Hadronic Contributions to the Photon Vacuum Polarization and their Role in Precision Physics

TL;DR

This work surveys the hadronic vacuum-polarization contributions to the running fine-structure constant and to the muon g-2, emphasizing nonperturbative low-energy QCD effects extracted from hadronic e+e- data via dispersion relations. It discusses theoretical progress from perturbative QCD and the Adler-function approach in the Euclidean region, and presents updated values such as DeltaAlpha_had^(5)(M_Z^2) ≈ 0.02757 ± 0.00036 and a_mu^had ≈ 6.836 × 10^-10, along with the current experimental-theoretical tension in a_mu. The paper highlights recent CMD-2 and BES II measurements that reduce uncertainties, the ongoing debate between e+e- and tau-based data, and future experimental avenues (KLOE, BABAR radiative returns) to reach percent-level precision. Ultimately, these advances refine electroweak predictions and strengthen tests for the Standard Model and potential new physics, especially in the context of M_W, sin^2 theta_W, and Higgs-sector constraints.

Abstract

I review recent evaluations of the hadronic contribution to the shift in the fine structure constant and to the anomalous magnetic moment of the muon. Substantial progress in a precise determination of these important observables is a consequence of substantially improved total cross section measurement by the CMD-2 and BES II collaborations and an improved theoretical understanding. Prospects for further possible progress is discussed.

Figures (7)

• Figure 1: The running of $\alpha$. The "negative" $E$ axis is chosen to indicate space-like momentum transfer. The vertical bars at selected points indicate the uncertainty.
• Figure 2: The Adler function: theory vs. experiment.
• Figure 3: Comparison of the distribution of contributions and errors (shaded areas scaled up by 10) in the standard (left) and the Adler function based approach (right), respectively.
• Figure 4: $a_\mu$-11659000 $\times 10^{-10}$: theory vs. experiment in the year 2002 for (g-2) of the muon. The new E821 experiment at Brookhaven reviled a 2.7 $\sigma$ deviation from the theory. The various types of SM contributions are shown in the lower part of the figure.
• Figure 5: The dominating low energy tail is given by the channel $e^+e^- \rightarrow \pi^+\pi^-$ which forms the $\rho$--resonance. We show a compilation of the measurements of the square of the pion form factor $|F_\pi(s)|^2=4\:R_{\pi\pi}(s)/\beta_\pi^3$ with $\beta_\pi=(1-4m_\pi^2/s)^{1/2}$.