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

TL;DR

This paper proposes a purely theoretical method to determine the leading order hadronic contribution to the muon g-2, avoiding $e^+ e^-$ data and highlighting potential discrepancies and tensions with experimental data.

Contribution

It introduces a novel theoretical approach based on the vector current correlator's derivative at zero-momentum, bypassing $e^+ e^-$ data and confirming results with lattice QCD.

Findings

Heavy-quark sector results match lattice QCD.

Light-quark sector estimates are larger than $e^+ e^-$ data-based values.

A new approach reduces the discrepancy by at least 40%.

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.