The $\pi^0\to e^+e^-$ and $\eta\to \mu^+ \mu^-$ Decays Revisited

The rare $\pi^0 \to e^+e^-$ and $\eta \to \mu^+\mu^-$ decays are calculated in different schemes, which are seen to be essentially equivalent to and produce the same results as conventional Vector-Meson Dominance. We obtain the theoretical predictions $B(\pi^0 \to e^+e^-) = (6.41 \pm 0.19)\times 10^{-8}$ and $B(\eta \to \mu^+\mu^-) = (1.14 +0.06 -0.03) \times 10^{-5}$ in agreement with recent experimental data.