Hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment from four-flavor lattice QCD

Abstract

We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from {the} connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from $a\approx 0.06$ to~0.15~fm. The up- and down-quark masses in our simulations have equal masses $m_l$. We obtain, in this world where all pions have the mass of the ${\pi }^0$, $10^{10}{a}_{\mu }^{ll}(conn.)=637.8(8.8)$, in agreement with independent lattice-QCD calculations. We then combine this value with published lattice-QCD results for the connected contributions from strange, charm, and bottom quarks, and an estimate of the uncertainty due to the fact that our calculation does not include strong-isospin breaking, electromagnetism, or contributions from quark-disconnected diagrams. Our final result for the total $\mathcal{O}({\alpha }^2)$ hadronic vacuum polarization to the muon's anomalous magnetic moment is~$10^{10}{a}_{\mu }^{\mathrm{HVP},\mathrm{LO}}=699(15{)}_{u,d}(1{)}_{s,c,b}$, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both {\it ab-initio} lattice-QCD calculations and phenomenological determinations from experimental $e^{+}{e}^{-}$-scattering data. It is $1.3\sigma$ below the "no new physics" value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of $a_{\mu }$ with theoretical calculations of the other contributions.

arXiv comment19 pages, 12 figures, 6 tables; updated to correct a small mistake in the finite volume correction resulting in small changes to the results, matches published version

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