Ratios of the hadronic contributions to the lepton g-2 from lattice QCD plus QED simulations

The ratios among the leading-order (LO) hadronic vacuum polarization (HVP) contributions to the anomalous magnetic moments of an electron, muon, and tau lepton, a(l=e,mu,tau)(HVP,LO) are computed using lattice QCD + QED simulations. The results include the effects at order O(alpha(2)(em)) as well as the electromagnetic and strong isospin-breaking corrections at orders O(alpha(3)(em)) and O(alpha(2)(em)(m(u) - m(d))), respectively, where (m(u) - m(d)) is the u- and d-quark mass difference. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration with N-f = 2 + 1 + 1 dynamical quarks at three values of the lattice spacing (a similar or equal to 0.062, 0.082, 0.089 fin) with pion masses in the range similar or equal to 210-450 MeV. The calculations are based on the quark-connected contributions to the HVP in the quenched-QED approximation, which neglects the charges of the sea quarks. The quark-disconnected terms are estimated from results available in the literature. We show that in the case of the electron-muon ratio the hadronic uncertainties in the numerator and in the denominator largely cancel out, while in the cases of the electron-tau and muon-tau ratios such a cancellation does not occur. For the electron-muon ratio we get R-e/mu (m(mu)/m(e))(2) (a(e)(HVP,LO)/a(mu)(HVP,LO)) = 1.1456(83) with an uncertainty of similar or equal to 0.7%. Our result, which represents an accurate Standard Model (SM) prediction, agrees very well with the estimate obtained using the results of dispersive analyses of the experimental e(+) e(-) -> hadrons data. Instead, it differs by similar or equal to 2.7 standard deviations from the value expected from present electron and muon (g - 2) experiments after subtraction of the current estimates of the QED, electroweak, hadronic light-by-light and higher-order HVP contributions, namely R-e/mu = 0.575(213). An improvement of the precision of both the experiment and the QED contribution to the electron (g - 2) by a factor of similar or equal to 2 could be sufficient to reach a tension with our SM value of the ratio R-e/mu, at a significance level of similar or equal to 5 standard deviations.