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 $(3/4) (2π/e)$ as well as $Z$-magnetic charge, where $2π/e$ denotes the unit Dirac magnetic charge. Its total magnetic charge is $\sqrt{3/8}(4π/e)$, 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.
We use large-scale numerical simulations to study the formation and evolution of non-topological defects in a generalized electroweak phase transition described by the Glashow-Salam-Weinberg model without fermions. Such defects include dumbbells, comprising a pair of monopoles joined by a segment of electroweak string. These exhibit complex dynamics, with some shrinking under the string tension and others growing due to the monopole-antimonopole attractions between near neighbours. We estimate the range of parameters where the network of dumbbells persists, and show that this region is narrowe…
We consider a Yang-Mills-Higgs theory with gauge group $G=SU(n)$ broken to $G_{v} = [SU(p)\times SU(n-p)\times U(1)]/Z$ by a Higgs field in the adjoint representation. We obtain monopole solutions whose magnetic field is not in the Cartan Subalgebra. Since their magnetic field vanishes in the direction of the generator of the electromagnetic group $U(1)_{em}$, we call them Dark Monopoles. These Dark Monopoles must exist in some Grand Unified Theories (GUTs) without the need to introduce a dark sector. We analyze the particular case of $SU(5)$ GUT, where we obtain that their mass is $M = 4πv \w…
Grand unified theories of fundamental forces predict that magnetic monopoles are inevitable in the Universe because the second homotopy group of the order parameter manifold is $\mathbb{Z}$. We point out that monopoles can annihilate in pairs due to an influence of Alice strings. As a consequence, a monopole charge is charactarized by $\mathbb{Z}_2$ rather than $\mathbb{Z}$ if the Universe can accommodate Alice strings, which is the case of certain grand unified theories.
A simple formal computation, and a variation on an old thought experiment, both indicate that QCD with light quarks may confine fundamental color magnetic charges, giving an explicit as well as elegant resolution to the `global color' paradox, strengthening Vachaspati's SU(5) electric-magnetic duality, opening new lines of inquiry for monopoles in cosmology, and suggesting a class of geometrically large QCD excitations -- loops of Z(3) color magnetic flux entwined with light-quark current. The proposal may be directly testable in lattice gauge theory or supersymmetric Yang-Mills theory. Recent…
We identify a previously untapped discovery channel for grand-unification monopoles, arising from their ability to catalyse the direct decay of protons into monoenergetic 459 MeV antineutrinos within the Sun. Previous analyses omit this possibility as it necessarily involves an electroweak suppression factor, and instead search for the unsuppressed 20-50 MeV neutrinos produced via two-stage proton decays. By accounting for the relative difference in interaction cross section and experimental background at typical neutrino detection experiments, we demonstrate that this new channel in fact poss…
Thermal fluctuations of the gauge field lead to monopole formation at the grand unified phase transition in the early Universe, even if the transition is merely a smooth crossover. The dependence of the produced monopole density on various parameters is qualitatively different from theories with global symmetries, and the monopoles have a positive correlation at short distances. The number density of monopoles may be suppressed if the grand unified symmetry is only restored for a short time by, for instance, nonthermal symmetry restoration after preheating.
Grand unified theories may display multiply interacting fields with strong coupling dynamics. This poses two new problems: (1) What is the nature of chaotic reheating after inflation, and (2) How is reheating sensitive to the mass spectrum of these theories ? We answer these questions in two interesting limiting cases and demonstrate an increased efficiency of reheating which strongly enhances non-thermal topological defect formation, including monopoles and domain walls. Nevertheless, the large fluctuations may resolve this monopole problem via a modified Dvali-Liu-Vachaspati mechanism in whi…
We show how in the standard electroweak model three $SU(2)_L$ Nambu monopoles, each carrying electromagnetic (EM) and Z- magnetic fluxes, can merge (through Z-strings) with a single $U(1)_Y$ Dirac monopole to yield a composite monopole that only carries EM magnetic flux. Compatibility with the Dirac quantization condition requires this composite monopole to carry six quanta ($12 π/e$) of magnetic charge, independent of the electroweak mixing angle $θ_w$. The Dirac monopole is not regular at the origin and the energy of the composite monopole is therefore divergent. We discuss how this problem …
The recent MoEDAL experiment at LHC to detect the electroweak monopole makes the theoretical prediction of the monopole mass an urgent issue. We discuss different ways to estimate the mass of the electroweak monopole. We first present a scaling argument which indicates that the mass of the electroweak monopole to be around 4 TeV. To justify this we construct finite energy analytic dyon solutions which could be viewed as the regularized Cho-Maison dyon, modifying the coupling strengths of the electromagnetic interaction of $W$-boson in the standard model. Our result demonstrates that a genuine …
Taken individually, magnetic monopoles and axions are both well-motivated aspects of physics beyond the Standard Model. We demonstrate that by virtue of the Witten effect, their interplay is furthermore nontrivial; monopoles break the corresponding axial symmetries explicitly and result in an axion potential lacking the usual instanton-derived exponential suppression factor. As axions are distinguished by their extremely weak interactions, any regime where their effects are enhanced may be of interest. As an application of these findings, we demonstrate that a phenomenologically acceptable pop…
We discuss a supersymmetric SU(6) grand unified theory with the GUT flat direction being lifted by soft supersymmetry breaking, and the doublet-triplet splitting being achieved with Higgs as a pseudo-Goldstone boson. The theory offers a simple solution to the false vacuum and monopole problems.
Interactions of different types of topological defects can play an important role in the aftermath of a phase transition. We study interactions of fundamental magnetic monopoles and stable domain walls in a Grand Unified theory in which $SU(5) \times Z_2$ symmetry is spontaneously broken to $SU(3)\times SU(2)\times U(1)/Z_6$. We find that there are only two distinct outcomes depending on the relative orientation of the monopole and the wall in internal space. In one case, the monopole passes through the wall, while in the other it unwinds on hitting the wall.
A gauge transformation provided by the three eigenfunctions of $\B^a(x) \cdot \B^b(x)$ (where $\B^a(x)$, with a=1,2,3, are the non-Abelian magnetic fields) exposes the topological configurations of the Yang-Mills fields. In particular, it gives Dirac monopoles interacting with `photons' and massless charged vector bosons. A magnetic dipole field at each monopole corresponds to infinitesimal translation of the monopole, and provides the functional measure a la collective coordinates. The grand canonical partition function of the monopole plasma is exactly equivalent to a local field theory with…
We employ a variety of symmetry breaking patterns in $SO(10)$ and $E_6$ Grand Unified Theories to demonstrate the appearance of topological defects including magnetic monopoles, strings, and necklaces. We show that independent of the symmetry breaking pattern, a topologically stable superheavy monopole carrying a single unit of Dirac charge as well as color magnetic charge is always present. Lighter intermediate mass topologically stable monopoles carrying two or three quanta of Dirac charge can appear in $SO(10)$ and $E_6$ models respectively. These lighter monopoles as well as topologically …
We present a solution to the cosmological problem encountered in (supersymmetric) grand unified theories due to copious monopole production at the end of hybrid inflation. By employing thermal inflation ``driven'' by the U(1) axion symmetry, the superheavy monopole flux can be naturally suppressed to values that should be accessible to dedicated large scale experiments. The U(1) axion symmetry also helps generate the right magnitude for the mu term of the minimal supersymmetric standard model. An important by-product is the predicted existence of stable or very long-living fermions possessing …
Dirac showed that the existence of one magnetic pole in the universe could offer an explanation of the discrete nature of the electric charge. Magnetic poles appear naturally in most Grand Unified Theories. Their discovery would be of greatest importance for particle physics and cosmology. The intense experimental search carried thus far has not met with success. I propose a Universe with magnetic poles which are not observed free because they hide in deeply bound monopole--anti-monopole states named monopolium. I study the feasibility of this proposal and establish signatures for confirming m…
We study the formation of monopoles and strings in a model where SU(3) is spontaneously broken to U(2)=[SU(2)\times U(1)]/\ZZ_2, and then to U(1). The first symmetry breaking generates monopoles with both SU(2) and U(1) charges since the vacuum manifold is \CC P^2. To study the formation of these monopoles, we explicitly describe an algorithm to detect topologically non-trivial mappings on \CC P^2. The second symmetry breaking creates \ZZ_2 strings linking either monopole-monopole pairs or monopole-antimonopole pairs. When the strings pull the monopoles together they may create stable monopole…
In this review, we discuss recent developments in both the theory and the experimental searches of magnetic monopoles in past, current and future colliders and in the Cosmos. The theoretical models include, apart from the standard Grand Unified Theories, extensions of the Standard Model that admit magnetic monopole solutions with finite energy and masses that can be as light as a few TeV. Specifically, we discuss, among other scenarios, modified Cho-Maison monopoles and magnetic monopoles in (string-inspired, higher derivative) Born-Infeld extensions of the hypercharge sector of the Standard M…
We consider the Grand Unified SU(5) model with a small or vanishing cubic term in the adjoint scalar field in the potential. This gives the model an approximate or exact Z$_2$ symmetry whose breaking leads to domain walls. The simplest domain wall has the structure of a kink across which the Higgs field changes sign ($Φ\to -Φ$) and inside which the full SU(5) is restored. The kink is shown to be perturbatively unstable for all parameters. We then construct a domain wall solution that is lighter than the kink and show it to be perturbatively stable for a range of parameters. The symmetry in the…
This review is devoted to the Multiple Point Principle (MPP), according to which several vacuum states with the same energy density exist in Nature. The MPP is implemented to the Standard Model (SM), Family replicated gauge group model (FRGGM) and phase transitions in gauge theories with/without monopoles. Lattice gauge theories are reviewed. The lattice results for critical coupling constants are compared with those of the Higgs Monopole Model (HMM), in which the lattice artifact monopoles are replaced by the point-like Higgs scalar particles with a magnetic charge. Considering our (3+1)-dime…
The existence of a magnetic monopole, if it exists, remains elusive. Experimental searches have been carried out and are continuing in this quest. Of great uncertainty is the mass of the monopole which is model-dependent and ranging from some Grand Unified scale to the electroweak scale. In this paper, we propose a model where topologically stable, finite-energy monopoles {\em à la} 't Hooft-Polyakov could exist with a mass proportional to the electroweak scale. This comes about in a model of neutrino masses where right-handed neutrinos are {\em non-sterile} whose electroweak-scale Majorana ma…
Dirac showed that the existence of one magnetic pole in the universe could offer an explanation for the discrete nature of the electric charge. Magnetic poles appear naturally in most Grand Unified Theories. Their discovery would be of greatest importance for particle physics and cosmology. The intense experimental search carried thus far has not met with success. Moreover, if the monopoles are very massive their production is outside the range of present day facilities. A way out of this impasse would be if the monopoles bind to form monopolium, a monopole- antimonopole bound state, which is …
The Standard Model (SM) of the microcosm provides an excellent description of the phenomena of the microcosm, with the triumph of the discovery of the Higgs boson. There are many reasons, however, to believe that the SM is incomplete and represents a valid theory at relatively low energies only. Of particular interest are the models based on complete symmetries, such as those attempting a true unification between leptons and quarks in terms of a single symmetry group (Grand Unified Theories, GUTs) and those attempting unification between fermions and bosons, such as the supersymmetry. This cha…
We show that the monopole problem in Grand Unified Theories as well as the domain wall problem may be easily solved if the lepton number asymmetry in the Universe is large enough.
Model-Building Implications from Light Magnetic Monopoles: A Case Study of Flavour Deconstruction
PSI Center for Neutron and Muon Sciences（瑞士保罗谢勒研究所中子与μ子科学中心）；Physik-Institut, Universität Zürich（苏黎世大学物理学院）；Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre and INFN Sezione di Roma Tre（罗马第三大学数学与物理系及意大利国家核物理研究院罗马第三分所）；Institut für Theoretische Physik, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Departement Physik, Universität Basel（巴塞尔大学物理系）
