Predictions for g-2 of the muon and alpha_QED(M_Z^2)

Abstract

We calculate (g-2) of the muon and the QED coupling alpha(M_Z^2), by improving the determination of the hadronic vacuum polarization contributions and their uncertainties. We include the recently re-analysed CMD-2 data on e^+e^- -> pi^+ pi^-. We carefully combine a wide variety of data for the e^+e^- production of hadrons, and obtain the optimum form of R(s) = sigma_had^0(s)/sigma_pt(s), together with its uncertainty. Our results for the hadronic contributions to g-2 of the muon are a_mu^(had, LO) = (692.4 +- 5.9_exp +- 2.4_rad) * 10^(-10) and a_mu^(had, NLO) = (-9.8 +- 0.1_exp +- 0.0_rad) * 10^(-10), and for the QED coupling Delta alpha^(5)_had (M_Z^2)= (275.5 +- 1.9_exp +- 1.3_rad) * 10^(-4). These yield (g-2)/2 = 0.00116591763(74), which is about 2.4 sigma below the present world average measurement, and alpha(M_Z^2)^(-1) = 128.954 +- 0.031. We compare our (g-2) value with other predictions and, in particular, make a detailed comparison with the latest determination of (g-2) by Davier et al.

Figures (28)

• Figure 1: Vacuum polarization correction factor $C_{\rm vp}^D$ in the low energy regime. The continuous line is the full result as applied in our analysis, whereas the dashed line is obtained when using $\alpha(-s)$ as an approximation for $\alpha(s)$. Both curves are for $\cos\theta_{\rm cut} = 0.5$ whereas the dotted lines are obtained for $\cos\theta_{\rm cut} = 0.8$.
• Figure 2: Two toy data sets chosen to illustrate the problems of combining precise with less precise data. The upper plot shows the result obtained with a very small 'cluster' size. The lower shows the data clustered in 50 MeV bins, which allows renormalization of the data within their systematic errors. Here the (much less precise) points of set 1 are renormalized by $1/1.35$ whereas the two precise points of set two are nearly unchanged ($1/0.9995$). The length of the error bars give the statistical plus systematic errors added in quadrature for each data point. The small horizontal lines in the bars indicate the size of the statistical errors. The error band of the clustered data is defined through the diagonal elements of the covariance matrix.
• Figure 3: Dependence of the fit on the cluster size parameter $\delta$ in the case of the $\pi^+ \pi^-$ channel: the band in the upper plot shows the contribution to $a_{\mu}$ and its errors for different choices of the cluster size. The three lines show $\bar{a}_\mu$ (solid), $\bar{a}_\mu +\Delta a_\mu$ and $\bar{a}_\mu-\Delta a_\mu$ (dotted), respectively. The lower plot displays the $\chi^2_{\rm min}/{\rm d.o.f.}$ (continuous line) together with the error size $\Delta a_{\mu}$ in % (dashed line).
• Figure 4: The behaviour of $R$ obtained from inclusive data and from the sum of exclusive channels, after clustering and fitting the various data sets. Note the suppressed zero of the vertical scale.
• Figure 5: Data for $\sigma^0(e^+e^-\to \pi^0\gamma)$. The shaded band shows the behaviour of the cross section after clustering and fitting the data. The second plot is an enlargement in the region of the $\omega$ resonance.