Lightest scalar in the SU(L)2 x SU(R)2 linear sigma model

We consider the lightest scalar meson in the frame of the SU(L)2 x SU(R)2 linear sigma model, keeping in mind that this model could be the low energy realization of two-flavor QCD. We show that the sigma field is described by its four-quark component at least in the sigma resonance energy (virtuality) region and the sigma-->gammagamma decay is the four-quark transition. We emphasize that residues of the sigma pole in the pipi-->pipi and gammagamma-->pipi amplitudes do not give an idea about the sigma meson nature, and the progress in studying the sigma meson production mechanisms in different processes could essentially further us in understanding its nature.     

SU(2)L×SU(2)R×U(1) gauge model

We determine here the most general electroweak interaction based on the groupSU(2)_L×SU(2)_R×U(1). When we rotate theZ ₁,Z ₂ basis to theZ,D basis such that the total interaction ofZ with the right-handed current is zero, we obtain an interaction that is free of triangle anomalies. This condition enables us to know the angle through whichZ ₁,Z ₂ basis is to be rotated. We show that the triangle anomaly free interaction obtained by others is contained here as a special case. We also determine the triangle anomaly free weak interaction whenever the neutral (Z,D) bosons are mass eigenstates and show that it reduces to the neutral sector of the standard model whenever g _R ² goes to infinity. The charged sector is also developed here. The most general elements of the masssquared matrix of theZ,D bosons are evaluated. The masses of the left- and right-handed charged bosons are also determined.     

SU(2) lattice gauge-Higgs model

Phase diagrams are investigated in theSU(2) gauge-Higgs theory with a defrost radial mode. The Higgs fields are considered in the fundamental representation. Phase diagrams are determined for different values of the scalar self-action constants. It is shown that the lines of first order phase transitions have the end points which are critical points, analogous to a phase diagram of the type “gas-liquid-ice”.     

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.     

Mean field phase diagram of the discrete Frenkel-Kontorova model

The mean field phase diagram of the discrete Frenkel-Kontorova model (harmonic chain of particles exposed to a sinusoidal potential) is studied using a fixed irrational value for the ratio of atoms and available sites as a boundary condition. Independent variables are the temperature and the height of the sinusoidal potential. The phase diagram contains two different solid phases, namely an intrinsically pinned incommensurate and an unpinned incommensurate phase. The position of the phase boundary and the nature of the phases are determined. We also investigate the influence of an electric field and the resulting pinning-unpinning transition for fields smaller than the threshold field.     

Study of the phase structure of an SU(3) Higgs model at finite temperature

We analyse numerically an SU(3) Higgs model with complete symmetry breaking and radial degree of freedom on asymmetric, periodic lattices. The character of both the Higgs and deconfining transitions is found to depend on the Higgs self-coupling and on a parameter which may simulate the number of flavours. In particular, an increase in the latter leads to the disappearance of the deconfining transition for small Higgs masses.     

Proton decay in theSU(4) c ×SU(2) L ×SU(2) R model

Possible proton decays in theSU(4) _C ×SU(2) _L ×SU(2) _R unification model are discussed. There are some characteristics in the decay products, which are different from those in the standardSU(5) orSO (10) model, in certain cases.     

The phase structure of the SU(3) lattice gauge-Higgs model

The phase structure of SU(3) symmetric gauge-Higgs theory with a fluctuating radial mode is investigated. The Higgs fields are considered in the fundamental representation of SU(3). It is shown that the phase structures of SU(3) and SU(2) symmetric models coincide qualitatively.