Vacuum polarization contribution to muon g-2 as an inverse problem

We analyze the electromagnetic current correlator at an arbitrary photon invariant mass q(2) by exploiting its associated dispersion relation. The dispersion relation is turned into an inverse problem, by which the involved vacuum polarization function Pi(q(2)) at low q(2) is solved with the perturbative input of Pi(q(2)) at large q(2). It is found that the result for Pi(q(2)), including its first derivative Pi'(q(2) = 0), agrees with those from lattice QCD, and its imaginary part accommodates the e(+)e(-)-annihilation data. The corresponding hadronic vacuum polarization (HVP) contribution a(mu)(HVP) = (641(-63)(+65)) x 10(-10) to the muon anomalous magnetic moment g - 2, where the uncertainty arises from the variation of the perturbative input, also agrees with those obtained in other phenomenological and theoretical approaches. We point out that our formalism is equivalent to imposing the analyticity constraint to the phenomenological approach solely relying on experimental data and can improve the precision of the a(mu)(HVP) determination in the Standard Model.