Ratios of the hadronic contributions to the lepton g−2 from lattice QCD+QED simulations

URN to cite this document:: urn:nbn:de:bvb:355-epub-454450
DOI to cite this document:: 10.5283/epub.45445

Giusti, D. ; Simula, S.

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Date of publication of this fulltext: 01 Apr 2021 14:01

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Abstract

The ratios among the leading-order (LO) hadronic vacuum polarization (HVP) contributions to the anomalous magnetic moments of an electron, muon, and τ lepton, aHVP,LOℓ=e,μ,τ, are computed using lattice QCD+QED simulations. The results include the effects at order O(α2em) as well as the electromagnetic and strong isospin-breaking corrections at orders O(α3em) and O(α2em(mu−md)), respectively, where (mu−md) is the u- and d-quark mass difference. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration with Nf=2+1+1 dynamical quarks at three values of the lattice spacing (a≃0.062, 0.082, 0.089 fm) with pion masses in the range ≃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-τ and muon-τ ratios such a cancellation does not occur. For the electron-muon ratio we get Re/μ≡(mμ/me)2(aHVP,LOe/aHVP,LOμ)=1.1456(83) with an uncertainty of ≃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 ≃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 Re/μ=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 ≃2 could be sufficient to reach a tension with our SM value of the ratio Re/μ at a significance level of ≃5 standard deviations.

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