Four-Flavour Leading-Order Hadronic Contribution To The Muon Anomalous Magnetic Moment

TL;DR

This paper reports a lattice QCD calculation of the leading-order hadronic contribution to the muon's anomalous magnetic moment, using four-flavour ensembles to improve accuracy and compare with phenomenological results.

Contribution

It provides a four-flavour lattice QCD determination of $a_ ext{ extmu}^{ m hvp}$ with controlled systematic uncertainties, aligning well with phenomenological estimates.

Findings

Final result: $a_ ext{ extmu}^{ m hvp} = 6.74(21)(18) imes 10^{-8}$

Good agreement with phenomenological determinations

Controlled extrapolation to physical pion mass

Abstract

We present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, $a_\mathrm{\mu}^{\rm hvp}$, arising from quark-connected Feynman graphs. It is based on ensembles featuring $N_f=2+1+1$ dynamical twisted mass fermions generated by the European Twisted Mass Collaboration (ETMC). Several light quark masses are used in order to yield a controlled extrapolation to the physical pion mass. We employ three lattice spacings to examine lattice artefacts and several different volumes to check for finite-size effects. Incorporating the complete first two generations of quarks allows for a direct comparison with phenomenological determinations of $a_\mathrm{\mu}^{\rm hvp}$. Our final result including an estimate of the systematic uncertainty $$a_{\mathrm{\mu}}^{\rm hvp} = 6.74(21)(18) \cdot 10^{-8}$$ shows a good overall agreement with these computations.