The strange and charm quark contributions to the anomalous magnetic moment of the muon from lattice QCD

TL;DR

This paper introduces a new lattice QCD technique using Padé approximants to accurately compute the strange and charm quark contributions to the muon's anomalous magnetic moment, achieving about 1% precision for the strange quark.

Contribution

The paper presents a novel method employing Padé approximants and time-moments of correlators to determine hadronic vacuum polarization contributions in lattice QCD.

Findings

Strange quark contribution: 53.41(59)×10^{-10}

Charm quark contribution: 14.42(39)×10^{-10}

Achieved 1% accuracy for strange quark contribution

Abstract

We describe a new technique (published in Phys. Rev. D89 114501) to determine the contribution to the anomalous magnetic moment of the muon coming from the hadronic vacuum polarisation using lattice QCD. Our method uses Pad\'e approximants to reconstruct the Adler function from its derivatives at $q^2=0$. These are obtained simply and accurately from time-moments of the vector current-current correlator at zero spatial momentum. We test the method using strange quark correlators calculated on MILC Collaboration's $n_f = 2+1+1$ HISQ ensembles at multiple values of the lattice spacing, multiple volumes and multiple light sea quark masses (including physical pion mass configurations). We find the (connected) contribution to the anomalous moment from the strange quark vacuum polarisation to be $a^s_\mu=53.41(59)\times 10^{-10}$, and the contribution from charm quarks to be $a^c_\mu=14.42(39)\times 10^{-10}$ - 1% accuracy is achieved for the strange quark contribution. The extension of our method to the light quark contribution and to that from the quark-line disconnected diagram is straightforward.