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Leading-order hadronic contributions to the lepton anomalous magnetic moments from the lattice

The hadronic leading-order (hlo) contribution to the lepton anomalous magnetic moments $a_l^\mathrm{hlo}$ of the Standard Model leptons still accounts for the dominant source of the uncertainty of the Standard Model estimates. We present the results of an investigation of the hadronic leading order anomalous magnetic moments of the electron, muon and tau lepton from first principles in twisted mass lattice QCD. With lattice data for multiple pion masses in the range $230 \mathrm{~MeV} \lesssim m_{PS} \lesssim 490 \mathrm{~MeV}$, multiple lattice volumes and three lattice spacings we perform the extrapolation to the continuum and to the physical pion mass and check for all systematic uncertainties in the lattice calculation. As a result we calculate $a_{l}^\mathrm{hlo}$ for the three Standard Model leptons with controlled statistical and systematic error in agreement with phenomenological determinations using dispersion relations and experimental data. In addition, we also give a first estimate of the hadronic leading order anomalous magnetic moments from simulations directly at the physical value of the pion mass.