Perturbative heavy quark contributions to the anomalous magnetic moment of the muon

Abstract

We discuss a method for calculating the heavy quark vacuum polarisation contribution to the muon anomalous magnetic moment, $a_{\mu }$, using perturbative QCD. This approach is independent of $e^{+}{e}^{-}$ cross-section data allowing a fully theoretical evaluation of these contributions. We confirm an existing result at lower orders in ${\alpha }_s$ and state a new explicit analytic formula which includes terms up to $\mathcal{O}\left({\alpha }_s^3\right)$. Numerically the charm quark contribution to $a_{\mu }$ is found to be $a_{\mu }^c=(14.5\pm 0.2)\times 10^{-10}$ and the bottom contributes $a_{\mu }^b=(0.302\pm 0.002)\times 10^{-10}$. Our uncertainty estimates include both parametric uncertainties from ${\hat{m}}_q({\hat{m}}_q)$ and ${\alpha }_s({\hat{m}}_q)$, and theoretical uncertainties in the perturbative expansion. Comparison is made between these results and alternative approaches such as lattice QCD or those based on a dispersion relation and cross-section data.

Comments: 8 pages, 2 figures, contribution to 16th International Workshop on Tau Lepton Physics (TAU2021), September 27 - October 1, 2021