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The muon $g$-2 and $\Delta \alpha$ connection
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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.
Forward citations
Cited by 8 Pith papers
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Precision evaluation of the $\eta$- and $\eta'$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
A new dispersive analysis of the eta and eta-prime transition form factors gives a_mu(eta-pole) = 14.7(9) x 10^-11 and a_mu(eta'-pole) = 13.5(7) x 10^-11, with combined pseudoscalar poles at 91.2(+2.9,-2.4) x 10^-11.
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Towards testing $(g-2)_\tau$ in $e^+e^-\to\tau^+\tau^-$: radiative corrections and projections for Belle II
A complete one-loop QED calculation for polarized e+e- to tau+tau- is implemented in the McMule Monte-Carlo code, showing that Belle II with a polarized beam could test the tau anomalous magnetic moment at the 10^-5 level.
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Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
Using a dispersive formalism with experimental transition form factors and short-distance constraints, the authors obtain a_mu^HLbL = 101.9(7.9) x 10^-11, halving the previous uncertainty.
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The running of the electroweak gauge couplings from first principles
Lattice QCD plus pQCD matching yields Δα_had^(5)(M_Z²)=0.027821(34)lat(35)pQCD at 0.17% precision and a up-to-7σ tension with e+e- data near 1 GeV².
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Dispersive analysis of the pion vector form factor without zeros
Imposing the absence of complex zeros in the pion vector form factor reduces the dominant systematic uncertainty and makes the tensions between CMD-3 and other e+e- data sets appear sharper, including in the pion char...
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Dispersion relation for hadronic light-by-light scattering: $\eta$ and $\eta'$ poles
A dispersive analysis of the eta and eta' transition form factors yields data-driven pole contributions to the muon g-2 of 14.7(9) x 10^-11 and 13.5(7) x 10^-11.
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Dispersion relation for hadronic light-by-light scattering: subleading contributions
A dispersive evaluation gives a_mu^HLbL subleading = 33.2(7.2) x 10^-11 and total = 101.9(7.9) x 10^-11.
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Searching for hadronic scale baryonic and dark forces at $(g-2)_\mu$'s lattice-vs-dispersion front
A flavor-universal GeV-scale vector boson's direct contribution to (g-2)_mu cancels against its on-shell contribution to the e+e- -> hadrons data when the data-driven HVP is used, redirecting the search to the lattice...
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