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It is shown that with a precise determination of a few derivatives of the hadronic vacuum polarization (HVP) self-energy function $\Pi(Q^2)$ at $Q^2=0$, from lattice QCD (LQCD) or from a dedicated low-energy experiment, one can obtain an evaluation of the lowest order HVP contribution to the anomalous magnetic moment of the muon $a_{\mu}^{\rm HVP}$ with an accuracy comparable to the one reached using the $e^+ e^-$ annihilation cross-section into hadrons.
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