Hadronic Vacuum Polarization Contribution to ${\mathbf{g}}_{\mathbf{\mu }}-2$ 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.

Comments: 15 pages, 7 figures, some corrections added