Hadronic effects in (g-2)_mu and alpha_QED (M_Z): Status and perspectives

TL;DR

This paper surveys the hadronic vacuum polarization contributions to the muon anomalous magnetic moment $a_\mu$ and to the effective fine-structure constant $\alpha(M_Z)$. It introduces a new estimate for the hadronic shift $\Delta\alpha^{(5)}_{had}(M_Z^2)$ using a perturbative Adler-function calculation that includes quark-mass effects up to three loops in a ${\mathrm{MOM}}$ scheme, yielding $\Delta\alpha^{(5)}_{had}(M_Z^2)\approx 0.0277$ and $\alpha^{-1}(M_Z)\approx 128.92$. The analysis contrasts data-driven and theory-driven approaches, discusses nonperturbative effects, and highlights improvements from $\tau$ data and perturbative QCD down to $\sim M_\tau$. It also outlines the Daphne facility’s potential to further reduce uncertainties by providing precise low-energy $e^+e^-$ cross sections, thereby tightening predictions for $a_\mu^{had}$ and $\Delta\alpha^{(5)}_{had}(M_Z^2)$. Overall, the work emphasizes the interplay between experimental measurements and theory in refining precision electroweak tests and guiding future experiments.

Abstract

I review recent evaluations of the hadronic contributions to the muon anomalous magnetic moment (g-2)_mu and to the effective fine structure constant alpha (M_Z). A new estimate for the hadronic shift delta_alpha hadronic = 0.027782 +/- 0.000254 is presented which implies 1/alpha (M_Z) = 128.913 +/- 0.035. It is based on a recent perturbative calculation of the Adler function which includes mass effects up to three-loops in a MOM scheme and requires little ad hoc assumptions. I then discuss perspectives for possible improvements in estimations of g-2 which we expect from the Phi--factory DAPHNE at Frascati.

Figures (5)

• Figure 1: Evaluations of $1/\alpha(M_Z)$.
• Figure 2: Different estimates of $a_\mu^{\mathrm{had}}\times 10^{10}$.
• Figure 3: Integral contour.
• Figure 4: Adler function: data versus theory (see Ref.$^{28}$).
• Figure 5: Multi--particle channels in $e^+e^-$--annihilation at low energy.