Reconsidered estimates of the 10th order QED contributions to the muon anomaly

The problem of estimating the 10th order QED corrections to the muon anomalous magnetic moment is reconsidered. The incorporation of the recently improved contributions to the $\alpha^4$ and $\alpha^5$- corrections to $a_{\mu}$ within the renormalization-group inspired scheme-invariant approach leads to the estimate $a_{\mu}^{(10)}\approx 643(\alpha/pi)^5$. It is in good agreement with the estimate $a_{\mu}^{(10)}= 663(20) (\alpha/\pi)^5$, obtained by Kinoshita and Nio from the numerical calculations of 2958 10-th order diagrams, which are considered to be more important than the still uncalculated 6122 10th-order $m_{\mu}/m_e$-dependent vertex graphs, and 12672 5-loop diagrams, responsible for the mass-independent constant contribution both to $a_{\mu}$ and $a_e$. This confirms Kinoshita and Nio guess about dominance of the 10-th order diagrams calculated by them. Comparisons with other estimates of the $\alpha^5$- contributions to $a_{\mu}$, which exist in the literature, are presented.