Hadronic Vacuum Polarization Contribution to the Anomalous Magnetic Moments of Leptons from First Principles

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 $u$, $d$, $s$, 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 $a_e^{\mathrm{LO}\text{−}\mathrm{HVP}}=189.3(2.6)(5.6)\times {10}^{-14}$, $a_{\mu }^{\mathrm{LO}\text{−}\mathrm{HVP}}=711.1(7.5)(17.4)\times {10}^{-10}$ and $a_{\tau }^{\mathrm{LO}\text{−}\mathrm{HVP}}=341.0(0.8)(3.2)\times {10}^{-8}$, where the first error is statistical and the second is systematic.

Figure 1

Comparison of our result for $a_{\mu }^{\mathrm{LO}\text{−}\mathrm{HVP}}$ with the only other two $N_f=2+1+1$ lattice QCD calculations [25, 34] and with recent ones obtained from phenomenology [8, 19, 20]. For the lattice results, the first error is statistical and the second is the total error, including systematics. The shaded region is the value that $a_{\mu }^{\mathrm{LO}\text{−}\mathrm{HVP}}$ would have to have to explain the experimental measurement of $a_{\mu }$, assuming no new physics.