Hadronic Vacuum Polarization:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">(</mml:mo><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>μ</mml:mi></mml:msub></mml:math>versus Global Electroweak Fits

Abstract

Hadronic vacuum polarization (HVP) is not only a critical part of the standard model (SM) prediction for the anomalous magnetic moment of the muon $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$, but also a crucial ingredient for global fits to electroweak (EW) precision observables due to its contribution to the running of the fine-structure constant encoded in $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{\text{had}}^{(5)}$. We find that with modern EW precision data, including the measurement of the Higgs mass, the global fit alone provides a competitive, independent determination of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{\text{had}}^{(5)}{|}_{\mathrm{EW}}=270.2(3.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. This value actually lies below the range derived from ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\text{hadrons}$ cross section data, and thus goes into the opposite direction as would be required if a change in HVP were to bring the SM prediction for $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ into agreement with the Brookhaven measurement. Depending on the energy where the bulk of the changes in the cross section occurs, reconciling experiment and SM predictions for $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ by adjusting HVP would thus not necessarily weaken the case for physics beyond the SM (BSM), but to some extent shift it from $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ to the EW fit. We briefly explore some options of BSM scenarios that could conceivably explain the ensuing tension.

Topics & Concepts