Anomalous magnetic moment of the muon, a hybrid approach

Abstract

A new QCD sum rule determination of the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_{\mu }^{\mathrm{hvp}}$, 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, ${\Pi }_{\mathrm{EM}}^{\prime }(0)$. The idea is based on the observation that, in the relevant kinematic domain, the integration kernel $K(s)$, entering the formula relating $a_{\mu }^{\mathrm{hvp}}$ 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 ${\Pi }_{\mathrm{EM}}^{\prime }(0)$, which can be calculated in lattice QCD. Using recent lattice results we find a good approximation for $a_{\mu }^{\mathrm{hvp}}$, but the precision is not yet sufficient to resolve the discrepancy between the $R(s)$ data-based results and the experimentally measured value.

Comments: 14 pages, added some clarifying text and two references, removed typos, results unchanged. Version to be published in Phys.Rev.D