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The hadronic vacuum polarization contribution to the anomalous magneticmoment of a lepton is considered as a function of the lepton mass. We show howthe analyticity properties of this function allow for its full reconstructionwhen it is only known in a restricted mass region. Assuming that LQCD couldevaluate it in an optimal mass region we show, within the framework of aphenomenological model, how to reconstruct the function elsewhere, inparticular at the muon mass value.

Hadronic Vacuum Polarization Contribution to $\boldsymbol{g_{\mu}-2}$ as a function of the external lepton mass