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

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 $e^{+}{e}^{-}\to \text{hadrons}$ cross section, ${\sigma }_{\mathrm{had}}(s)$, are used as input into dispersion relations to estimate the hadronic vacuum polarization contributions, $a_{\mu }^{\mathrm{had},\mathrm{VP}}$, as well as the five-flavor hadronic contribution to the running QED coupling at the $Z$-pole, $\Delta {\alpha }_{\mathrm{had}}^{(5)}(M_Z^2)$, which enters natural relations and global EW fits. The EW fit prediction of $\Delta {\alpha }_{\mathrm{had}}^{(5)}(M_Z^2)=0.02722(41)$ agrees well with $\Delta {\alpha }_{\mathrm{had}}^{(5)}(M_Z^2)=0.02761(11)$ obtained from the dispersion relation approach, but exhibits a smaller central value suggestive of a larger discrepancy $\Delta a_{\mu }=a_{\mu }^{\exp }-a_{\mu }^{\mathrm{SM}}$ than currently expected. Postulating that the $\Delta a_{\mu }$ difference may be due to missing ${\sigma }_{\mathrm{had}}(s)$ contributions, implications for $M_W$, ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{lep}}$ and $M_H$ obtained from global EW fits are investigated. Shifts in ${\sigma }_{\mathrm{had}}(s)$ 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, $a_e^{\mathrm{SM}}$, the ratio $R_{e/\mu }=(m_{\mu }/m_e{)}^2(a_e^{\mathrm{had},\mathrm{LO}\mathrm{VP}}/a_{\mu }^{\mathrm{had},\mathrm{LO}\mathrm{VP}})$ and the running of the weak mixing angle at low energies, although the consequences of these are currently less constraining.

33 pages, 16 figures

References in corpus (22)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
• Measurement of the fine-structure constant as a test of the Standard Model
• The global electroweak fit at NNLO and prospects for the LHC and ILC
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• New determination of the fine structure constant and test of the quantum electrodynamics
• Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
• Improved predictions for g-2 of the muon and α_{\rm QED}(M_Z^2)
• Towards a data-driven analysis of hadronic light-by-light scattering
• A new approach to evaluate the leading hadronic corrections to the muon g-2
• Contributions of axion-like particles to lepton dipole moments
• The muon g-2 and the bounds on the Higgs boson mass
• Light-by-light scattering sum rules in light of new data
• Electroweak two-loop corrections to the effective weak mixing angle
• The hadronic contribution to (g-2) of the muon
• Precision measurements of sigma_hadronic for alpha_eff(E) at ILC energies and (g-2)_mu
• Electroweak Precision Tests of the Standard Model after the Discovery of the Higgs Boson
• The MOLLER Experiment: An Ultra-Precise Measurement of the Weak Mixing Angle Using Møller Scattering
• On Constraints Between $\Delta {\alpha }_{\mathrm{had}}(M_Z^2)$ and $(g_{\mu }-2{)}_{\mathrm{HVP}}$
• The Muon $g-2$ experiment at Fermilab
• Top-quark loops and the muon anomalous magnetic moment

Cited by in corpus (2)

• QED at NNLO with McMule
• On Constraints Between $\Delta {\alpha }_{\mathrm{had}}(M_Z^2)$ and $(g_{\mu }-2{)}_{\mathrm{HVP}}$