Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles

18 pages, 8 figures (in 13 PDF files), RevTeX 4.1International audienceWe 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 $u$, $d$, $s$ and $c$ quarks and are performed directly at the physical values of the quark masses and in volumes of linear extent larger than 6 fm. All connected and disconnected Wick contractions are calculated. Continuum limits are carried out using six lattice spacings. We obtain $a_e^\mathrm{LO-HVP}=188.5(2.6)(5.5)\times 10^{-14}$, $a_\mu^\mathrm{LO-HVP}=711.0(7.5)(17.3)\times 10^{-10}$ and $a_\tau^\mathrm{LO-HVP}=341.1(0.8)(3.2)\times 10^{-8}$, where the first error is statistical and the second is systematic