Number of Neutrinos in the Standard Model and its Extensions to Supersymmetry

The measured ratio of production cross sections of $W$ to $Z$, $R=\frac{{\sigma }^{W^{+}+W^{-}}B(W\to e\nu )}{{\sigma }^{Z}B(Z\to e^{+}{e}^{-})}$, is barely consistent with the standard model with three families, and puts stringent limits on the number of neutrinos $N_{\nu }$. The effect of supersymmetric extension of the standard model is to strengthen these limits further. Improvement in the measured value of $R$ could not only limit $N_{\nu }$, but also remove from contention some extensions of the standard model.