The muon $g$-2 and $\Delta \alpha$ connection

TL;DR

This paper explores the connection between the muon g-2 anomaly and electroweak precision measurements through hadronic vacuum polarization, analyzing data-driven estimates and implications for Standard Model parameters and potential new physics.

Contribution

It provides a detailed analysis of the hadronic contributions to muon g-2 and electroweak observables, highlighting the implications of current data discrepancies and constraints on missing hadronic effects.

Findings

The EW fit prediction of Δα_had^(5)(M_Z^2) aligns with dispersion results but suggests a larger muon g-2 discrepancy.

Shifts in hadronic cross sections needed to explain muon g-2 are excluded above 0.7 GeV at 95% CL.

Hypothetical modifications to hadronic data below 0.7 GeV are unlikely to resolve the muon g-2 anomaly without affecting other observables.

Abstract

The discrepancy between the Standard Model theory and experimental measurement of the muon magnetic moment anomaly, $a_{\mu}=\left(g_{\mu}-2\right)/2$, is connected to precision electroweak (EW) predictions via their common dependence on hadronic vacuum polarization effects. The same data for the total $e^+e^- \rightarrow \text{hadrons}$ cross section, $\sigma_{\rm had}(s)$, are used as input into dispersion relations to estimate the hadronic vacuum polarization contributions, $a_{\mu}^{\rm had,\,VP}$, as well as the five-flavor hadronic contribution to the running QED coupling at the $Z$-pole, $\Delta\alpha_{\rm had}^{(5)}(M_{Z}^2)$, which enters natural relations and global EW fits. The EW fit prediction of $\Delta\alpha_{\rm had}^{(5)}(M_{Z}^2) = 0.02722(41)$ agrees well with $\Delta\alpha_{\rm had}^{(5)}(M_{Z}^2) = 0.02761(11)$ obtained from the dispersion relation approach, but exhibits a smaller central value suggestive of a larger discrepancy $\Delta a_{\mu}=a_{\mu}^{\rm exp} - a_{\mu}^{\rm SM}$ than currently expected. Postulating that the $\Delta a_{\mu}$ difference may be due to missing $\sigma_{\rm had}(s)$ contributions, implications for $M_W$, $\sin^2 \! \theta^{\rm lep}_{\rm eff}$ and $M_H$ obtained from global EW fits are investigated. Shifts in $\sigma_{\rm had}(s)$ needed to bridge $\Delta a_{\mu}$ are found to be excluded above $\sqrt{s} \gtrsim 0.7$ GeV at the 95\%CL. Moreover, prospects for $\Delta a_{\mu}$ originating below that energy are deemed improbable given the required increases in the cross section. Such hypothetical changes to the hadronic data are also found to affect other related observables, such as the electron anomaly, $a_e^{\rm SM}$, the ratio $R_{e/\mu} = (m_\mu/m_e)^2 (a_{e}^{\rm had,\,LO\,VP}/a_{\mu}^{\rm had,\,LO\,VP})$ and the running of the weak mixing angle at low energies, although the consequences of these are currently less constraining.