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, $a_{\mu }^{\mathrm{h}\mathrm{v}\mathrm{p}}$, 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, ${\mathrm{\Pi }}_{\mathrm{E}\mathrm{M}}^{\mathrm{\prime }}(0)$. The idea is based on the observation that, in the relevant kinematic domain, the integration kernel $K(s)$, entering the formula relating $a_{\mu }^{\mathrm{h}\mathrm{v}\mathrm{p}}$ to $e^{+}{e}^{-}$ annihilation data, behaves like $1\mathrm{/}s$ times a very smooth function of $s$, the squared energy. We find an expression for $a_{\mu }$ in terms of ${\mathrm{\Pi }}_{\mathrm{E}\mathrm{M}}^{\mathrm{\prime }}(0)$, which can be calculated in lattice QCD. Using recent lattice results we find a good approximation for $a_{\mu }^{\mathrm{h}\mathrm{v}\mathrm{p}}$, but the precision is not yet sufficient to resolve the discrepancy between the $R(s)$ data-based results and the experimentally measured value.