The one and a half monopoles solution of the SU(2) Yang–Mills–Higgs field theory

Recently we have reported on the existence of finite energy SU(2) Yang–Mills–Higgs particle of one-half topological charge. In this paper, we show that this one-half monopole can co-exist with a ’t Hooft–Polyakov monopole. The magnetic charge of the one-half monopole is of opposite sign to the magnetic charge of the ’t Hooft–Polyakov monopole. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive z$z$-axis that carries the other half of the magnetic monopole charge. The solution possesses gauge potentials that are singular along the z$z$-axis, elsewhere they are regular. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ$\lambda$. However the dipole separation and the magnetic dipole moment decrease with λ$\lambda$. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.     

Ann monopole solution with 4n — 1 degrees of freedom

An exact static monopole solution, possessingn units of magnetic charge and (4n-1) degrees of freedom, is constructed, generalising the recent work of Ward on two monopole solutions. The equations solved are those of anSU(2) gauge theory with adjoint representation Higgs field in the (BPS) limit of vanishing Higgs potential. The number of degrees of freedom is maximal for self-dual solutions. The construction is described in a deductive way, within the framework of the Atiyah-Ward formalism for self-dual gauge fields.     

Kertész line in the three-dimensional compact U(1) lattice Higgs model

The three-dimensional lattice Higgs model with compact U(1) gauge symmetry and unit charge is investigated by means of Monte Carlo simulations. The full model with fluctuating Higgs amplitude is simulated, and both energy as well as topological observables are measured. The data show a Higgs and a confined phase separated by a well-defined phase boundary, which is argued to be caused by proliferating vortices. For fixed gauge coupling, the phase boundary consists of a line of first-order phase transitions at small Higgs self-coupling, ending at a critical point. The phase boundary then continues as a Kertész line across which thermodynamic quantities are non-singular. Symmetry arguments are given to support these findings.     

On the Higgs mass generation mechanism in the Standard Model

The mass-generation mechanism is the most urgent problem of modern particle physics. The discovery and study of the Higgs boson with the Large Hadron Collider at CERN are the highest priority steps to solve the problem. In this paper, the Standard Model Higgs mechanism of elementary particle mass generation is reviewed with pedagogical details. The discussion of the Higgs quadric self-coupling λ parameter and the bounds to the Higgs boson mass are presented. In particular, the unitarity, triviality, and stability constraints on the Higgs boson mass are discussed. The generation of a finite value for the λ parameter due to quantum corrections via effective potential is illustrated. Some simple predictions for the top quark and the Higgs boson masses are given when both the top Yukawa coupling and the Higgs self-coupling λ are equal to 1. The text was submitted by the authors in English.     

Magnetic Bag Like Solutions to the SU(2) Monopole Equations on {{\mathbb R}^{3}}

Solutions to the SU(2) monopole equations in the Bogolmony limit are constructed that look very much like Bolognesis conjectured magnetic bag solutions. Three theorems are also stated and proved that give bounds in terms of the topological charge for the radii of balls where the solutions Higgs field has very small norm.     

Efficient coannihilation process through strong Higgs self-coupling in LKP dark matter annihilation

We point out that the lightest Kaluza–Klein particle (LKP) dark matter in universal extra dimension (UED) models efficiently annihilates through the coannihilation process including the first KK Higgs bosons when the Higgs mass is slightly heavy as 200–230 GeV, which gives the large Higgs self-coupling. The large self-coupling naturally leads the mass degeneracy between the LKP and the first KK Higgs bosons and large annihilation cross sections of the KK Higgs bosons. These are essential for the enhancement of the annihilation of the LKP dark matter, which allows large compactification scale ∼1 TeV to be consistent with cosmological observations for the relic abundance of dark matter. We found that the thermal relic abundance of the LKP dark matter could be reconciled with the stringent constraint of electroweak precision measurements in the minimal UED model.     

Stationary Dyonic regular and black hole solutions

We consider globally regular and black hole solutions in SU(2) Einstein–Yang–Mills–Higgs theory, coupled to a dilaton field. The basic solutions represent magnetic monopoles, monopole–antimonopole systems or black holes with monopole or dipole hair. When the globally regular solutions carry additionally electric charge, an angular momentum density results, except in the simplest spherically symmetric case. We evaluate the global charges of the solutions and their effective action, and analyze their dependence on the gravitational coupling strength. We show, that in the presence of a dilaton field, the black hole solutions satisfy a generalized Smarr type mass formula. B. Kleihaus gratefully acknowledges support by the German Aerospace Center. F. Navarro-Lérida gratefully acknowledges support by the Ministerio de Educación y Ciencia under grant EX2005-0078.     

Measuring the Higgs boson self-coupling at the Large Hadron Collider

Inclusive standard model Higgs boson pair production and subsequent decay to same-sign dileptons via weak gauge W+/- bosons at the CERN Large Hadron Collider (LHC) has the capability to determine the Higgs boson self-coupling, lambda. The large top quark mass limit is found not to be a good approximation for the signal if one wishes to utilize differential distributions in the analysis. We find that it should be possible at the LHC with design luminosity to establish that the standard model Higgs boson has a nonzero self-coupling and that lambda/lambda(SM) can be restricted to a range of 0-3.7 at 95% confidence level if its mass is between 150 and 200 GeV.     

Correlations and static energies in the standard Higgs model

Correlations in the W-boson and Higgs boson channels and the static energy of an external SU(2) doublet charge pair are investigated by Monte Carlo calculations in the SU(2) lattice gauge theory with a scalar Higgs doublet field. The mass ratio m_W/m_H and the shape of the static potential are used to obtain information on the renormalization group trajectories in the three-dimensional coupling constant space. As a function of an appropriately chosen varibale, the measured quantities are, within errors, independent from the scalar self-coupling (λ) in a wide range 0.1 ⩽ λ ⩽ ∝. In the Higgs phase, a lower bound m_W/m_H ⩾ (1.0 ± 0.3) is obtained for the ratio of the Higgs boson mass to the W-boson mass.     

Higgs self-coupling in the fusion channel at the international linear collider

We investigate the Higgs pair production process at the international linear collider (ILC), focusing on the measurement of the trilinear self-coupling of the Higgs boson in the fusion channel. The sensitivity of this measurement is discussed in the Higgs mass range 140–200 GeV at a center-of-mass energy between 1 TeV and 1.5 TeV.      

Interacting monopoles

The Bogomolny equation for interacting monopoles of like charge in the case of vanishing Higgs mass is fulfilled by an asymptotic expansion in powers of the inverse monopole distance. Consequently, the monopoles exert no long range forces on each other. However, the expansion is not summable. The degrees of freedom of the multi-monopole system are discussed.     

Resonant excitations of the 't Hooft-Polyakov monopole

The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled to a massless Higgs field is shown to possess an infinite number of resonances or quasinormal modes. These modes are eigenfunctions of the isospin 1 perturbation equations with complex eigenvalues, E(n)=omega(n)-igamma(n), satisfying the outgoing radiation condition. For n--> infinity, their frequencies omega(n) approach the mass of the vector boson, M(W), while their lifetimes 1/gamma(n) tend to infinity. The response of the monopole to an arbitrary initial perturbation is largely determined by these resonant modes, whose collective effect leads to the formation of a long living breatherlike excitation with an amplitude decaying at late times as t(-5/6).     

Higgs self-coupling beta-function in the Standard Model at three loops

We present the results for three-loop beta-function for the Higgs self-coupling calculated within the unbroken phase of the Standard Model. We also provide the results for three-loop beta-function for Higgs mass parameter, which was easily extracted from our calculation. Our results coincide with that of recent paper of K. Chetyrkin and M. Zoller (2013) [1]. In addition, the expression for the Higgs field anomalous dimension is given.     

Exact monopole solutions in gauge theories for an arbitrary semisimple compact group

We construct an exact n-parametric monopole and dyon solutions for an arbitrary compact gauge group G of rank n by using the symmetry between cylindrically symmetric instanton equations in Euclidean space R ₄ and monopole equations in Minkowski space R _3,1 (with Higgs scalar field in adjoint representation). The solutions are spherically symmetric with respect to the total momentum operator represents the minimal embedding of SU(2) in G. Explicit expressions for the monopole magnetic charge and mass matrices are obtained. The remarkable aspect of our results is the existence of discrete series of the monopole solutions, which are labelled by n quantum numbers and degenerated in the latter ones at a fixed monopole mass matrix.     

A U(1) gauge-Higgs system with a radial degree of freedom

The phase diagram of a lattice U(1) gauge-Higgs model is derived without freezing the Higgs field length. For sufficienly small Higgs self-coupling strength, the “confinement” and “Higgs” phases are separated, in contrast to what is observed in the fixed length model.     

Monte Carlo study of the 3-dimensional abelian Higgs model with radially variable Higgs field

The three-dimensional U(1)-Higgs model with a radially variable Higgs field is studied using a Monte Carlo method. The Higgs fields and the U(1) gauge field variables are considered in the same (fundamental) representation. For various small values of the scalar field self-coupling parameter λ, phase transitions (likely first order) between two completely distinct phases of the theory, are observed.     

Hyperbolic Multi-Monopoles with Arbitrary Mass

On a complete manifold, such as or hyperbolic space , the limit at infinity of the norm of the Higgs field is called the mass of the monopole. We show the existence, on , of monopoles with given magnetic charge and arbitrary mass. Previously, aside from charge one monopoles, existence was known only for monopoles with integral mass (since these arise from U(1) invariant instantons on ). The method of proof is based on Taubes’ gluing procedure, using well-separated, explicit, charge one monopoles. The analysis is carried out in a weighted Sobolev space and necessitates eliminating the possibility of point spectra.     

Self-dual monopoles and toda molecules

Stable static solutions to a gauge field theory with a Higgs field in the adjoint representation and with vanishing self-coupling are self-dual in the sense of Bogomolny. Leznov and Saveliev showed that a specific form of spherical symmetry reduces these equations to a modified form of the Toda molecule equations associated with the overall gauge symmetry G. Values of the constants of integration are found in terms of the distant Higgs field, guaranteeing regularity of the solution at the origin. The expressions hold for any simple Lie group G, depending on G via its root system.     

The Higgs sector of the minimal supersymmetric standard model including radiative corrections

We discuss the Higgs sector of the minimal supersymmetric standard model including effects of radiative corrections. The formalism is explained in detail for computing radiative corrections to the masses and the coupling constants of the Higgs bosons. The radiative corrections to the masses are studied in the on-shell renormalization scheme. The radiative corrections to the mixing angles between the two CP-even Higgs bosons and the Higgs self-coupling constants are investigated in a simple procedure. The explicit analytic expressions are given for the radiative corrections due to the loops containing the top and bottom quarks and their superpartners. Simple approximate formulae are derived from the analytic expressions obtained in the on-shell renormalization scheme. We numerically study the effects of radiative corrections on the mass of the lighter Higgs boson and the mixing angles between the two CP-even Higgs bosons.     

Classical solutions of Yang-Mills and CP n−1 models with scalar fields

We present a study of classical solutions of the SU(2) Yang-Mills (YM) theory with a massless Higgs doublet, and of the CP ^n?1 model coupled to a scalar field. In both cases the scalar field tends to suppress instantons but not merons (this is a purely classical effect). In the YM theory a static Wu-Yang-like monopole solution with variable magnetic charge is found and its connection with the meron solution of this theory is discussed.