The hadronic contribution to (g-2) of the muon

TL;DR

The paper addresses the precision of the Standard Model prediction for the muon anomalous magnetic moment $a_\mu$, whose uncertainty is dominated by hadronic vacuum polarization. It updates the hadronic input to the dispersion integral with new $e^+e^- \to$ hadrons data from CMD-2, SND, and BaBar (via radiative return), and assesses the impact of $\tau$-based spectral functions corrected for isospin breaking. The resulting $a_\mu^{\rm had,LO}$ and SM value achieve a precision comparable to the experimental measurement, but the $e^+e^-$-based SM prediction remains about $3.3\sigma$ below the BNL result, while the $\tau$-based estimate agrees better with experiment yet cannot resolve the tension due to a persistent $\tau$/$e^+e^-$ discrepancy. The work emphasizes the remaining systematic issues, notably the normalization difference in $\tau$ decays and $e^+e^-$ data (including KLOE), and highlights forthcoming BaBar and KLOE measurements as critical to clarifying whether the deviation signals new physics or unresolved hadronic effects.

Abstract

The evaluation of the hadronic contribution to the muon magnetic anomaly $a_μ$ is revisited, taking advantage of new experimental data on $e^+e^-$ annihilation into hadrons: SND and CMD-2 for the $π^+π^-$ channel, and \babar for multihadron final states. Discrepancies are observed between KLOE and CMD-2/SND data, preventing one from averaging all the $e^+e^-$ results. The long-standing disagreement between spectral functions obtained from $τ$ decays and $e^+e^-$ annihilation is still present, and not accounted by isospin-breaking corrections, for which new estimates have been presented. The updated Standard Model value for $a_μ$ based on $e^+e^-$ annihilation data is now reaching a precision better than experiment, and it disagrees with the direct measurement from BNL at the 3.3$σ$ level, while the $τ$-based estimate is in much better agreement. The $τ$/$e^+e^-$ discrepancy, best revealed when comparing the measured branching fraction for $τ^- \to π^- π^0 ν_τ$ to its prediction from the isospin-breaking-corrected $e^+e^-$ spectral function, remains a serious problem to be understood.

Figures (8)

• Figure 1: Relative comparison of the $\pi^+\pi^-$ spectral functions from $e^+e^-$-annihilation data and isospin-breaking-corrected $\tau$ data, expressed as a ratio to the $\tau$ spectral function. The shaded band indicates the errors of the $\tau$ data. The $e^+e^-$ data are from KLOE kloe_pipi, CMD-2 cmd2_new, CMD, OLYA and DM1 (references given in Ref. dehz03). The right hand plot emphasizes the region of the $\rho$ peak.
• Figure 2: The measured branching ratios for $\tau^-\rightarrow\nu_\tau\pi^-\pi^0$ compared to the prediction from the $e^+e^-\rightarrow\pi^+\pi^-$ spectral function applying the isospin-breaking correction factors discussed in Ref. dehz. The measured branching ratios are from ALEPH aleph_new, CLEO cleo_bpipi0 and OPAL opal_bpipi0. The L3 and OPAL results are obtained from their $h \pi^0$ branching ratio, reduced by the small $K \pi^0$ contribution measured by ALEPH aleph_ksum and CLEO cleo_kpi0.
• Figure 3: The measured cross section for $e^+e^- \rightarrow\xspace \pi^+\pi^-\pi^0$ from B A B A Rbabar_3pi (indicated by full squares) compared to previous measurements (see references in Ref. dehz).
• Figure 4: The measured cross section for $e^+e^- \rightarrow\xspace 2\pi^+2\pi^-$ from B A B A Rbabar_4pi (indicated by full circles) compared to previous measurements and results from $\tau^- \rightarrow\xspace \pi^- 3\pi^0$ (see references in Ref. dehz).
• Figure 5: The measured cross section for $e^+e^- \rightarrow\xspace 3\pi^+3\pi^-$ from B A B A Rbabar_6pi (indicated by open circles) compared to previous measurements (see references in Ref. dehz).