= Chiral Z-boson partial width
{title2=$\Gamma_f\propto N_c(g_L^2+g_R^2)$}
At leading order, for final <fermions> much lighter than the <Z boson>, the partial <decay width> is proportional to $N_c(|g_L|^2+|g_R|^2)$. Here $N_c$ is the final-state <color multiplicity in a decay width>, and $g_L=T_{3L}-Q\sin^2\theta_W$, $g_R=T_{3R}-Q\sin^2\theta_W$ are the dimensionless left- and right-<chirality> couplings. The common normalization cancels in ratios.
For an <Electron>, $g_L=-1/2+\sin^2\theta_W$, $g_R=\sin^2\theta_W$. For one active <neutrino> flavour, $g_L=1/2$, $g_R=0$. Therefore
$$
\frac{\Gamma(Z\to\nu\bar\nu)}{\Gamma(Z\to e^-e^+)}=\frac{1/4}{(-1/2+\sin^2\theta_W)^2+\sin^4\theta_W}.
$$
There is no extra flavour factor for a single specified <neutrino> species. Summing the three active species produces three times that invisible partial width, within the same massless approximation.
Back to article page
