Mean field theory and the SU(2) adjoint Higgs model

Three versions of the mean field approximation are applied to determine the phase diagram of the SU(2) adjoint Higgs model. In two of these, one with gauge fixing and one without, the Higgs action is integrated exactly. In the third version, the Higgs and Wilson parts of the action are treated on equal footing. The results, when compared to those from Monte Carlo simulations, suggest that more accurate simulations are needed in the crossover region.     

The renormalization flow in the adjoint SU(2) lattice Higgs model

Applying the Monte Carlo renormalization group method we investigate the flow of coupling constants for the 8⁴ and 16⁴ SU(2) lattice Higgs model with triplet Higgs fields. The couplings of the renormalized actions are determined using Schwinger-Dyson equations. From the flow we find new evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β but no indication for a discontinuity fixed point.     

On Nambu monopole dynamics in a SU(2) lattice Higgs model

It is shown that an SU(2) Higgs model on a lattice is equivalent to the Georgi-Glashow model in the limit of a small coupling constant between the Higgs and gauge fields. It can therefore be concluded that the transition between the confinement and symmetric phases in a 3 + 1 dimensional SU(2) Higgs model at finite temperature is accompanied by condensation of Nambu monopoles. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 577–580 (10 November 1997)     

Coupled gap equations for the screening masses in the SU(2) Higgs model

The complete set of static screening masses is determined for the SU(2) Higgs model from one-loop coupled gap equations. Results from the version containing scalar fields both in the fundamental and adjoint representations are compared with the model arising when integration over the adjoint scalar field is performed. A non-perturbative and non-linear mapping between the couplings of the two models is proposed which exhibits perfect decoupling of the heavy adjoint scalar field. Also the alternative of a gauge invariant mass resummation is investigated in the high temperature phase. Received: 7 May 1999 / Revised version: 6 July 1999 / Published online: 16 November 1999     

SU (5) + adjoint Higgs model at finite temperature

A three-dimensional effective theory of the finite-temperature SU(5) + adjoint Higgs model is constructed using the method of dimensional reduction. The resulting theory can be used for computer simulations of the GUT phase transition of the early universe. In this paper the transition is analyzed at two-loop level in perturbation theory. The structure of the effective theory does not essentially depend on the matter contents of the original four-dimensional one. Therefore the analysis of this paper applies also to more realistic theories.     

Monte Carlo analysis of gauge invariant two-point functions in an SU(2) Higgs model

New order parameters involving ratios of gauge invariant correlation functions for distinguishing different phases - confined/screened or free charges - in systems with lattice gauge fields coupled to matter fields have been proposed by Fredenhagen and Marcu and by Bricmont and Fröhlich. Our Monte Carlo analysis of those quantities for an SU(2) gauge field coupled to scalar matter fields in the fundamental representation supports the theoretically expected behaviour. Also a new mass parameter determining the exponential decay of two-point functions is observed.     

Strong coupling expansion for the mass gap in SU(2) lattice gauge theory with mixed action

We perform a strong coupling expansion up to O(β⁷) for the mass-gap in SU(2) lattice gauge theory with mixed action. A novel feature of the strong coupling expansion is discussed. The strong coupling series appears to approach the scaling region more smoothly and Padé approximants become more stable than in the case with simple Wilson action. The region of validity of a recently proposed resummation of perturbation theory as applied to the determination of the asymptotic scaling behavior is investigated. Results of a strong coupling calculation for the heat kernel action, which is related to the mixed action for a special choice of parameters, are also reported.     

Phase structure of the SU(2) lattice gauge Higgs theory

Phase structure of the SU(2) lattice gauge Higgs theory is investigated by the Monte Carlo method and by an approximate calculation of an effective potential. Higgs fields are considered in the fundamental representation, and the radial mode of Higgs fields is not frozen. Two different radial measures for a radially varied Higgs field are used.Phase diagrams of the theory are determined, and a strong dependence on the choice of radial measure of scalar fields is manifested.     

Running of neutrino parameters and the Higgs self-coupling in a six-dimensional UED model

We investigate a six-dimensional universal extra-dimensional model in the extension of an effective neutrino mass operator. We derive the β  -functions and renormalization group equations for the Yukawa couplings, the Higgs self-coupling, and the effective neutrino mass operator in this model. Especially, we focus on the renormalization group running of physical parameters such as the Higgs self-coupling and the leptonic mixing angles. The recent measurements of the Higgs boson mass by the ATLAS and CMS Collaborations at the LHC as well as the current three-flavor global fits of neutrino oscillation data have been taken into account. We set a bound on the six-dimensional model, using the vacuum stability criterion, that allows five Kaluza–Klein modes only, which leads to a strong limit on the cutoff scale. Furthermore, we find that the leptonic mixing angle _θ12${\theta }_{12}$ shows the most sizeable running, and that the running of the angles _θ13${\theta }_{13}$ and _θ23${\theta }_{23}$ are negligible. Finally, it turns out that the findings in this six-dimensional model are comparable with what is achieved in the corresponding five-dimensional model, but the cutoff scale is significantly smaller, which means that it could be detectable in a closer future.     

Asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction

An asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction is constructed. The gauge coupling constants are taken equal (in the order of magnitude) to the electromagnetic one. The strong interaction and the quark confinement is provided for by a gluonic mechanism. Some physical consequence of the model are briefly discussed.