Muon <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> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>α</mml:mi></mml:math> connection
A. Keshavarzi, William J. Marciano, M. Passera, A. Sirlin
Abstract
The discrepancy between the Standard Model theory and experimental measurement of the muon magnetic moment anomaly, ${a}_{\ensuremath{\mu}}=({g}_{\ensuremath{\mu}}\ensuremath{-}2)/2$, is connected to precision electroweak (EW) predictions via their common dependence on hadronic vacuum polarization effects. The same data for the total ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\text{hadrons}$ cross section, ${\ensuremath{\sigma}}_{\text{had}}(s)$, are used as input into dispersion relations to estimate the hadronic vacuum polarization contributions, ${a}_{\ensuremath{\mu}}^{\text{had},\mathrm{VP}}$, as well as the five-flavor hadronic contribution to the running QED coupling at the $Z$-pole, $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{\text{had}}^{(5)}({M}_{Z}^{2})$, which enters natural relations and global EW fits. The EW fit prediction of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{\text{had}}^{(5)}({M}_{Z}^{2})=0.02722(41)$ agrees well with $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{\text{had}}^{(5)}({M}_{Z}^{2})=0.02761(11)$ obtained from the dispersion relation approach, but exhibits a smaller central value suggestive of a larger discrepancy $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}={a}_{\ensuremath{\mu}}^{\mathrm{exp}}\ensuremath{-}{a}_{\ensuremath{\mu}}^{\mathrm{SM}}$ than currently expected. Postulating that the $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$ difference may be due to unforeseen missing ${\ensuremath{\sigma}}_{\text{had}}(s)$ contributions, implications for ${M}_{W}$, ${\mathrm{sin}}^{2}{\ensuremath{\theta}}_{\mathrm{eff}}^{\mathrm{lep}}$ and ${M}_{H}$ obtained from global EW fits are investigated. Shifts in ${\ensuremath{\sigma}}_{\text{had}}(s)$ needed to bridge $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$ are found to be excluded above $\sqrt{s}\ensuremath{\gtrsim}0.7\text{ }\text{ }\mathrm{GeV}$ at the 95% C.L. Moreover, prospects for $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$ originating below that energy are deemed improbable given the required increases in the hadronic cross section. Such hypothetical changes to the hadronic data are also found to affect other related observables, such as the electron anomaly, ${a}_{e}^{\text{SM}}$, the rescaled ratio ${R}_{e/\ensuremath{\mu}}=\phantom{\rule{0ex}{0ex}}({m}_{\ensuremath{\mu}}/{m}_{e}{)}^{2}({a}_{e}^{\text{had},\mathrm{LO}\text{ }\mathrm{VP}}/{a}_{\ensuremath{\mu}}^{\text{had},\mathrm{LO}\text{ }\mathrm{VP}})$, and the running of the weak mixing angle at low energies, although the consequences of these are currently less constraining.