Confronting Spectral Functions from e+e- Annihilation and tau Decays: Consequences for the Muon Magnetic Moment

Abstract

Vacuum polarization integrals involve the vector spectral functions which can be experimentally determined from two sources: (i) e+e- annihilation cross sections and (ii) hadronic tau decays. Recently results with comparable precision have become available from CMD-2 on one side, and ALEPH, CLEO and OPAL on the other. The comparison of the respective spectral functions involves a correction from isospin-breaking effects which is evaluated. After correction it is found that the dominant 2pi spectral functions do not agree within experimental and theoretical uncertainties. Some problems are also found for the 4pi spectral functions where different experiments do not agree well with each other. The consequences of these discrepancies for vacuum polarization calculations are presented, with emphasis on the muon anomalous magnetic moment. The work includes a complete reevaluation of all exclusive cross sections, taking into account the most recent data that became available in particular from the Novosibirsk experiments and applying corrections for the missing radiative corrections. The values found for the lowest-order hadronic vacuum polarization contributions are a_mu[had,LO] = (684.7 +- 6.0[exp] +- 3.6[rad])x10^(-10) [e^+e^- -based], and a_mu[had,LO] = (709.0 +- 5.1[exp] +- 1.2[rad] +- 2.8[SU(2)])x10^(-10) [tau-based]. The errors have been separated according to their sources: experimental, radiative corrections in e+e- data, and isospin-breaking. We observe deviations of the full SM prediction with the recent BNL measurement at the 3.0 (e+e-) and 0.9 (tau) sigma level, when adding experimental and theoretical errors in quadrature.

Figures (10)

• Figure 3: Comparison between the shapes of the ALEPH, CLEO and OPAL $\pi\pi$ spectral functions normalized to the world-average branching ratio $B_{\pi\pi^0}$. The normalization errors, correlated between the shapes, are not contained in the error bars.
• Figure 4: Mass-squared-dependent corrections applied to the $\pi^-\pi^0$ spectral function from $\tau$ data, following the analysis of Ref. ecker2.
• Figure 5: Comparison of the $\pi^+\pi^-$ spectral functions from $e^+e^-$ and isospin-breaking corrected $\tau$ data, expressed as $e^+e^-$ cross sections. The band indicates the combined $e^+e^-$ and $\tau$ result within $1\sigma$ errors. It is given for illustration purpose only.
• Figure 6: Relative comparison of the $\pi^+\pi^-$ spectral functions from $e^+e^-$ and isospin-breaking corrected $\tau$ data, expressed as a ratio to the $\tau$. The band shows the uncertainty on the latter.
• Figure 8: Comparison of the $2\pi^+2\pi^-$ spectral functions from $e^+e^-$ and isospin-breaking corrected $\tau$ data, expressed as $e^+e^-$ cross sections.