Anomalous magnetic moment of the muon, a hybrid approach

TL;DR

This paper introduces a hybrid QCD sum rule method combining experimental data, perturbative QCD, and lattice QCD to calculate the muon's anomalous magnetic moment, aiming to improve theoretical precision.

Contribution

It proposes a novel approach that integrates multiple data sources to determine the hadronic vacuum polarization contribution to the muon g-2.

Findings

Good approximation for $a_{ m hvp}$ using recent lattice results

Method aligns with existing data-based results but lacks precision to resolve discrepancies

Highlights potential for future lattice QCD improvements

Abstract

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