The leading hadronic vacuum polarization contribution to the muon anomalous magnetic moment using $N_f=2+1$ O($a$) improved Wilson quarks

TL;DR

This paper reports a lattice QCD calculation of the leading hadronic vacuum polarization contribution to the muon g-2, achieving about 2% precision by using noise reduction and systematic error estimation.

Contribution

It provides a new high-precision lattice QCD determination of the muon g-2 hadronic contribution using $N_f=2+1$ improved Wilson quarks, including systematic error analysis.

Findings

Final result: $a_\mu^{\rm hvp} = (720.0\pm 12.4 \pm 6.8)\times 10^{-10}$

Achieved approximately 2% total uncertainty

Systematic errors from finite size effects and quark contributions are well-controlled

Abstract

We present a lattice calculation of the leading hadronic contribution to the anomalous magnetic moment of the muon. This work is based on a subset of the CLS ensembles with $N_f = 2+1$ dynamical quarks and a quenched charm quark. Noise reduction techniques are used to improve significantly the statistical precision of the dominant light quark contribution. The main source of systematic error comes from finite size effects which are estimated using the formalism described in Ref. [7] and based on our knowledge of the timelike pion form factor. The strange and charm quark contributions are under control and an estimate of the quark-disconnected contribution is included. Isospin breaking effects will be studied in a future publication but are included in the systematic error using an estimate based on published lattice results. Our final result, $a_\mu^{\rm hvp} = (720.0\pm 12.4 \pm 6.8)\times 10^{-10}$, has a precision of about 2%.