Ratios of the hadronic contributions to the lepton $g-2$ from Lattice QCD+QED simulations

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.

33 pages, 4 figures, 4 tables. Extended discussion of error propagation and chiral extrapolation added. New table IV with lattice data included. Version to appear in PRD

References in corpus (11)

• Measurement of the fine-structure constant as a test of the Standard Model
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks
• The muon $g$-2 and $\Delta \alpha$ connection
• Electromagnetic and strong isospin-breaking corrections to the muon $g-2$ from Lattice QCD+QED
• The ${\rm Y}$ and ${{\rm Y}}^{\prime }$ Leptonic Widths, $a_{\mu }^b$ and $m_b$ from full lattice QCD
• Strange and charm HVP contributions to the muon ($g-2)$ including QED corrections with twisted-mass fermions
• Moment Analysis of Hadronic Vacuum Polarization - Proposal for a lattice QCD evaluation of $g_{\mu }-2$
• Connected, Disconnected and Strange Quark Contributions to HVP
• Lepton anomalous magnetic moments in Lattice QCD+QED
• The hadronic vacuum polarization contribution to $(g_{\mu }-2)$: Lattice QCD+QED calculations

Cited by in corpus (10)

• The anomalous magnetic moment of the muon in the Standard Model
• The muon $g$-2 and $\Delta \alpha$ connection
• The anomalous magnetic moment of the muon in the Standard Model: an update
• Pion and Kaon box contribution to $a_{\mu }^{\text{HLbL}}$
• The anomalous magnetic moment of the muon: status of Lattice QCD calculations
• NNLO virtual and real leptonic corrections to muon-electron scattering
• Towards muon-electron scattering at NNLO
• Exploring the Null Results in the Direct Detection Experiments, $(g-2{)}_{\ell }$ and Neutrino Mass in an Extended $U(1{)}_{L_{\mu }-L_{\tau }}$ Model Constrained through the $Z\to {\ell }^{+}{\ell }^{-}$ Decays
• Rotated twisted-mass: a convenient regularization scheme for isospin breaking QCD and QED lattice calculations
• Towards NNLO corrections to muon-electron scattering