Search Results (17)

Charged quasiparticles, which are constrained to move on a plane, interact by means of electromagnetic (EM) fields which are not subject to this constraint, living, thus, in three-dimensional space. We have, consequently, a hybrid situation where the particles of a given system and the EM fields (through which they interact) live in different dimensions. Pseudo-Quantum Electrodynamics (PQED) is a U(1) gauge field theory that, despite being strictly formulated in two-dimensional space, precisely describes the real EM interaction of charged particles confined to a plane. PQED is completely different from QED(2 + 1), namely, Quantum Electrodynamics of a planar gauge field. It produces, for instance, the correct $1/r$ Coulomb potential between static charges, whereas QED(2 + 1) produces $lnr$ potential. In spite of possessing a nonlocal Lagrangian, it has been shown that PQED preserves both causality and unitarity, as well as the Huygens principle. PQED has been applied successfully to describe the EM interaction of numerous systems containing charged particles constrained to move on a plane. Among these are p-electrons in graphene, silicene, and transition-metal dichalcogenides; systems exhibiting the Valley Quantum Hall Effect; systems inside cavities; and bosonization in (2 + 1)D. Here, we present a review article on PQED (also known as Reduced Quantum Electrodynamics). Full article

The Standard Model of electroweak interactions is based on the fundamental SU(2)_weak × U(1)_elect representation. It assumes massless neutrinos and purely left-handed massive $W^{\pm }$ and Z⁰ bosons to which one should add the massless photon. The existence, verified experimentally, of neutrino oscillations poses a challenge to this scheme, since the oscillations take place between at least three massive neutrinos belonging to a mass hierarchy still to be determined. One should also take into account the possible existence of sterile neutrino species. In a somehow different context, the fundamental nature of the strong interaction component of the forces in nature is described by the, until now, extremely successful representation based on the SU(3)_strong group which, together with the confining rule, give a description of massive hadrons in terms of quarks and gluons. To this is added the minimal U(1) Higgs group to give mass to the otherwise massless generators. This representation may also be challenged by the existence of both dark matter and dark energy, of still unknown composition. In this note, we shall discuss a possible connection between these questions, namely the need to extend the SU(3)_strong × SU(2)_weak × U(1)_elect to account for massive neutrinos and dark matter. The main point of it is related to the role of axions, as postulated by Roberto Peccei and Helen Quinn. The existence of neutral pseudo-scalar bosons, that is, the axions, has been proposed long ago by Peccei and Quinn to explain the suppression of the electric dipole moment of the neutron. The associated U(1)_PQ symmetry breaks at very high energy, and it guarantees that the interaction of other particles with axions is very weak. We shall review the axion properties in connection with the apparently different contexts of neutrino and dark matter physics. Full article

The anomalous dimension ${\gamma }_m=1$ in the infrared region near the conformal edge in the broken phase of the large $N_f$ QCD has been shown by the ladder Schwinger–Dyson equation and also by the lattice simulation for $N_f=8$ and for $N_c=3$. Recently, Zwicky made another independent argument (without referring to explicit dynamics) for the same result, ${\gamma }_m=1$, by comparing the pion matrix element of the trace of the energy-momentum tensor $⟨\pi \left(p_2\right)|(1+{\gamma }_m)·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=⟨\pi \left(p_2\right)|{\theta }_{\mu }^{\mu }|\pi \left(p_1\right)⟩=2M_{\pi }^2$ (up to trace anomaly) with the estimate of $⟨\pi \left(p_2\right)|2·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=2M_{\pi }^2$ through the Feynman–Hellmann theorem combined with an assumption $M_{\pi }^2\sim m_f$ characteristic of the broken phase. We show that this is not justified by the explicit evaluation of each matrix element based on the dilaton chiral perturbation theory (dChPT): $⟨\pi \left(p_2\right)|2·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=2M_{\pi }^2+[(1-{\gamma }_m)M_{\pi }^2·2/(1+{\gamma }_m)]=2M_{\pi }^2·2/(1+{\gamma }_m)\ne 2M_{\pi }^2$ in contradiction with his estimate, which is compared with $⟨\pi \left(p_2\right)|(1+{\gamma }_m)·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=(1+{\gamma }_m)M_{\pi }^2+\left[(1-{\gamma }_m)M_{\pi }^2\right]=2M_{\pi }^2$ (both up to trace anomaly), where the terms in $\left[\right]$ are from the $\sigma$ (pseudo-dilaton) pole contribution. Thus, there is no constraint on ${\gamma }_m$ when the $\sigma$ pole contribution is treated consistently for both. We further show that the Feynman–Hellmann theorem is applied to the inside of the conformal window where dChPT is invalid and the $\sigma$ pole contribution is absent, and with $M_{\pi }^2\sim m_f^{2/(1+{\gamma }_m)}$ instead of $M_{\pi }^2\sim m_f$, we have the same result as ours in the broken phase. A further comment related to dChPT is made on the decay width of $f_0\left(500\right)$ to $\pi \pi$ for $N_f=2$. It is shown to be consistent with the reality, when $f_0\left(500\right)$ is regarded as a pseudo-NG boson with the non-perturbative trace anomaly dominance. Full article

Six-dimensional spinors with $Spin(3,3)$ symmetry are utilized to efficiently encode three generations of matter. $E_{8(-24)}$ is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations of the standard model fermions, and Higgs bosons. Pati–Salam, $SU\left(5\right)$, and $Spin\left(10\right)$ grand unified theories are found when a single generation is isolated. For spacetime symmetries, $Spin(4,2)$ may be used for conformal symmetry, $Ad{S}_5\to d{S}_4$, or simply broken to $Spin(3,1)$ of a Minkowski space. Another class of representations finds $Spin(2,2)$ and can give $Ad{S}_3$ with various GUTs. An action for three generations of fermions in the Majorana–Weyl spinor $\mathbf{128}$ of $Spin(4,12)$ is found with $Spin\left(3\right)$ flavor symmetry inside $E_{8(-24)}$. The 128 of $Spin(12,4)$ can be regarded as the tangent space to a particular pseudo-Riemannian form of the octo-octonionic Rosenfeld projective plane $E_{8(-24)}/Spin(12,4)=\left(\mathbb{O}sx\mathbb{O}\right){\mathbb{P}}^2$. Full article

We review and extend recent studies of dilaton effective field theory (dEFT) that provide a framework for the description of the Higgs boson as a composite structure. We first describe the dEFT as applied to lattice data for a class of gauge theories with near-conformal infrared behavior. This includes the dilaton associated with the spontaneous breaking of (approximate) scale invariance and a set of pseudo-Nambu–Goldstone bosons (pNGBs) associated with the spontaneous breaking of an (approximate) internal global symmetry. The theory contains two small symmetry-breaking parameters. We display the leading-order (LO) Lagrangian and review its fit to lattice data for the $SU\left(3\right)$ gauge theory with $N_f=8$ Dirac fermions in the fundamental representation. We then develop power-counting rules to identify the corrections emerging at next-to-leading order (NLO) in the dEFT action. We list the NLO operators that appear and provide estimates for the coefficients. We comment on implications for composite Higgs model building. Full article

In this work, we study the thermodynamics of a hybrid system based on the Da Providencia–Schütte Hamiltonian. The model consists of bosons, i.e., photons in a cavity, interacting with an ensemble of spins through a pseudo-Hermitian Hamiltonian. We compute the exact partition function of the system, and from it, we derive the statistical properties of the system. Finally, we evaluate the work that can be extracted from the system by performing an Otto cycle and discuss the advantages of the proposed pseudo-Hermitian interaction. Full article

We consider a fully pseudo-bosonic Swanson model and we show how its Hamiltonian H can be diagonalized. We also deduce the eigensystem of $H^{†}$, using the general framework and results deduced in the context of pseudo-bosons. We also construct, using different approaches, the bi-coherent states for the model, study some of their properties, and compare the various constructions. Full article

Grand unified theories (GUTs) may result in the $E_6$-inspired composite Higgs model (E${}_6$CHM) at low energies, almost stabilizing the electroweak scale. We consider an orbifold GUT in 6 dimensions in which the $E_6$-gauge group is broken to the gauge symmetry of the standard model (SM) while different multiplets of the SM fermions come from different 27-plets. The strongly coupled sector of the E${}_6$CHM is confined on the brane where $E_6$ is broken down to its $SU(6)$ subgroup. Near the scale of $f\gtrsim 5\mathrm{TeV}$, this approximate $SU(6)$ symmetry is expected to be further broken down to its $SU(5)$ subgroup, which contains the SM-gauge group. Such a breakdown leads to a set of pseudo-Nambu–Goldstone bosons (pNGBs) that includes an SM-like Higgs doublet. The approximate gauge coupling unification in the E${}_6$CHM takes place at high energies when the right-handed top quark is a composite fermion. To ensure anomaly cancellation, the weakly coupled sector of this model contains extra exotic matter beyond the SM. We discuss the mechanism of the generation of matter–antimatter asymmetry within the variant of the E${}_6$CHM in which the baryon number and CP invariance are violated. Full article

We explore a possibility to detect dark components in the Universe via stimulated photon–photon collisions by focusing two-frequency coherent electromagnetic fields in a vacuum. Those fields are assumed to be pulsed reaching Fourier transform limits in near-infrared, THz, and GHz frequency bands, respectively. The numbers of signal photons as a result of exchange of a pseudoscalar-type pseudo Nambu–Goldstone boson have been evaluated in the individual frequency bands. Within presently available beam intensities, we found that the QCD axion scenarios are thoroughly testable in the mass range ${10}^{-6}$–${10}^0$ eV based on the common method. Furthermore, we show a possibility to reach the weak coupling domain even beyond the gravitationally weak coupling strength if pulse compression in the GHz band is realized in the near future development. Full article

There are many methods of searching for traces of the so-called new physics in particle physics. One of them, and the main focus of this paper, is athe study of the Z-boson decay in $e^{+}{e}^{-}$ collisions. An improvement in the precision of calculations of the Standard Model (SM) electroweak pseudo-observables, such as scattering asymmetries, effective weak mixing angles, and decay widths, related to the Z-boson will meet severe experimental requirements at the planned $e^{+}{e}^{-}$ colliders and will increase the chance to detect non-standard effects in experimental analysis. To reach this goal, one has to calculate the next order of perturbative SM theory, namely three-loop Feynman integrals. We discuss the complexity of the problem, as well as the methods crucial for completing three-loop calculations. We show several numerical solutions for some three-loop Feynman integrals using sector decomposition, Mellin–Barnes (MB), and differential equation methods. Full article

In a recent paper (A. Fring and T. Frith, Phys. Rev A 100, 101102 (2019)), a Dyson scheme to deal with density matrix of non-Hermitian Hamiltonians has been used to investigate the entanglement of states of a PT-symmetric bosonic system. They found that von Neumann entropy can show a different behavior in the broken and unbroken regime. We show that their results can be recast in terms of an abstract model of pseudo-Hermitian random matrices. It is found however that although the formalism is practically the same, the entanglement is not of Fock states but of Bell states. Full article

The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group G are governed by the well-known Wigner–Eckart relations. In the case of infinite-dimensional systems, with G spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases. Full article

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit. Full article

The birth of the Universe, its dark components, and the next fundamental level of matter are briefly discussed. The classical cosmological solution for our Universe with a Λ-term has two branches divided by a gap. The quantum process of tunneling between branches took place. A model of a slowly swelling Universe in the result of the multiple reproductions of cosmological cycles arises naturally. The occurrence of baryon asymmetry is briefly discussed. The problem of the cosmological constant is solved and, thus, the crisis of physics connected with this constant is overcome. But we note that dark energy is evolving. Dark matter (part or all) consists of familon-type pseudo-Goldstone bosons with a mass of 10⁻⁵–10⁻³ eV. It follows the composite model of particles. This model reproduces three relativistic phase transitions in the medium of familons at different red shifts, forming a large scale structure of the Universe dark matter that was “repeated” by baryons. Here three generations of elementary particles are absolutely necessary. Full article

The 125 GeV boson is quite consistent with the Higgs boson of the Standard Model (SM), but there is a challenge from Anderson as to whether this particle is in the Lagrangian. As Large Hadron Collider (LHC) Run 2 enters its final year of running, we ought to reflect and make sure we have gotten everything right. The ATLAS and CMS combined Run 1 analysis claimed a measurement of 5.4$\sigma$ vector boson fusion (VBF) production which is consistent with SM, which seemingly refutes Anderson. However, to verify the source of electroweak symmetry breaking (EWSB), we caution that VBF measurement is too important for us to be imprudent in any way, and gluon–gluon fusion (ggF) with similar tag jets must be simultaneous measured, which should be achievable in LHC Run 2. The point is to truly test the dilaton possibility—the pseudo-Goldstone boson of scale invariance violation. We illustrate EWSB by dynamical mass generation of a sequential quark doublet (Q) via its ultrastrong Yukawa coupling and argue how this might be consistent with a 125 GeV dilaton, $\mathcal{D}$. The ultraheavy $2m_Q\gtrsim 4$–5 TeV scale explains the absence of New Physics so far, while the mass generation mechanism shields us from the UV theory for the strong Yukawa coupling. Collider and flavor physics implications are briefly touched upon. Current Run 2 analyses show correlations between the ggF and VBF measurements, but the newly observed $t\overline{t}H$ production at LHC poses a challenge. Full article