Bounds of the mass of Z' and the neutral mixing angles in general SU(2)_L x SU(2)_R x U(1) models

We consider phenomenological constraints on the mass $M_{Z^{\prime}}$ and the two mixing angles $\theta_R$ and $\xi$ of the neutral sector in a very general class of $SU(2)_L \times SU(2)_R \times U(1)$ models using electroweak data. We do not make any specific assumptions such as left-right symmetry or the Higgs structure. The analysis of the neutral sector has the advantage that it has relatively fewer parameters compared to the charged sector since the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements in the right-handed sector do not enter into the analysis, hence the number of various possibilities from a big parameter space is reduced. We utilize theoretical considerations on the masses of the gauge particles and the mixing angles. We combine the precision electroweak data from LEP I and the low-energy neutral-current experimental data to constrain the parameters introduced in the model. It turns out that $M_{Z^{\prime}}> 400$ GeV, $-0.0028 <\xi <0.0065$ with little constraint on $\theta_R$. In the left-right symmetric theory, $M_{Z^{\prime}}$ should be larger than 900 GeV. With these constraints, we compare the values for $\sigma (e^+ e^- \to \mu^+ \mu^-)$, $\sigma (e^+ e^- \to b\bar{b})$ and $A_{FB}^{\ell}$ at LEP II with experimental values.