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

Abstract

The hadronic vacuum polarization contribution to the anomalous magnetic moment of a lepton is considered as a function of the lepton mass. We show how the analyticity properties of this function allow for its full reconstruction when it is only known in a restricted mass region. Assuming that LQCD could evaluate it in an optimal mass region we show, within the framework of a phenomenological model, how to reconstruct the function elsewhere, in particular at the muon mass value.