Lepton anomalous magnetic moments in Lattice QCD+QED

TL;DR

This paper presents a lattice QCD+QED calculation of the hadronic vacuum polarization contributions to the anomalous magnetic moments of the electron, muon, and tau, including isospin-breaking effects and a specific contribution for MUonE experiment coverage.

Contribution

It provides the first lattice QCD+QED determination of HVP contributions to lepton magnetic moments with isospin-breaking corrections and MUonE-specific contributions, using extensive gauge configurations.

Findings

Calculated $a_e^{ m HVP}$, $a_4_ m HVP$, and $a_ au^{ m HVP}$ with uncertainties.

Provided $a_{MUonE}^{ m HVP}$ contribution relevant for MUonE experiment.

Results obtained with $N_f=2+1+1$ dynamical quarks at multiple lattice spacings.

Abstract

We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution to the anomalous magnetic moments of the electron, $a_e^{\rm HVP}$, the muon, $a_\mu^{\rm HVP}$, and the tau, $a_\tau^{\rm HVP}$, including both the isospin-symmetric QCD term and the leading-order strong and electromagnetic isospin-breaking corrections. Moreover, the contribution to $a_\mu^{\rm HVP}$ not covered by the MUonE experimen, $a_{MUonE}^{\rm HVP}$, is provided. We get $a_e^{\rm HVP} = 185.8~(4.2) \cdot 10^{-14}$, $a_\mu^{\rm HVP} = 692.1~(16.3) \cdot 10^{-10}$, $a_\tau^{\rm HVP} = 335.9~(6.9) \cdot 10^{-8}$ and $a_{MUonE}^{\rm HVP} = 91.6~(2.0) \cdot 10^{-10}$. Our results are obtained in the quenched-QED approximation using the QCD gauge configurations generated by the European (now Extended) Twisted Mass Collaboration (ETMC) with $N_f=2+1+1$ dynamical quarks, at three values of the lattice spacing varying from $0.089$ to $0.062$ fm, at several values of the lattice spatial size ($L \simeq 1.8 \div 3.5$ fm) and with pion masses in the range between $\simeq 220$ and $\simeq 490$ MeV.