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The explanation for lepton $g-2$ anomalies is provided with the nonlocal QEDwhich is the simple extension of the standard model. This solution is based onthe same gauge symmetry as QED without introducing any new particles andinteractions. The correlation functions in the nonlocal strength tension andlepton-photon interaction make it possible to explain the discrepancies of both$\Delta a_\mu$ and $\Delta a_e$. With the same approach, the discrepancy ofanomalous magnetic moment of $\tau$ lepton from standard model is estimated inthe range $1.19\times10^{-5}$ to $3.21\times10^{-3}$ which is covered by thecurrent experimental uncertainty.

Solution of lepton $g-2$ anomalies with nonlocal QED