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 $H \to γγ$ decay rate. We construct generalizations of the CKY model that are compatible with the $H \to γγ$ 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.
We describe electroweak monopoles within the Born-Infeld extension of $SU(2)_L\times U(1)_Y$ electroweak theory. We argue for topological stability of these monopoles and computed their mass in terms of the Born-Infeld mass parameters. We then propose a new mechanism for electroweak baryogenesis which takes advantage of the following salient features of the electroweak monopoles: (i) monopoles support extra CP violation in the topological sector of the electroweak theory; (ii) they mediate unsuppressed baryon number violating interactions; (iii) non-thermal production of monopoles during the e…
We present finite energy analytic monopole and dyon solutions whose size is fixed by the electroweak scale. Our result shows that genuine electroweak monopole whose mass is around 6.7 TeV could exist, which could be detected at LHC.
We consider an isolated electroweak monopole solution within the Standard Model with a non-linear 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 $M\gtrsim 9.3\cdot 10^3$ TeV, while the nucleosynthesis constraints on the abundance of relic monopoles impose the bound $M\lesssim 2.3\…
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.
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 …
We apply a generalized field ansatz to describe the spherically symmetric sector of classical solutions of the electroweak theory. This sector contains Abelian magnetic monopoles labeled by their magnetic charge $n=\pm 1,\pm 2,\ldots$, the non-Abelian monopole for $n=\pm 2$ 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 p…
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 phas…
If the dark sector contains 't Hooft-Polyakov monopoles and a small enough dark gauge coupling, dark monopoles could be a macroscopic dark matter candidate. Its Higgs-portal coupling to the Standard Model can modify the electroweak vacuum in the monopole interior. In the most striking cases, dark monopoles could even contain electroweak-symmetric cores and generate multi-hit signals at large-volume detectors. If they are produced via parametric resonance in the early Universe, monopoles with radii up to one micron and masses up to ten kilotonnes could account for all of dark matter.
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 $B_λ\propto λ^{-2}$, where $λ$ is a smearing length scale.…
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. …
We discuss the cosmological production and the successive evolution of the electroweak (Cho-Maison) monopole in the standard model, and estimate the remnant monopole density at present universe. We confirm that, although the electroweak phase transition is of the first order, it is very mildly the first order. So 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, while the monopoles are produced copiously around the Ginzburg temperature $T_G\simeq 59.6~{\rm TeV}$, mos…
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…
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 ${\rm sin}^2θ_W = 1/4$, where $θ_W$ is the weak mixing angle at the energy scale set by the monopole mass. A leading-order renormalization-group analysis yields the va…
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 $|H|^{2n}(F_{μν})^2$ in the low-energy effective theory. This leads to …
Topological Stabilization via Higgs and $Z$-Boson Mediated Repulsions in Electroweak Monopole-Antimonopole Pairs
Southern Center for Nuclear Science Theory, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；School of Physics, Universiti Sains Malaysia（马来西亚理科大学物理学院）
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 …
We present exact solutions to Cho-Maison magnetic monopole in a family of effective electroweak models that have a Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We find that the lower bound to the mass of the magnetic monopole is $M \geq 2πv/ g \approx 2.37\,\,\mathrm{TeV}$. We argue that this bound holds universally, not just in theories with a BPS limit.
Laboratoire Univers et Particules de Montpellier (LUPM), University of Montpellier & CNRS, Montpellier, France（蒙彼利埃大学与法国国家科学研究中心联合宇宙与粒子物理实验室）；Service de Physique Théorique, Université Libre de Bruxelles (ULB), Brussels, Belgium（布鲁塞尔自由大学理论物理系）；Laboratoire de Physique Théorique et Hautes Énergies (LPTHE), CNRS & Sorbonne Université, 4 Place Jussieu, Paris, France（索邦大学与法国国家科学研究中心联合理论物理与高能物理实验室）
We find a topologically non-trivial structure of the Nambu monopole in two Higgs doublet model (2HDM), which is a magnetic monopole attached by two topologically stable $Z$ strings ($Z$ flux tubes) from two opposite sides. The structure is in sharp contrast to the topological triviality of the Nambu monopole in the standard model (SM), which is attached by a single non-topological $Z$ string. It is found that the Nambu monopole in 2HDM possesses the same fiber bundle structure with those of the `t Hooft-Polyakov monopole and the Wu-Yang description of the Dirac monopole, as a result of the fac…
In a recent work, a successful prediction has been made for $\sin^2 θ_W$ at an energy scale of O(TeV) based on the Dirac quantization condition of an electroweak monopole of the EW-$ν_R$ model. The fact that such a prediction can be made has prompted the following question: Can $SU(2)$ be unified with $U(1)$ at O(TeV) scale since a prediction for $\sin^2 θ_W$ necessarily relates the $U(1)$ coupling $g^{\prime}$ to the $SU(2)$ weak coupling $g$? It is shown in this manuscript that this can be accomplished by embedding $SU(2) \times U(1)$ into $SU(3)_W$ (The Weak Eightfold Way) with the followin…
The absence of supersymmetry or other new physics at the Large Hadron Collider (LHC) has lead many to question naturalness arguments. With Bayesian statistics, we argue that natural models are most probable and that naturalness is not merely an aesthetic principle. We calculate a probabilistic measure of naturalness, the Bayesian evidence, for the Standard Model (SM) with and without quadratic divergences, confirming that the SM with quadratic divergences is improbable. We calculate the Bayesian evidence for the Constrained Minimal Supersymmetric Standard Model (CMSSM) with naturalness priors …
Vector-boson scattering into two Z bosons at the LHC is a key channel for the exploration of the electroweak sector of the Standard Model. It allows for the full reconstruction of the scattering process but at the price of a huge irreducible background. For the first time, we present full next-to-leading-order predictions for $pp \to e^+e^-μ^+μ^-jj+X$ including all electroweak and QCD contributions for vector-boson scattering signal and irreducible background. The results are presented in the form of cross sections and differential distributions. A particular emphasis is put on the newly compu…
We classify effective field theory (EFT) deformations of the Standard Model (SM) according to the analyticity property of the Lagrangian as a function of the Higgs doublet H. Our distinction in analytic and non-analytic corresponds to the more familiar one between linearly and non-linearly realized electroweak symmetry, but offers deeper physical insight. From the UV perspective, non-analyticity occurs when the new states acquire mass from electroweak symmetry breaking, and thus cannot be decoupled to arbitrarily high scales. This is reflected in the IR by the anomalous growth of the interacti…
