Theoretical determination of the hadronic (g-2) of the muon

Abstract

An approach is discussed on the determination of the leading order hadronic contribution to the muon anomaly, $a_{\mu }^{HAD}$, based entirely on theory. This method makes no use of $e^{+}{e}^{-}$ annihilation data, a likely source of the current discrepancy between theory and experiment beyond the $3\sigma$ level. What this method requires is essentially knowledge of the first derivative of the vector current correlator at zero-momentum. In the heavy-quark sector this is obtained from the well known heavy quark expansion in perturbative QCD, leading to values of $a_{\mu }^{HAD}$ in the charm- and bottom-quark region which were fully confirmed by later lattice QCD (LQCD) results. In the light-quark sector, using recent preliminary LQCD results for the first derivative of the vector current correlator at zero-momentum leads to the value $a_{\mu }^{HAD}=(729-871)\times 10^{-10}$, which is significantly larger than values obtained from using $e^{+}{e}^{-}$ data. A separate approach based on the operator product expansion (OPE), and designed to quench the contribution of these data, reduces the discrepancy by at least 40\%. In addition, it exposes a tension between the OPE and $e^{+}{e}^{-}$ data, thus suggesting the blame for the discrepancy on the latter.

Comments: Invited talk at the Workshop on Determination of the Fundamental Parameters in QCD, Mainz Institute of Theoretical Physics, Johannes Gutenberg University of Mainz. To be published in Mod. Phys. Lett. A