<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:math> of charged leptons, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi><mml:mo mathvariant="bold" stretchy="false">(</mml:mo><mml:msubsup><mml:mi>M</mml:mi><mml:mi>Z</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo mathvariant="bold" stretchy="false">)</mml:mo></mml:math>, and the hyperfine splitting of muonium

Abstract

Following updates in the compilation of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\text{hadrons}$ data, this work presents reevaluations of the hadronic vacuum polarization contributions to the anomalous magnetic moments of the electron (${a}_{e}$), muon (${a}_{\ensuremath{\mu}}$) and tau lepton (${a}_{\ensuremath{\tau}}$), to the ground-state hyperfine splitting of muonium and also updates the hadronic contributions to the running of the QED coupling at the mass scale of the $Z$ boson, $\ensuremath{\alpha}({M}_{Z}^{2})$. Combining the results for the hadronic vacuum polarization contributions with recent updates for the hadronic light-by-light corrections, the electromagnetic and the weak contributions, the deviation between the measured value of ${a}_{\ensuremath{\mu}}$ and its Standard Model prediction amounts to $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}=(28.02\ifmmode\pm\else\textpm\fi{}7.37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, corresponding to a muon $g\ensuremath{-}2$ discrepancy of $3.8\ensuremath{\sigma}$.