Electroweak Monopole Research Articles

Electroweak strings in the standard model

We argue that the existence of the electroweak monopole predicts the existence of the electroweak string in the standard model made of monopole–antimonopole pair separated infinitely apart, which carry the quantized magnetic flux 4πn/e\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4 \\pi n/e$$\\end{document}. We show how to construct such quantized magnetic flux string solution. Our result strongly indicates that genuine fundamental electromagnetic string could exist in nature which could actually be detected. We discuss the physical implications of our result in cosmology.

Hidden BPS states of electroweak monopoles and a new bound estimate

Using the BPS Lagrangian method, we obtain a distinct set of Bogomolny equations for the Cho–Maison monopoles from the bosonic sector of a regularized electroweak theory. In the limit of n→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\rightarrow \\infty $$\\end{document} of the permittivity regulator, ϵρn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon \\left( \\rho ^n\\right) $$\\end{document}, the mass of the monopole can be estimated as MW∼3.56\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W\\sim 3.56$$\\end{document} TeV. This value is within the latest theoretical window, 2.98–3.75 TeV. We also discuss some possible regularization mechanisms of the electroweak monopole in the Yang–Mills sector and the existence of its BPS state.

Has telescope array discovered electroweak monopole?

We propose the ultra high energy cosmic ray recently detected by Telescope Array to be the electroweak monopole, and present theoretical arguments which support this. This strongly motivates the necessity for the “cosmic” MoEDAL experiment which could back up our proposal. To confirm this we propose Telescope Array to measure the magnetic charge of the ultra high energy cosmic ray particles with SQUID.

The electroweak monopole–antimonopole pair in the standard model

We present the first numerical solution that corresponds to a pair of Cho–Maison monopoles and antimonopoles (MAPs) in the SU(2) × U(1) Weinberg–Salam (WS) theory. The monopoles are finitely separated, while each pole carries a magnetic charge ±4π/e. The positive pole is situated in the upper hemisphere, whereas the negative pole is in the lower hemisphere. The Cho–Maison MAP is investigated for a range of Weinberg angles, 0.4675≤tanθW≤10 , and Higgs self-coupling, 0 ≤ β ≤ 1.7704. The magnetic dipole moment (μ m) and pole separation (d z ) of the numerical solutions are calculated and analyzed. The total energy of the system, however, is infinite due to point singularities at the locations of monopoles.

Electroweak multi-monopoles

We construct the multi-charge generalizations for the electroweak magnetic monopole solution of Cho and Maison within a wide range of values of the magnetic charge. We use the same ansatz for the axially symmetric fields as the one previously employed to construct the electroweak sphalerons and compare the internal structure of monopoles with that of sphalerons. The monopoles have zero dipole moment but a finite quadrupole momentum that rapidly increases with growing magnetic charge. For large charges, the monopole configurations are strongly squashed and show inside a bubble of symmetric phase filled with a U(1) hypercharge field produced by a pointlike magnetic charge at the origin, strong enough to suppress all other fields and restore the full gauge symmetry. The bubble is surrounded by a large belt of broken phase containing a magnetically charged ring filled with a nonlinear W-condensate, squeezed between two superconducting rings of opposite electric currents. In the far field region there remains only the magnetic field supported by the total magnetic charge contained at the origin and in the magnetic ring. The axially symmetric monopoles are probably just a special case of more general monopole solutions not possessing any continuous symmetries. The Cho-Maison monopole is stable but the stability of its multi-charge generalizations is not yet confirmed. All electroweak monopoles have infinite energy due to the pointlike U(1) charge at the origin, but the energy is expected to become finite after taking gravity into account, which should provide a cutoff via creating an event horizon to shield the U(1) charge.

Electroweak monopoles and their stability

We apply a generalized field ansatz to describe the spherically symmetric sector of classical solutions in the electroweak theory. This sector contains Abelian magnetic monopoles labeled by their magnetic charge n=±1,±2,…, the non-Abelian monopole for n=±2 found previously by Cho and Maison (CM), and also the electric oscillating solutions. All magnetic monopoles have infinite energy. We analyze their perturbative stability and use the method of complex spacetime tetrad to separate variables and reduce the perturbation equations to multi-channel Schroedinger-type eigenvalue problems. The spectra of perturbations around the CM monopole do not contain negative modes, hence this solution is stable. The n=±1 Abelian monopole is also stable, but all monopoles with |n|≥2 are unstable with respect to perturbations with angular momentum j=|n|/2−1. The Abelian |n|=2 monopole is unstable only within the j=0 sector whereas the CM monopole also has |n|=2 and belongs to the same sector, hence it may be viewed as a stable remnant of the decay of the Abelian monopole. One may similarly conjecture that stable remnants exist also for monopoles with |n|>2, hence the CM monopole is just the first member of a sequence of non-Abelian monopoles with higher magnetic charges. Only the CM monopole is spherically symmetric while all non-Abelian monopoles with |n|>2 are not rotationally invariant.

Kibble mechanism for electroweak magnetic monopoles and magnetic fields

The vacuum manifold of the standard electroweak model is a three-sphere when one considers homogeneous Higgs field configurations. For inhomogeneous configurations we argue that the vacuum manifold is the Hopf fibered three sphere and that this viewpoint leads to general criteria to detect electroweak monopoles and Z-strings. We extend the Kibble mechanism to study the formation of electroweak monopoles and strings during electroweak symmetry breaking. The distribution of magnetic monopoles produces magnetic fields that have a spectrum Bλ ∝ λ−2, where λ is a smearing length scale. Even as the magnetic monopoles annihilate due to the confining Z-strings, the magnetic field evolves with the turbulent plasma and may be relevant for cosmological observations.

Gravitating Cho\u2013Maison monopole

We study numerical solutions corresponding to spherically symmetric gravitating electroweak monopole and magnetically charged black holes of the Einstein–Weinberg–Salam theory. The gravitating electroweak monopole solutions are quite identical to the gravitating monopole solution in SU(2) Einstein–Yang–Mills–Higgs theory, but with distinctive characteristics. We also found solutions representing radially excited monopole, which has no counterpart in flat space. Both of these solutions exist up to a maximal gravitational coupling before they cease to exist. Lastly we also report on magnetically charged non-Abelian black holes solutions that is closely related to the regular monopole solutions, which represents counterexample to the ‘no-hair’ conjecture.

Electroweak monopoles with a non-linearly realized weak hypercharge

We present a finite-energy electroweak-monopole solution obtained by considering non-linear extensions of the hypercharge sector of the Electroweak Theory, based on logarithmic and exponential versions of electrodynamics. We find constraints for a class of non-linear extensions and also work out an estimate for the monopole mass in this scenario. We finally derive a lower bound for the energy of the monopole and discuss the simpler case of a Dirac magnetic charge.

An electroweak monopole, Dirac quantization and the weak mixing angle

We consider an extension of the Standard Model that was proposed recently by one of the current authors (PQH), which admits magnetic monopoles with a mass of order of a few TeV. We impose, in addition to topological quantization in the SU(2) sector of the model, the Dirac Quantization Condition (DQC) required for consistency of the quantum theory of a charged electron in the presence of the monopole. This leads to the prediction sin2θW=1/4, where θW is the weak mixing angle at the energy scale set by the monopole mass. A leading-order renormalization-group analysis yields the value of sin2θW≃0.231 at the Z-boson mass, as measured by experiment, under suitable conditions on the spectrum of the extra particles in the model.

Electroweak monopoles and magnetic dumbbells in grand unified theories

We use the $SU(5)$ model to show the presence in grand unified theories of an electroweak monopole and a magnetic dumbbell ("meson") made up of a monopole-antimonopole pair connected by a $Z$-magnetic flux tube. The monopole is associated with the spontaneous breaking of the weak $SU(2)_L$ gauge symmetry by the induced vacuum expectation value of a heavy scalar $SU(2)_L$ triplet with zero weak hypercharge contained in the adjoint Higgs 24-plet. This monopole carries a Coulomb magnetic charge of $(3/4) (2\pi/e)$ as well as $Z$-magnetic charge, where $2\pi/e$ denotes the unit Dirac magnetic charge. Its total magnetic charge is $\sqrt{3/8}(4\pi/e)$, which is in agreement with the Dirac quantization condition. The monopole weighs about 700 GeV, but because of the attached $Z$-magnetic tube it exists, together with the antimonopole, in a magnetic dumbbell configuration whose mass is expected to lie in the TeV range. The presence of these topological structures in $SU(5)$ and $SO(10)$ and in their supersymmetric extensions provides an exciting new avenue for testing these theories in high-energy colliders.

Regularization of electroweak monopole by charge screening and BPS energy bound

We show that the electroweak monopole can be regularized with a non-vacuum electromagnetic permittivity. This allows us to set a new BPS bound for the monopole mass, which implies that the mass may not be smaller than 2.98 TeV, more probably 3.75 TeV. We demonstrate that the same method can also regularize the Dirac monopole, which enhances the possibility to construct the Dirac monopole of mass of a few hundred meV in condensed matters. We discuss the physical implications of our result.

Physical implications of electroweak monopole.

The electroweak monopole in the standard model, the existence, characteristic features, cosmological production and physical implications are discussed. The discovery of the Higgs particle has been thought to be the 'final' test of the standard model. If the standard model is correct, however, it must have the electroweak monopole as the electroweak generalization of the Dirac monopole. This means that the detection of this monopole should become the final and topological test of the standard model. If detected, it becomes the first magnetically charged and stable topological elementary particle in the history of physics. Moreover, it has deep implications in physics. In cosmology, it could generate the primordial magnetic black holes which could explain the dark matter, become the seed of the large-scale structures of the universe, and be the source of the intergalactic magnetic field. Just as importantly, it could generate the hitherto unknown magnetic current which could have huge practical applications. Furthermore, the existence of the monopole requires us to reformulate the perturbative expansion in quantum field theory. This makes the detection of the electroweak monopole a most urgent issue. We discuss useful tips for the MoEDAL detector at LHC and similar experiments on how to detect the monopole successfully. This article is part of a discussion meeting issue 'Topological avatars of new physics'.

Localization of the Standard Model via the Higgs mechanism and a finite electroweak monopole from non-compact five dimensions

We propose a minimal and self-contained model in non-compact flat five dimensions which localizes the Standard Model (SM) on a domain wall. Localization of gauge fields is achieved by the condensation of Higgs field via a Higgs dependent gauge kinetic term in five-dimensional Lagrangian. The domain wall connecting vacua with unbroken gauge symmetry drives the Higgs condensation which provides both electroweak symmetry breaking and gauge field localization at the same time. Our model predicts higher-dimensional interactions $|H|^{2n}(F_{\mu\nu})^2$ in the low-energy effective theory. This leads to two expectations: The one is a new tree-level contribution to $H \to \gamma\gamma$ ($H \to gg$) decay whose signature is testable in future LHC experiment. The other is a finite electroweak monopole which may be accessible to the MoEDAL experiment. Interactions of translational Nambu-Goldstone boson is shown to satisfy a low-energy theorem.

Cosmological Implications of Electroweak Monopole

In this talk we review the basic features of the electroweak monopole, and estimate the remnant electroweak monopole density of the standard model in the present universe. We show that, although the electroweak phase transition is of the first order, the monopole production comes from the thermal fluctuations of the Higgs field after the phase transition, not the vacuum bubble collisions during the phase transition. Moreover, most of the monopoles produced initially are annihilated as soon as created, and this annihilation continues very long time, longer than the muon pair annihilation time. As the result the remnant monopole density at present universe becomes very small, of 10-11 of the critical density, too small to be the dark matter. We discuss the physical implications of our results on the ongoing monopole detection experiments.

Cosmological Implication of Electroweak Monopole

We estimate the remnant electroweak monopole density of the standard model in the present universe. We show that, although the electroweak phase transition is of the first order, the monopole production comes from the thermal fluctuations of the Higgs field after the phase transition, not the vacuum bubble collisions during the phase transition. Moreover, most of the monopoles produced initially are annihilated as soon as created, and this annihilation continues very long time, longer than the muon pair annihilation time. As the result the remnant monopole density at present universe becomes very small, of 10-11 of the critical density, too small to be the dark matter. We discuss the physical implications of our results on the ongoing monopole detection experiments.

Electroweak monopoles and the electroweak phase transition

We consider an isolated electroweak monopole solution within the Standard Model with a nonlinear Born–Infeld extension of the hypercharge gauge field. Monopole (and dyon) solutions in such an extension are regular and their masses are predicted to be proportional to the Born–Infeld mass parameter. We argue that cosmological production of electroweak monopoles may delay the electroweak phase transition and make it more strongly first order for monopole masses Mgtrsim 9.3 ,{cdot }, 10^3 TeV, while the nucleosynthesis constraints on the abundance of relic monopoles impose the bound Mlesssim 2.3cdot 10^4 TeV. The monopoles with a mass in this shallow range may be responsible for the dynamical generation of the matter–antimatter asymmetry during the electroweak phase transition.

Gravitationally coupled electroweak monopole

We present a family of gravitationally coupled electroweak monopole solutions in Einstein-Weinberg-Salam theory. Our result confirms the existence of globally regular gravitating electroweak monopole which changes to the magnetically charged black hole as the Higgs vacuum value approaches to the Planck scale. Moreover, our solutions could provide a more accurate description of the monopole stars and magnetically charged black holes.

Mass of the electroweak monopole

We present three independent methods to estimate the mass of the electroweak monopole. Our result strongly implies the existence of a genuine electroweak monopole of mass around 4–10 TeV, which could be detected by MoEDAL at present Large Hadron Collider (LHC). We emphasize that the discovery of the electroweak monopole should be the final test of the Standard Model.

The price of an electroweak monopole

In a recent paper, Cho, Kim and Yoon (CKY) have proposed a version of the SU(2) $\times$ U(1) Standard Model with finite-energy monopole and dyon solutions. The CKY model postulates that the effective U(1) gauge coupling $\to \infty$ very rapidly as the Englert-Brout-Higgs vacuum expectation value $\to 0$, but in a way that is incompatible with LHC measurements of the Higgs boson $H \to \gamma \gamma$ decay rate. We construct generalizations of the CKY model that are compatible with the $H \to \gamma \gamma$ constraint, and calculate the corresponding values of the monopole and dyon masses. We find that the monopole mass could be $< 5.5$ TeV, so that it could be pair-produced at the LHC and accessible to the MoEDAL experiment.