Theoretical determination of the hadronic g − 2 of the muon

An approach is discussed on the determination of the leading order hadronic contribution to the muon anomaly, aμHAD, 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 3σ 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 aμHAD 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 aμHAD = (729–871) × 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.