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Corresponding author.

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We compute the leading, strong-interaction contribution to the anomalous magnetic moment of the electron, muon, and tau using lattice quantum chromodynamics (QCD) simulations. Calculations include the effects of

Ever since the discovery of the electron’s spin

In the case of the muon, the precision of the measurement

The same argument should make

Theoretically, the leading source of uncertainty in the SM prediction of

Here we present lattice QCD calculations of the LO-HVP contribution to the anomalous magnetic moments of all three leptons. The calculations include all contributions from

A unified treatment of the HVP contribution to the three lepton anomalous magnetic moments provides important cross-checks that validate the methods used. As the typical virtualities probed by these moments are around

We consider the zero three-momentum two-point function of the quark electromagnetic current in Euclidean time

It is straightforward to obtain the corresponding LO-HVP contributions to the anomalous magnetic moment of lepton

On a

The replacement of the FV sum over

We employ a tree-level improved Symanzik gauge action

For the electromagnetic current correlator, we use the conserved lattice current at the source and sink so that no renormalization is necessary. We calculate the connected contributions to the correlators using point sources. We use the all-mode-averaging (AMA) technique of Ref.

Even with our high statistics, the signal deteriorates quickly with increasing distance in our light and disconnected correlators. Thus, in implementing Eqs.

We limit the integral over

This analysis yields the continuum extrapolated flavor quantities,

The perturbative contributions,

The procedure described above yields

In the absence of a systematic study with simulations in a variety of volumes, only model estimates of FV effects can be made. As argued in Refs.

Compared to phenomenological determinations of

We quote our final results for

LO-HVP contribution to the anomalous magnetic moments of the

It is interesting to compare these results with those in the literature. There are only two lattice QCD determinations of the LO-HVP contribution to the muon anomalous moment which include the contributions of quarks up to the charm

We plot all of these results in Fig.

Comparison of our result for

Regarding

We thank S. Dürr for contributions in the early stages of this project and Z. Zhang for noticing a typo in our final result for

Recently, a work reporting on an