  Analysis of cosmic microwave background radiation fluctuations favors an
effective number of neutrinos, $N_\nu>3$. This motivates a reinvestigation of
the neutrino freeze-out process. Here we characterize the dependence of $N_\nu$
on the Standard Model (SM) parameters that govern neutrino freeze-out. We show
that $N_\nu$ depends on a combination $\eta$ of several natural constants
characterizing the relative strength of weak interaction processes in the early
Universe and on the Weinberg angle $\sin^2\theta_W$. We determine numerically
the dependence $N_\nu(\eta,\sin^2\theta_W)$ and discuss these results. The
extensive numerical computations are made possible by two novel numerical
procedures: a spectral method Boltzmann equation solver adapted to allow
emerging chemical non-equilibrium, and a method to evaluate Boltzmann equation
collision integrals that generates a smooth integrand.
