arXiv subjects

Khai-Ming Wong

Publications and source records attributed to Khai-Ming Wong.

At least 19 recordsLinked to original sources

arXiv2026

First mass determination of electroweak vortex rings in the Standard Model

We report the first rigorous evaluation of the physical mass of electroweak vortex rings, establishing precise values of 18.01 and 26.80 TeV for solutions characterized by different winding numbers. Analysis of the internal structure reveals that repulsive interactions shape the geometry of these configurations, while complex current distributions lead to a neutral analogue of Ampere's circuital law, suggesting a corresponding self-stabilizing pinch mechanism. These findings set the energy scales for the potential observation of such configurations at future colliders and offer a framework for understanding topological structures in the Standard Model.

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arXiv2025

Topological Stabilization via Higgs and $Z$-Boson Mediated Repulsions in Electroweak Monopole-Antimonopole Pairs

We identify two distinct repulsive mechanisms in the Cho-Maison monopole-antimonopole pair (MAP) configuration. Our results show that the Higgs-mediated repulsion exhibits a non-monotonic dependence on both topological charge and Higgs self-coupling, confirming its topological origin while revealing a mass-controlled range transition that deviates from the exponential form of a Yukawa potential. Simultaneously, the $Z$-boson field generates localized repulsive cores of radius $R_c\approx0.8\,m_W^{-1}$, consistent with the weak interaction scale. The collaborative effect of these mechanisms -- operating in different physics regimes -- counteracts the magnetic attraction, establishing a stabilization paradigm for the Cho-Maison MAP that extends naturally to other topological solitons in the Standard Model and various systems described by effective field theories.

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arXiv2024

Generalized Half-Dyon in Weinberg-Salam Theory

We construct and study numerical solutions corresponding to generalized electrically charged half-monopole in Weinberg-Salam theory, denoted as Type I and Type II solutions. These solutions possess magnetic charge $q_m = +2 n π/e$ ($-2 n π/e$) and electric charge $q_{e}$ that depends on the electric charge parameter $η$, as well as net zero neutral charge. Other properties of this half-dyon configurations such as magnetic dipole moment and angular moment are studied. The energy of this half-dyon configuration is infinite due to singularity at the location of the half-dyon.

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arXiv2024

Generalized Half-Dyon in SU(2) Yang-Mills-Higgs Theory

We report on generalized half-dyon solutions in SU(2) Yang-Mills-Higgs theory, namely Type I and Type II solutions. These solutions are constructed by considering $ϕ$-winding number $1\leq n \leq 4$, electric charge parameter $0 \leqη<η_{max}$ and Higgs self-coupling constant $0 \leq β\leq 1$. They represent system of magnetic charge $+2nπ/g$ ($-2nπ/g$) and electric charge $Q$ that lies along the negative (positive) $z$-axis. Fundamental properties such as total energy, electric charge, dipole moment are explored and discussed.

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arXiv2023

Electroweak Monopole-antimonopole Pair in the Standard Model

We present the first numerical solution that corresponds to a pair of Cho-Maison monopole and antimonopole (MAP) in the SU(2)$\times$U(1) Weinberg-Salam (WS) theory. The monopoles are finitely separated, while each pole carries magnetic charge $\pm 4π/e$. The positive pole is situated in the upper hemisphere, whereas the negative pole is in the lower hemisphere. The Cho-Maison MAP was investigated for a range of Weinberg angle, $0.4675\leq\tanθ_W\leq10$, and Higgs self-coupling, $0\leqβ\leq1.7704$. Magnetic dipole moment ($μ_m$) and pole separation ($d_z$) of the numerical solutions are calculated and analyzed. Total energy of the system, however, is infinite due to point singularities at the locations of monopoles.

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arXiv2022

Oscillating monopole-antimonopole pair in the Weinberg-Salam model

We investigate further the properties of axially symmetrical monopole-antimonopole pair in the standard Weinberg-Salam theory. These numerical solutions behave quite differently from their counterparts in the SU(2) Yang-Mills-Higgs theory as the poles are now bounded by a flux string. Our results confirm that the energy of these solutions resides in a range of 13.17 - 21.02 TeV. In addition, we found strong evidence suggesting this configuration is time-dependent and discovered an energy oscillation phenomenon between the monopole and anti-monopole, which is associated with the symmetry of the solution. Finally, we calculate numerically the magnetic charge of the solution and confirm that its value is indeed $\frac{4π}{e}\sin^2θ_{\scalebox{.5} {W}}$, as predicted by Y. Nambu in the 1970s. Counterintuitively, the magnetic charge is spread out and distributed along the string instead of concentrated near the poles.

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arXiv2022

System of excited monopole-antimonopole pair in the Weinberg-Salam model

We investigate further the properties of axially symmetric monopole-antimonopole pair in the standard Weinberg-Salam model. By using a novel data sampling approach, we have obtained and analyzed 300 numerical solutions corresponding to physical Higgs self-coupling $β=0.7782$ and the Weinberg angle $\tanθ_W=0.5358$. We calculate the energy of these solutions and confirm that they reside in a range of 13.1690 - 21.0221 TeV. In addition, a unique pattern is shown when the data are arranged according to an algorithm based on the system's symmetry, which seems to indicate the system is oscillating. We also calculate numerically the magnetic charge of the solutions and confirm that their values are indeed $\pm\frac{4π}{e}\sin^2θ_W$.

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arXiv2021

Bounded System of Monopole and Half-monopole in the Weinberg-Salam Model

In this work, we study the one plus half-monopole configuration in Weinberg-Salam model, covering $ϕ$-winding number $n$ = 1. We observed that while the finite separation between the one-monopole and the half-monopole becomes larger as compared to the same configuration in SU(2) Yang-Mills-Higgs theory, a flux tube is established, creating a bound-state of one-monopole and half-monopole in Weinberg-Salam model. There is no electromagnetic current loop circulating the pair of one-monopole and half-monopole, but the system possesses non-vanishing magnetic dipole moment. The non-Abelian gauge potential and the electromagnetic gauge potential are singular along the negative $z$-axis, but the total energy is finite. The solutions are investigated by fixing the Weinberg angle while varying the Higgs self-coupling constant and vice versa. It is shown that this configuration in Weinberg-Salam model possesses different behaviours than its counterpart in SU(2) Yang-Mills-Higgs theory.

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arXiv2021

Bifurcating Branches of Multiple Charged One-Plus-Half Monopole In SU(2) Yang-Mills-Higgs Theory

In this paper, we study on the one-plus-half monopole configuration in SU(2) Yang-Mills-Higgs theory when the $ϕ$-winding number, $n$, runs from 2 to 4 and for a range of Higgs coupling constant, $λ_b \leq λ\leq 40$, where $λ_b$ is the lower bound, below which no solution can be found. Bifurcation and transition are observed for $n > 2$ when the Higgs coupling constant is larger than some critical value $λ_c$ and transitional value $λ_t$, respectively. Two different branches with energy higher than the fundamental solution are observed for both $n = 3$ and $4$. We also observed a new branch with even higher energy for $n = 4$. Unlike other branches which display transition behavior, the new branch corresponds to a full vortex-ring configuration. All the solutions possess finite energy. Plots of magnetic charge density, Higgs modulus and energy density are presented and analyzed.

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arXiv2021

Monopole-Antimonopole Pair With Higher Energy Branch In SU(2) x U(1) Weinberg-Salam Theory

We investigate the monopole-antimonopole pair solution in the SU(2) x U(1) Weinberg-Salam theory with $ϕ$-winding number, $n=3$ for bifurcation phenomena. The magnetic monopole merges with antimonopole to form a vortex ring with finite diameter at $n=3$. Other than the fundamental solution, two new bifurcating solution branches were found when Higgs coupling constant $λ$, reaches a critical value $λ_c$. The two new branches possess higher energies than the fundamental solutions. These bifurcating solutions behave differently from the vortex ring configuration in SU(2) Yang-Mills-Higgs theory since thery are full vortex-ring. We investigate on the total energy $E$, vortex ring diameter $d_ρ$, and magnetic dipole moment $μ_m$, for $0 \leq λ\leq 49$.

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arXiv2021

Gravitating Cho-Maison 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) Einsten-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.

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arXiv2015

MAP, MAC, and Vortex-rings Configurations in the Weinberg-Salam Model

We report on the presence of new axially symmetric monopoles, antimonopoles and vortex-rings solutions of the SU(2)$\times$U(1) Weinberg-Salam model of electromagnetic and weak interactions. When the $ϕ$-winding number $n=1$, and 2, the configurations are monopole-antimonopole pair (MAP) and monopole-antimonopole chain (MAC) with poles of alternating sign magnetic charge arranged along the $z$-axis. Vortex-rings start to appear from the MAP and MAC configurations when the winding number $n=3$. The MAP configurations possess zero net magnetic charge whereas the MAC configurations possess net magnetic charge of $4πn/e$. In the MAP configurations, the monopole-antimonopole pair is bounded by the ${\cal Z}^0$ field flux string and there is an electromagnetic current loop encircling it. The monopole and antimonopole possess magnetic charges $\pm\frac{4πn}{e}\sin^2θ_W$ respectively. In the MAC configurations there is no string connecting the monopole and the adjacent antimonopole and they possess magnetic charges $\pm\frac{4πn}{e}$ respectively. The MAC configurations possess infinite total energy and zero magnetic dipole moment whereas the MAP configurations which are actually sphalerons possess finite total energy and magnetic dipole moment. The configurations were investigated for varying values of Higgs self-coupling constant $0\leq λ\leq 40$ at Weinberg angle $θ_W=\fracπ{4}$.

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arXiv2014

Multiple bifurcations and transitions for electrically charged monopole-antimonopole chain and vortex-ring solutions

The dependence of physical properties of the electrically charged two-poles monopole-antimonopole pair (MAP) solutions in the Higgs self-coupling constant is previously investigated. In this paper we study the three-poles monopole-antimonopole chain (MAC) solutions. The study includes $ϕ$-winding number $n=2,3,4$, and $5$. For the case of $n=2$, there is no bifurcating branch along with the fundamental solution. Also no transition happens for this solution for the Higgs self-coupling interval of $0\leq λ\leq 144$. For the case of $n=3$, two transitions happen along the fundamental solution. Also at a higher energy, there are two bifurcating branches. The lower energy branch of these bifurcating branches, merges with the fundamental solution and both terminate at the convergence point and do not survive for larger values of $λ$. For $n=4$, a bifurcation is observed at higher energy in comparison with the fundamental solution. Here there are three transitions. One is observed along the fundamental solution and the others happen along the higher energy bifurcating branch. For the case of $n=5$, the pattern is more complex. A bifurcation in $λ= λ_{b1}$ happens with a higher energy than the fundamental solution. A second bifurcation is observed at $λ= λ_{b2}$. The two branches of the second bifurcation are both very close in energy to the lower energy branch of the first bifurcation, but they have different electrical and geometrical properties. Therefore, for the case of $n=5$, we have three distinct solution for the interval of $λ_{b1}\leq λ\leq λ_{b2}$ and five distinct solutions for $λ_{b2}\leq λ\leq 300$. Also two transitions are observed in the higher energy branch of the first bifurcation.

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arXiv2014

Half-Monopole in the Weinberg-Salam Model

We present new axially symmetric half-monopole configuration of the SU(2)$\times$U(1) Weinberg-Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge $2π/e$ which is half the magnetic charge of a Cho-Maison monopole. The electromagnetic gauge potential is singular along the negative $z$-axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant $λ^{1/2}$ at $\sin^2θ_W=0.2312$. In the U(1) magnetic field, the half-monopole is just a one dimensional finite length line magnetic charge extending from the origin $r=0$ and lying along the negative $z$-axis. In the SU(2) 't Hooft magnetic field, it is a point magnetic charge located at $r=0$. The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant $λ^{1/2}$ at $\sin^2θ_W=0.2312$.

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arXiv2014

Electrically Charged One and a Half Monopole Solution

Recently, we have discussed the coexistence of a finite energy one-half monopole and a 't Hooft-Polyakov monopole of opposite magnetic charges. In this paper, we would like to introduce electric charge into this new monopoles configuration, thus creating a one and a half dyon. This new dyon possesses finite energy, magnetic dipole moment and angular momentum and is able to precess in the presence of an external magnetic field. Similar to the other dyon solutions, when the Higgs self-coupling constant, $λ$, is nonvanishing, this new dyon solution possesses critical electric charge, total energy, magnetic dipole moment, and dipole separation as the electric charge parameter, $η$, approaches one. The electric charge and total energy increase with $η$ to maximum critical values as $η\rightarrow1$ for all nonvanishing $λ$. However, the magnetic dipole moment decreases with $η$ when $λ\geq0.1$ and the dipole separation decreases with $η$ when $λ\geq1$ to minimum critical values as $η\rightarrow1$.

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arXiv2012

Monopole-Antimonopole Pair Dyons with Critical Electric Charges

In this paper, we investigate some electrically charged magnetic solutions of the SU(2) Yang-Mills-Higgs field theory in the net zero topological charge sector. We only examine the case when the Higgs field vanishes at two points along the z-axis and when the Higgs field vanishes along a ring with the z-axis as its symmetry axis. We study the possible electric charges the dyons can carry in relation to the electric-magnetic charge separations and calculate for the finite total energy and magnet dipole moment of these dyons. These stationary dyon solutions do not satisfy the first order Bogomol'nyi equations and are non BPS solutions. They are axially symmetric saddle point solutions and are characterized by the electric charge parameter, $-1<η< 1$, which determines the net electric charges of these dyons. These dyon solutions are solved numerically when the magnetic charges are $n$ = 1, 2, 3, 4, and 5; and when the strength of the Higgs field potential is non vanishing with $λ=1$. When $λ=1$, we found that the net electric charge approaches a finite critical value as $η$ approaches $\pm 1$. Hence the electromagnetic charge separation, total energy, and magnet dipole moment of the dyon also approach finite critical value.

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arXiv2012

Rotating One-Half Topological Charge Dyon

Recently, we have shown the existence of a finite energy one-half monopole. In this paper, we would like to introduce electric charge into the one-half monopole configuration, thus creating a one-half dyon. This one-half dyon possesses finite energy, magnetic dipole moment and angular momentum. Hence it is able to rotate in the presence of an external magnetic field. Similar to the single pole dyons and the MAP dyons, this one-half dyon possesses critical (maximum) electric charge, total energy, and magnetic dipole moment when the Higgs self-coupling constant is nonvanishing, and the electric charge parameter approaches one. This one-half dyon solution does not satisfy the first order Bogomol'nyi equations and is a non-BPS solution in the limit of vanishing Higgs self-coupling constant.

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arXiv2012

Jacobi Elliptic Monopole-Antimonopole Pair Solutions

We present new classical generalized Jacobi elliptic one monopole - antimonopole pair (MAP) solutions of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. These generalized 1-MAP solutions are solved with $θ$-winding number $m$=1 and $ϕ$-winding number $n$=1, 2, 3, ... 6. Similar to the generalized Jacobi elliptic one monopole solutions, these generalized 1-MAP solutions are solved by generalizing the large distance behaviour of the solutions to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing ($λ$=0) and non vanishing ($λ$=1). These generalized 1-MAP solutions possess total energies that are comparable to the total energy of the standard 1-MAP solution with winding number $m$=1. However these total energies are significantly lower than the total energy of the standard 1-MAP solution with winding number $m$=2. All these new generalized solutions are regular numerical finite energy non-BPS solutions of the Yang-Mills-Higgs field theory.

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