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, via 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. The corresponding hadronic vacuum polarization contribution a_mu^{HVP}= (687^{+64}_{-56})\times 10^{-10} to the muon anomalous magnetic moment g-2 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.
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