Contribution of the $\mathbf{\pi^0\gamma}$ and $\mathbf{\eta\gamma}$ intermediate states to the vacuum polarization and the muon anomalous magnetic moment

Using new experimental data, we calculate the contribution to the anomalous magnetic moment of the muon from the $\pi^0\gamma$ and $\eta\gamma$ intermediate states in the vacuum polarization with high precision taking into account the correction for using the trapezoidal rule: $a_{\mu}(\pi^0\gamma)+a_{\mu}(\eta\gamma)=(53.1\pm 1.5)\cdot 10^{-11}$. We also find the small contribution from $e^+e^-\pi^0,\ e^+e^-\eta$ and $\mu^+\mu^-\pi^0$ intermediate states equal to $0.5\cdot 10^{-11}$.