Higher-Order Hadronic Contributions to the Anomalous Magnetic Moment of Leptons

Higher-order hadronic contributions to the anomalous magnetic moment of the electron, muon, and $\tau$ lepton are considered in detail. As a main result we find a reduction by $-18 \times 10^{-11}$ for the g-2 of the muon as compared to previous calculations. Analytical expressions for the kernel functions of higher-order hadronic effects are presented. We employ the method of asymptotic expansions to calculate kernel functions analytically in terms of a series expansion in the lepton mass.