Bounding the Number of Light Neutrinos Species in a Left-Right Symmetric Model

Using the experimental values for the rates $R^{LEP} _{exp}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.016$, $R^{Giga-Z_1}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.012$ (most conservative) and $R^{Giga-Z_1}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.006$ (most optimistic) we derive constraints on the number of neutrinos light species $(N_\nu)_{LRSM}$ with the invisible width method in the framework of a left-right symmetric model (LRSM) as a function of the LR mixing angle $\phi$. Using the LEP result for $N_\nu$ we may place a bound on this angle, $-1.6\times 10^{-3}\leq\phi \leq 1.1\times 10^{-3}$, which is stronger than those obtained in previous studies of the LRSM.