Reevaluation of the hadronic contribution to the muon magnetic anomaly using new e+e- -> pi+pi- cross section data from BABAR

TL;DR

This work reevaluates the leading-order hadronic contribution to the muon anomalous magnetic moment using new BABAR ISR data for $e^+e^- \to \pi^+\pi^-$ and a sophisticated data- combination framework (HVPTools) to properly propagate uncertainties and account for correlations. The $\pi\pi$ contribution from $e^+e^-$ inputs increases the hadronic term, while the tension between $e^+e^-$ and $\tau$ spectral functions in this channel decreases to $1.5\sigma$, though local discrepancies remain. When all hadronic channels are included, the Standard Model prediction remains about $3.2\sigma$ below the experimental value, with the level of tension sensitive to specific dataset choices. The study highlights remaining hadronic-systematic challenges and the value of diverse, high-precision measurements in sharpening the $a_\mu$ prediction.

Abstract

Using recently published, high-precision pi+pi- cross section data by the BABAR experiment from the analysis of e+e- events with high-energy photon radiation in the initial state, we reevaluate the lowest order hadronic contribution a_mu[had,LO] to the anomalous magnetic moment of the muon. We employ newly developed software featuring improved data interpolation and averaging, more accurate error propagation and systematic validation. With the new data, the discrepancy between the e+e- and tau-based results for the dominant two-pion mode reduces from previously 2.4 sigma to 1.5 sigma in the dispersion integral, though significant local discrepancies in the spectra persist. We obtain for the e+e- based evaluation amu[had,LO] = (695.5 +- 4.1) 10^-10, where the error accounts for all sources. The full Standard Model prediction of a_mu differs from the experimental value by 3.2 sigma.

Figures (6)

• Figure 1: Rescaling factor accounting for inconsistencies among experiments versus $\sqrt{s}$ (see text). The peak around 0.4 GeV is introduced by a discrepancy between CMD2 and TOF measurements versus BABAR. The peaks around 0.65 and 0.74$\mathrm{\,Ge V}$ are introduced by outlier from CMD. The sharp peak at 0.78 GeV is due to local discrepancies along the $\rho$--$\omega$ interference. The bump between 0.85 and 0.95 GeV is due to a discrepancy between KLOE and BABAR. Finally, between 1.45 and 1.65 GeV measurements from MEA and DM2 significantly exceed the BABAR cross sections.
• Figure 2: Cross section for $e^+e^-\xspace\to\pi^+\pi^-\xspace$ annihilation measured by the different experiments for the entire energy range (top), and zoomed energy intervals (all other plots). The errors bars contain both statistical and systematic errors, added in quadrature. The shaded (green) band represents the average of all the measurements obtained by HVPTools, which is used for the numerical integration following the procedure discussed in Sec. \ref{['sec:hvptools']}.
• Figure 3: Relative cross section comparison between individual experiments (symbols) and the HVPTools average (shaded band) computed from all measurements considered. Shown are BABAR (top left), KLOE (top right), CMD2 (bottom left) and SND (bottom right).
• Figure 5: Relative comparison between the combined $\tau$ (dark shaded) and $e^+e^-$ spectral functions (light shaded), normalised to the $e^+e^-$ result. The apparently oscillating structure around 0.5 GeV is due to two Belle measurements fluctuating to large cross section values. Clearly visible is the interference due to $\rho$--$\phi$ mixing around 1 GeV, which is not included in the isospin-breaking corrections applied to the $\tau$ data. It is also visible in the upper, and lower right hand plots of Fig. \ref{['fig:xsec']}. The deviation between 0.8 and 0.95 GeV is due to the discrepancy between $\tau$ and KLOE data, which dominate in this region (cf. Fig. \ref{['fig:weights']} left). Comparing the $\tau$ data with the combined $e^+e^-$ data instead of a fit to a single experiment CMD-2 limited to 1 GeV as it was done for Fig. 4 in Ref. jegerproc and Fig. 28 in Ref. jeger, we observe a reduced discrepancy, in particular between 1.0GeV and 1.4GeV. We therefore disagree with the conclusion reached in these references, where the difference goes up to a factor 4, and is even in the opposite direction with respect to the one we observe.
• Figure 6: Cross section measurements $e^+e^-\xspace\to\pi^+\pi^-\xspace2\pi^0\xspace$ used in the calculation of $a_\mu\xspace^{\rm had,LO}[\pi\pi2\pi^0\xspace]$. The shaded band depicts the HVPTools interpolated average within $1\sigma$ errors. The individual measurements are referenced in dehz02.