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, [Formula: see text], based entirely on theory. This method makes no use of [Formula: see text] annihilation data, a likely source of the current discrepancy between theory and experiment beyond the 3[Formula: see text] 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 quantum chromodynamics (QCD), leading to values of [Formula: see text] 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 [Formula: see text], which is significantly larger than values obtained from using [Formula: see text] 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 [Formula: see text] data, thus suggesting the blame for the discrepancy on the latter.