Z2 × Z2 Discrete Symmetry in the Left-Right Symmetric Model SU(2)L × SU(2)R × U(l)B-L

From the point that the Higgs fields can be regarded as the gauge fields on a discrete group, we construct a gauge theory of the leftright symmetric model SU(2)_L × SU(2)_R × U(1)_B-L (LRSM) over Z₂ ⊙ Z₂ discrete symmetry.     

Transition from SU(2)L × SU(2)R × U(1)B-L representation to SU(2)L × U(1)Y by q-deformation and the corresponding classical breaking term of chiral U(2)

The minimal Standard Model exhibits a nontrivial chiral U(2) symmetry if the VEV and the hypercharge splitting Δ = (y-y)/2 of right-handed leptons (quarks) in a family vanish and Q = T₀ + Y independently in each helicity sector. As a generalization, we start with SU(2)_L × SU(2)_R × U(1)_(B-L) and introduce Δ as a continuous parameter which is a measure of explicit symmetry breakdown. Values 0 ? Δ ? 1/2 take the neutral generator of the isospin ½ representation to the singlet representation, i.e. ‘deformes’ the LR representation into the minimal Standard one. The corresponding classical O(3)-breaking term is a magnetic field perpendicular to the x₃-axis. A simple mapping on the fundamental Drinfeld-Jimbo q-deformed SU(2) representation is given.     

Fermion masses generated by radiative corrections in aSU(2) L ×SU(2) R ×U(1) B-L model

A new model based on aSU(2) ^R ×SU(2) ^L ×U(1) ^B-L gauge symmetry group is presented. Fermion masses are generated by radiative corrections.     

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.     

Scale Invariance and Minimum Extension of the SU(2)×U(1) Model

In this note, we discuss a minimum extension of the SU(2)×U(1) model to include both gauge invariance and scale invariance by introducing a complex phase transformation and related complex gauge field, in which the imaginary part corresponds to the Weyl's vector field.     

SU(3)L × U(l)X Model and N-Particle as Dark Matter Particle

We proposed an SU(3)_L × U(l)_X gauge model for the electroweak interactions. In the model each lepton family contains two neutral particles. We show that the new neutral lepton (N-particle) can play the role of dark matter particle.     

Axion depending on the Higgs sector inSU(2)L×SU(2)R×U(1)

Using Higgses with quantum numbers of fermion bilinears we discuss the axion in four different Higgs sectors inSU(2)_L×SU(2)_R×U(1). Three of the cases are similar to the “standard axion” in the Salam-Weinberg model and in one case the axion can be made invisible.     

VACUUM OF 2+1 DIMENSIONAL SU(2) LGT WITH FERMIONS AND SPONTANEOUS CHIRAL SYMMETRY BREAKING

By incorporating the exact ground state of pure gauge theory and the variational fermion vacuum state,the vacuum structure of 2+1 dimensional SU(2) LGT with fermions is studied.We calculate the fermion condensate <ψψ>,and obtain a good scaling behavior.

     

Flavour non-conservation induced by Higgs particle exchange inSU(2)L×SU(2)R×U(1) model

The VEV of the Higgs field inSU(2)_L×SU(2)_R×U(1) model is discussed in the context of the flavour changing neutral currents. The lower bound of Higgs particle mass is found (m _H ?3 TeV).     

SUPERSYMMETRIC SU(1|2) GAUDIN MODEL

In this paper, we propose a supersymmetric SU(1|2) Gaudin model and have derived its eigenvalues. We also present the well-defined eigenstates through the quasi-classical limit of the eigenstates in the supersymmetric t-J model.     

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.     

Supersymmetric SU C (4) × SU L (2) × SU R (2) and spontaneous breakdown of symmetries

A supersymmetric version of the left right symmetric partial unification group SU _C (4) × SU _L (2) × SU _R (2) is presented. The spontaneous breakdown of gauge symmetry in a favourable chain of descent has been studied in detail. The mass spectra have been calculated. The method of O’Raifeartaigh has been used to break supersymmetry. The lifting of degeneracy of mass levels between physical multiplets has been shown to occur due to radiative corrections.     

SU(2)×U(1) gauge gravity

We propose a Lorentz-covariant Yang-Mills “spin-gauge” theory, where the function-valued Pauli matrices play the role of a nonscalar Higgs field. As symmetry group we choose SU(2) × U(1) of the 2-spinors describing particle/antiparticle states. After symmetry breaking, a nonscalar Lorentz-covariant Higgsfield gravity appears, which can be interpreted within a classical limit as Einstein's metrical theory of gravity, where we restrict ourselves in a first step to its linearized version.