Anomalous magnetic moment of the muon, a hybrid approach

A new QCD sum rule determination of the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, \(a_{\mu}^{\rm hvp}\), is proposed. This approach combines data on \(e^{+}e^{-}\) annihilation into hadrons, perturbative QCD and lattice QCD results for the first derivative of the electromagnetic current correlator at zero momentum transfer, \(\Pi_{\rm EM}^\prime(0)\). The idea is based on the observation that, in the relevant kinematic domain, the integration kernel \(K(s)\), entering the formula relating \(a_{\mu}^{\rm hvp}\) to \(e^{+}e^{-}\) annihilation data, behaves like \(1/s\) times a very smooth function of \(s\), the squared energy. We find an expression for \(a_{\mu}\) in terms of \(\Pi_{\rm EM}^\prime(0)\), which can be calculated in lattice QCD. Using recent lattice results we find a good approximation for \(a_{\mu}^{\rm hvp}\), but the precision is not yet sufficient to resolve the discrepancy between the \(R(s)\) data-based results and the experimentally measured value.