Electroweak Symmetry Breaking Research Articles

The low-energy effective theory of axions and ALPs

Axions and axion-like particles (ALPs) are well-motivated low-energy relics of high-energy extensions of the Standard Model, which interact with the known particles through higher-dimensional operators suppressed by the mass scale Λ of the new-physics sector. Starting from the most general dimension-5 interactions, we discuss in detail the evolution of the ALP couplings from the new-physics scale to energies at and below the scale of electroweak symmetry breaking. We derive the relevant anomalous dimensions at two-loop order in gauge couplings and one-loop order in Yukawa interactions, carefully considering the treatment of a redundant operator involving an ALP coupling to the Higgs current. We account for one-loop (and partially two-loop) matching contributions at the weak scale, including in particular flavor-changing effects. The relations between different equivalent forms of the effective Lagrangian are discussed in detail. We also construct the effective chiral Lagrangian for an ALP interacting with photons and light pseudoscalar mesons, pointing out important differences with the corresponding Lagrangian for the QCD axion.

On the evaluation of two-loop electroweak box diagrams for e+e\u2212 \u2192 HZ production

Precision studies of the Higgs boson at future e+e− colliders can help to shed light on fundamental questions related to electroweak symmetry breaking, baryogenesis, the hierarchy problem, and dark matter. The main production process, e+e−→ HZ, will need to be controlled with sub-percent precision, which requires the inclusion of next-to-next-to-leading order (NNLO) electroweak corrections. The most challenging class of diagrams are planar and non-planar double-box topologies with multiple massive propagators in the loops. This article proposes a technique for computing these diagrams numerically, by transforming one of the sub-loops through the use of Feynman parameters and a dispersion relation, while standard one-loop formulae can be used for the other sub-loop. This approach can be extended to deal with tensor integrals. The resulting numerical integrals can be evaluated in minutes on a single CPU core, to achieve about 0.1% relative precision.

Mass–action equivalence with respect to Explicit Symmetry Breaking

The mass–action equivalence emerges naturally as the consequence of Relativistic Heisenberg Uncertainty (RHU). It changes the structure of relativistic energy–momentum equation that has been underpinning the chosen Lagrangian of the Standard Model, i.e., the Lagrangian which the Higgs mechanism works. The transition from the mass–energy to the mass–action equivalence zone occurs at a certain value of the particle’s wave group velocity $$v_{{\text{g}}}$$ indicating the crossing curve between relativistic energy and action. Due to this transition, particles in the Standard Model are not going to gain inertial mass coming from the Higgs mechanism and related Higgs field, but from another mechanism which can break the Lagrangian symmetry of the Standard Model. This mechanism corresponds to Explicit Symmetry Breaking by generating the new type of field, i.e., the X-Higgs-like field and works based on the mass–action equivalence. This field provides the mass for the X Matter as well as Higgs field for Ordinary Matter. The gaining mass of particles due to this mechanism is not related to the form of ordinary relativistic energy, but to the form of relativistic action. It leads us to the new dynamical equation instead of the ordinary Klein–Gordon and Dirac equation. There are two phenomena due to the increasing and decreasing of particle’s velocity in this mechanism. From the lower to the higher velocity, particle gains additional inertial mass from the X Matter, while conversely particle loses its inertial mass. It is reasonable for us to view that the missing inertial mass of particles in the Standard Model is compensated as the Dark Matter. The X-Higgs-like field breaking to be the Dark-Higgs-like and recognized Higgs field can be considered to explain the origin of the Dark and Ordinary Matter from the X Matter.

Thermodynamics of Barrow Holographic Dark Energy with Specific Cut-Off

Motivated by the work of Saridakis (Phys. Rev. D102, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. The literature demonstrates that dark energy (DE) may result from electroweak symmetry breaking that triggers a phase transition from early inflation to late-time acceleration. In the present study, we incorporated viscosity in the Barrow HDE. A reconstruction scheme is presented for the parameters associated with Barrow holographic dark energy under the purview of viscous cosmology. The equation of state (EoS) parameter is reconstructed in this scenario and quintessence behaviour is observed. Considering Barrow HDE as a specific case of Nojiri–Odintsov (NO) HDE, we have observed quintom behaviour of the EoS parameter and for some values of n the EoS has been observed to be very close to −1 for the current universe. The generalised second law of thermodynamics has come out to be valid in all the scenarios under consideration. Physical viability of considering Barrow HDE as a specific case of NO HDE is demonstrated in this study. Finally, it has been observed that the model under consideration is very close to ΛCDM and cannot go beyond it.

Remarks on an Anomalous Triple Gauge Boson Couplings

We address the effect of an anomalous triple gauge boson couplings on a physical observable for the electroweak sector of the Standard Model, when the S U 2 L ⊗ U 1 Y symmetry is spontaneously broken by the Higgs mechanism to U 1 e m . Our calculation is done within the framework of the gauge-invariant, but path-dependent variable formalism is an alternative to the Wilson loop approach. Our result shows that the interaction energy is the sum of a Yukawa and a linear potential, leading to the confinement of static probe charges. The point we wish to emphasize, however, is that the anomalous triple gauge boson couplings ( Z γ γ ) contributes to the confinement for distances on the intranuclear scale.

Vector dark matter production from inflation with symmetry breaking

We present a scenario of vector dark matter production from symmetry breaking at the end of inflation. In this model, the accumulated energy density associated with the quantum fluctuations of the dark photon accounts for the present energy density of dark matter. The inflaton is a real scalar field while a heavy complex scalar field, such as the waterfall of hybrid inflation, is charged under the dark gauge field. After the heavy field becomes tachyonic at the end of inflation, rolling rapidly towards its global minimum, the dark photon acquires mass via the Higgs mechanism. To prevent the decay of the vector field energy density during inflation, we introduce couplings between the inflaton and the gauge field such that the energy is pumped to the dark sector. The setup can generate the observed dark matter abundance for a wide range of the dark photon's mass and with the reheat temperature around $10^{12}$ GeV. The model predicts the formation of cosmic strings at the end of inflation with the tensions which are consistent with the CMB upper bounds.

Glueballs and strings in Sp(2N) Yang-Mills theories

Motivated in part by the pseudo-Nambu Goldstone boson mechanism of electroweak symmetry breaking in composite Higgs models, in part by dark matter scenarios with strongly coupled origin, as well as by general theoretical considerations related to the large-$N$ extrapolation, we perform lattice studies of the Yang-Mills theories with $Sp(2N)$ gauge groups. We measure the string tension and the mass spectrum of glueballs, extracted from appropriate two-point correlation functions of operators organized as irreducible representations of the octahedral symmetry group. We perform the continuum extrapolation and study the magnitude of finite-size effects, showing that they are negligible in our calculation. We present new numerical results for $N=1$, 2, 3, 4, combine them with data previously obtained for $N=2$, and extrapolate toward $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We confirm explicitly the expectation that, as already known for $N=1$, 2 also for $N=3$, 4 a confining potential rising linearly with the distance binds a static quark to its antiquark. We compare our results to the existing literature on other gauge groups, with particular attention devoted to the large-$N$ limit. We find agreement with the known values of the mass of the ${0}^{++}$, ${0}^{++*}$, and ${2}^{++}$ glueballs obtained taking the large-$N$ limit in the $SU(N)$ groups. In addition, we determine for the first time the mass of some heavier glueball states at finite $N$ in $Sp(2N)$ and extrapolate the results toward $N\ensuremath{\rightarrow}+\ensuremath{\infty}$ taking the limit in the latter groups. Since the large-$N$ limit of $Sp(2N)$ is the same as in $SU(N)$, our results are relevant also for the study of QCD-like theories.

Sauter-Schwinger Effect in a Bardeen-Cooper-Schrieffer Superconductor.

Since the 1960s a deep and surprising connection has followed the development of superconductivity and quantum field theory. The Anderson-Higgs mechanism and the similarities between the Dirac and Bogoliubov-de Gennes equations are the most intriguing examples. In this last analogy, the massive Dirac particle is identified with a quasiparticle excitation and the fermion mass energy with the superconducting gap energy. Here we follow further this parallelism and show that it predicts an outstanding phenomenon: the superconducting Sauter-Schwinger effect. As in the quantum electrodynamics Schwinger effect, where an electron-positron couple is created from the vacuum by an intense electric field, we show that an electrostatic field can generate two coherent excitations from the superconducting ground-state condensate. Differently from the dissipative thermal excitation, these form a new macroscopically coherent and dissipationless state. We discuss how the superconducting state is weakened by the creation of this kind of excitations. In addition to shedding a different light and suggesting a method for the experimental verification of the Sauter-Schwinger effect, our results pave the way to the understanding and exploitation of the interaction between superconductors and electric fields.

Extended Time-Dependent Ginzburg–Landau Theory

We formulate the gauge invariant Lorentz covariant Ginzburg-Landau theory which describes nonstationary regimes: relaxation of a superconducting system accompanied by eigen oscillations of internal degrees of freedom (Higgs mode and Goldstone mode), and also forced oscillations under the action of an external gauge field. The theory describes Lorentz covariant electrodynamics of superconductors where Anderson-Higgs mechanism occurs, at the same time the dynamics of conduction electrons remains non-relativistic. It is demonstrated that Goldstone oscillations cannot be accompanied by oscillations of charge density and they generate the transverse field only. In addition, we consider Goldstone modes and features of Anderson-Higgs mechanism in two-band superconductors. We study dissipative processes, which are caused by movement of the normal component of electron liquid and violate the Lorentz covariance, on the examples of the damped oscillations of the order parameter and the skin-effect for electromagnetic waves. An experimental consequence of the extended time-dependent Ginzburg-Landau theory regarding the penetration of the electromagnetic field into a superconductor is proposed.

Is SMEFT enough?

There are two canonical approaches to treating the Standard Model as an Effective Field Theory (EFT): Standard Model EFT (SMEFT), expressed in the electroweak symmetric phase utilizing the Higgs doublet, and Higgs EFT (HEFT), expressed in the broken phase utilizing the physical Higgs boson and an independent set of Goldstone bosons. HEFT encompasses SMEFT, so understanding whether SMEFT is sufficient motivates identifying UV theories that require HEFT as their low energy limit. This distinction is complicated by field redefinitions that obscure the naive differences between the two EFTs. By reformulating the question in a geometric language, we derive concrete criteria that can be used to distinguish SMEFT from HEFT independent of the chosen field basis. We highlight two cases where perturbative new physics must be matched onto HEFT: (i) the new particles derive all of their mass from electroweak symmetry breaking, and (ii) there are additional sources of electroweak symmetry breaking. Additionally, HEFT has a broader practical application: it can provide a more convergent parametrization when new physics lies near the weak scale. The ubiquity of models requiring HEFT suggests that SMEFT is not enough.

Electroweak symmetry breaking in the inverse seesaw mechanism

We investigate the stability of Higgs potential in inverse seesaw models. We derive the full two-loop RGEs of the relevant parameters, such as the quartic Higgs self-coupling, taking thresholds into account. We find that for relatively large Yukawa couplings the Higgs quartic self-coupling goes negative well below the Standard Model instability scale ∼ 1010 GeV. We show, however, that the “dynamical” inverse seesaw with spontaneous lepton number violation can lead to a completely consistent and stable Higgs vacuum up to the Planck scale.

Vacuum structure of the \u21242 symmetric Georgi-Machacek model

We discuss the vacuum structure of a version of the Georgi-Machecek model with an exact ℤ2 symmetry acting on the triplet fields. Besides the usual custodial-symmetric model, with ρ = 1 at tree-level, a model with a dark matter candidate is also viable. The other phases of the model lead to electric charge breaking, a wrong pattern of electroweak symmetry breaking or to ρ ≠ 1 at tree-level. We derive conditions to have an absolute minimum in each of the two viable phases, the custodial and the dark matter phases.

Implications of dark sector mixing on leptophilic scalar dark matter

We propose a new viable outlook to the mixing between a singlet and a doublet leptonic dark sector fields. This choice relaxes the dark matter (DM) search constraints on the quintessential scalar singlet DM as well as presents new opportunities for its detection in the lab. The mixing produces an arbitrary mass difference between the two components of the extra doublet in a gauge-invariant way, without introducing any new scale of electroweak symmetry breaking in the theory. It also provides a useful handle to distinguish between the dark sector particles of different isospins, which is a challenging task other-wise. As the dark leptons coannihilate non-trivially, the mixing effectively enhances the viable parameter space for the relic density constraint. In low DM mass regime, our analysis shows that with a non-zero mixing, it is possible to relax the existing indirect search bounds on the upper limit of the DM-Standard Model coupling. From the analysis of the 3tau +{E}_T^{mathrm{miss}} and mathrm{ell}tau +{E}_T^{mathrm{miss}} channels for LHC at sqrt{s} = 13 TeV, we show that one ensures the presence of the mixing parameter between the dark sector particles of the theory by looking at the peak and tail positions of the kinematic distributions. Even with a tweak in the values of other free parameters within the viable parameter region, the distinct peak and tail positions of the kinematic distributions remains a constant feature of the model. While both the channels present us the opportunity to detect the mixing signature at the LHC/HL-LHC, the former gives better results in terms of a larger region of mixing parameter. From the fiducial cross section, the projected statistical significance for the integrated luminosity, mathcal{L} = 3 ab−1, are shown for a combined parameter region obeying all the existing constraints, where there is the best possibility to detect such a signature.

Dirac neutrinos and Neff. Part II. The freeze-in case

We discuss Dirac neutrinos whose right-handed component νR has new interac­tions that may lead to a measurable contribution to the effective number of relativistic neutrino species Neff. We aim at a model-independent and comprehensive study on a variety of possibilities. Processes for νR-genesis from decay or scattering of thermal species, with spin-0, spin-1/2, or spin-1 initial or final states are all covered. We calculate numerically and analytically the contribution of νR to Neff primarily in the freeze-in regime, since the freeze-out regime has been studied before. While our approximate analytical results apply only to freeze-in, our numerical calculations work for freeze-out as well, including the transition between the two regimes. Using current and future constraints on Neff, we obtain limits and sensitivities of CMB experiments on masses and couplings of the new interactions. As a by-product, we obtain the contribution of Higgs-neutrino interactions, Δ Neff SM ≃ 7.5 × 10-12, assuming the neutrino mass is 0.1 eV and generated by the standard Higgs mechanism.

Standard model meets gravity: Electroweak symmetry breaking and inflation

We propose a model for combining the Standard Model (SM) with gravity. It relies on a non-minimal coupling of the Higgs field to the Ricci scalar and on the Palatini formulation of gravity. Without introducing any new degrees of freedom in addition to those of the SM and the graviton, this scenario achieves two goals. First, it generates the electroweak symmetry breaking by a non-perturbative gravitational effect. In this way, it does not only address the hierarchy problem but opens up the possibility to calculate the Higgs mass. Second, the model incorporates inflation at energies below the onset of strong-coupling of the theory. Provided that corrections due to new physics above the scale of inflation are not unnaturally large, we can relate inflationary parameters to data from collider experiments.

Gauge Invariance for Classical Massless Particles with Spin

Wigner’s quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a classical-particle version of the Higgs mechanism.

NLO QCD predictions for doubly-polarized WZ production at the LHC

Accessing the polarization of weak bosons provides an important probe for the mechanism of electroweak symmetry breaking. Relying on the double-pole approximation and on the separation of polarizations at the amplitude level, we study WZ production at the LHC, with both bosons in a definite polarization mode, including NLO QCD effects. We compare results obtained defining the polarization vectors in two different frames. Integrated and differential cross-sections in a realistic fiducial region are presented.

Investigating bottom-quark Yukawa interaction at Higgs factory * *The work of JG is sponsored by the National Natural Science Foundation of China (11875189, 11835005) and the MOE Key Lab for Particle Physics, Astrophysics and Cosmology. The research of QB, KC, YL and HZ is supported by the funding from the Institute of High Energy Physics, Chinese Academy of Sciences (Y6515580U1)

Measuring the fermion Yukawa coupling constants is important for understanding the origin of the fermion masses and their relationship with spontaneously electroweak symmetry breaking. In contrast, some new physics (NP) models change the Lorentz structure of the Yukawa interactions between standard model (SM) fermions and the SM-like Higgs boson, even in their decoupling limit. Thus, the precise measurement of the fermion Yukawa interactions is a powerful tool of NP searching in the decoupling limit. In this work, we show the possibility of investigating the Lorentz structure of the bottom-quark Yukawa interaction with the 125 GeV SM-like Higgs boson for future colliders.

Light quantum control of persisting Higgs modes in iron-based superconductors

The Higgs mechanism, i.e., spontaneous symmetry breaking of the quantum vacuum, is a cross-disciplinary principle, universal for understanding dark energy, antimatter and quantum materials, from superconductivity to magnetism. Unlike one-band superconductors (SCs), a conceptually distinct Higgs amplitude mode can arise in multi-band, unconventional superconductors via strong interband Coulomb interaction, but is yet to be accessed. Here we discover such hybrid Higgs mode and demonstrate its quantum control by light in iron-based high-temperature SCs. Using terahertz (THz) two-pulse coherent spectroscopy, we observe a tunable amplitude mode coherent oscillation of the complex order parameter from coupled lower and upper bands. The nonlinear dependence of the hybrid Higgs mode on the THz driving fields is distinct from any known SC results: we observe a large reversible modulation of resonance strength, yet with a persisting mode frequency. Together with quantum kinetic modeling of a hybrid Higgs mechanism, distinct from charge-density fluctuations and without invoking phonons or disorder, our result provides compelling evidence for a light-controlled coupling between the electron and hole amplitude modes assisted by strong interband quantum entanglement. Such light-control of Higgs hybridization can be extended to probe many-body entanglement and hidden symmetries in other complex systems.

Spontaneous symmetry breaking: A view from derived geometry

We examine symmetry breaking in field theory within the framework of derived geometry, as applied to field theory via the Batalin–Vilkovisky formalism. Our emphasis is on the standard examples of Ginzburg–Landau and Yang–Mills–Higgs theories and is primarily interpretive. The rich, sophisticated language of derived geometry captures the physical story elegantly, allowing for sharp formulations of slogans (e.g., for the Higgs mechanism, that the unstable ghosts feed the Goldstone bosons to a hungry, massless gauge boson). Rewriting these results in the BV formalism provides, as one nice payoff, a reformulation of ’t Hooft’s family of gauge-fixing conditions for spontaneously broken gauge theory that behaves well in the ξ→∞ limit.