly free chiral fermion/gauge theory (e.g., Weyl fermions with ${3}_{L}\text{\ensuremath{-}}{4}_{L}\text{\ensuremath{-}}{5}_{R}\text{\ensuremath{-}}{0}_{R}$ U(1) charges) is demonstrated in detail. As an analogy to the superfluid-insulator or order-disorder quantum phase transition, in contrast to the conventional Peccei-Quinn solution sitting in the (quasi-long-range-order)-superfluid ordered phase, our solution is in the SMG insulator disordered phase.