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.     

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.