No Arabic abstract
The ratios among the leading-order (LO) hadronic vacuum polarization (HVP) contributions to the anomalous magnetic moments of electron, muon and tau-lepton, $a_{ell=e,mu tau}^{HVP,LO}$, are computed using lattice QCD+QED simulations. The results include the effects at order $O(alpha_{em}^2)$ as well as the electromagnetic and strong isospin-breaking corrections at orders $O(alpha_{em}^3)$ and $O(alpha_{em}^2(m_u-m_d))$, 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 ($a simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range 210 - 450 MeV. 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 $R_{e/mu } equiv (m_mu/m_e)^2 (a_e^{HVP,LO} / a_mu^{HVP,LO}) = 1.1456~(83)$ with an uncertainty of $simeq 0.7 %$. 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 $e^+ e^- to$ hadrons data. Instead, it differs by $simeq 2.7$ standard deviations from the value expected from present electron and muon (g - 2) experiments after subtraction of the current estimates of the QED, electro-weak, 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 $simeq 2$ could be sufficient to reach a tension with our SM value of the ratio $R_{e/mu }$ at a significance level of $simeq 5$ standard deviations.
We calculate the leading-order hadronic correction to the anomalous magnetic moments of each of the three charged leptons in the Standard Model: the electron, muon and tau. Working in two-flavor lattice QCD, we address essentially all sources of systematic error: lattice artifacts, finite-size effects, quark-mass extrapolation, momentum extrapolation and disconnected diagrams. The most significant remaining systematic error, the exclusion of the strange and charm quark contributions, will be addressed in our four-flavor calculation. We achieve a statistical accuracy of 2% or better for the physical values for each of the three leptons and the systematic errors are at most comparable.
We present a calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_mu^{mathrm hvp}$, in lattice QCD employing dynamical up and down quarks. We focus on controlling the infrared regime of the vacuum polarization function. To this end we employ several complementary approaches, including Pade fits, time moments and the time-momentum representation. We correct our results for finite-volume effects by combining the Gounaris-Sakurai parameterization of the timelike pion form factor with the Luscher formalism. On a subset of our ensembles we have derived an upper bound on the magnitude of quark-disconnected diagrams and found that they decrease the estimate for $a_mu^{mathrm hvp}$ by at most 2%. Our final result is $a_mu^{mathrm hvp}=(654pm32,{}^{+21}_{-23})cdot 10^{-10}$, where the first error is statistical, and the second denotes the combined systematic uncertainty. Based on our findings we discuss the prospects for determining $a_mu^{mathrm hvp}$ with sub-percent precision.
We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution to the anomalous magnetic moments of the electron, $a_e^{rm HVP}$, the muon, $a_mu^{rm HVP}$, and the tau, $a_tau^{rm HVP}$, including both the isospin-symmetric QCD term and the leading-order strong and electromagnetic isospin-breaking corrections. Moreover, the contribution to $a_mu^{rm HVP}$ not covered by the MUonE experimen, $a_{MUonE}^{rm HVP}$, is provided. We get $a_e^{rm HVP} = 185.8~(4.2) cdot 10^{-14}$, $a_mu^{rm HVP} = 692.1~(16.3) cdot 10^{-10}$, $a_tau^{rm HVP} = 335.9~(6.9) cdot 10^{-8}$ and $a_{MUonE}^{rm HVP} = 91.6~(2.0) cdot 10^{-10}$. Our results are obtained in the quenched-QED approximation using the QCD gauge configurations generated by the European (now Extended) Twisted Mass Collaboration (ETMC) with $N_f=2+1+1$ dynamical quarks, at three values of the lattice spacing varying from $0.089$ to $0.062$ fm, at several values of the lattice spatial size ($L simeq 1.8 div 3.5$ fm) and with pion masses in the range between $simeq 220$ and $simeq 490$ MeV.
We compute the vacuum polarisation on the lattice in quenched QCD using non-perturbatively improved Wilson fermions. Above Q^2 of about 2 GeV^2 the results are very close to the predictions of perturbative QCD. Below this scale we see signs of non-perturbative effects which we can describe by the use of dispersion relations. We use our results to estimate the light quark contribution to the muons anomalous magnetic moment. We find the result 446(23) x 10^{-10}, where the error only includes statistical uncertainties. Finally we make some comments on the applicability of the Operator Product Expansion to our data.
We study systematic uncertainties in the lattice QCD computation of hadronic vacuum polarization (HVP) contribution to the muon $g-2$. We investigate three systematic effects; finite volume (FV) effect, cutoff effect, and integration scheme dependence. We evaluate the FV effect at the physical pion mass on two different volumes of (5.4 fm$)^4$ and (10.8 fm$)^4$ using the PACS10 configurations at the same cutoff scale. For the cutoff effect, we compare two types of lattice vector operators, which are local and conserved (point-splitting) currents, by varying the cutoff scale on a larger than (10 fm$)^4$ lattice at the physical point. For the integration scheme dependence, we compare the results between the coordinate- and momentum-space integration schemes at the physical point on a (10.8 fm$)^4$ lattice. Our result for the HVP contribution to the muon $g-2$ is given by $a_mu^{rm hvp} = 737(9)(^{+13}_{-18})times 10^{-10}$ in the continuum limit, where the first error is statistical and the second one is systematic.