Improved predictions for g-2 of the muon and α_{\rm QED}(M_Z^2)

Abstract

We update the Standard Model predictions of the anomalous magnetic moment of the muon, a_μ= (g-2)/2, and the value of the QED coupling at the Z-boson mass, incorporating the new e^+e^- \to ππdata obtained by CMD-2 and KLOE, as well as the corrected SND data, and other improvements. The prediction for a_μ=11659180.4 (5.1) \times 10^{-10} is about 3 \times 10^{-10} lower than before, and has a smaller uncertainty, which corresponds to a 3.4σdeviation from the measured value. The prediction for the QED coupling is α(M_Z^2)^{-1}= 128.937 \pm 0.030.

Figures (5)

• Figure 1: The lower continuous (red) line shows the contribution of the $e^+e^- \to \pi^+ \pi^-$ data in the energy region $0.32 < \sqrt{s} < 1.43$ GeV to $a_\mu^{\rm had,LO}$ of (\ref{['eq:disprel1']}), as a function of the data cluster size parameter $\delta$. The (orange) band corresponds to the uncertainty in the contribution. All the new $\pi^+\pi^-$ data are included except those from KLOE, see text. The upper dashed (blue) curve, and the error corridor given by the dotted lines, are the corresponding results obtained with the data as they were available for our previous 2003 analysis HMNT2003.
• Figure 2: $\pi\pi$ data in the low and high energy $\rho$-resonance tail regions (upper and lower panels), compared to our fits using a clustering size of $\delta=4.0$ MeV. The light (orange) band indicates the error band of the fit without the recent CMD-2 (2006) and SND data which became available after our previous analysis HMNT2003, whereas the (blue) line and darker (red) band correspond to the mean value and error band of the new fit including all data as indicated in the two panels.
• Figure 3: Mean value of the fit of all $\pi\pi$ data in the $\rho$ central region (blue line) compared to the fit without the KLOE data (red band), together with data from CMD-2, SND and KLOE (as indicated).
• Figure 4: In the lower half of the plot we compare the experimental value BNL of the anomalous magnetic moment of the muon, $(g-2)/2 \equiv a_\mu$, with the SM prediction calculated in the text. We see that there is now a 3.4 $\sigma$ discrepancy between experiment and the SM prediction. In the upper part of the plot we show four earlier determinations HMNT2003early of $a_\mu$ that were made before the CMD-2 CMDloCMDmedCMDhi, KLOE KLOE and SND SNDSNDreanal$e^+e^- \to \pi\pi$ data became available. The light-by-light contribution used in these determinations varies from $(8.6 \pm 3.5) \times 10^{-10}$ in DEHZ(03) to the more recent estimate MV of $(13.6 \pm 2.5) \times 10^{-10}$ used in HMNT(03b,06), see (\ref{['eq:lbl']}).
• Figure 5: The contours in the minimal SUGRA $m_{1/2}$, $m_0$ plane allowed by the difference $a_{\mu}^{\rm exp} - a_{\mu}^{\rm SM} = (27.6 \pm 8.1) \times 10^{-10}$ at 1-$\sigma$, 2-$\sigma$ and 3-$\sigma$. The other parameters are $\tan\beta=10$, $A_0=-300$ GeV, $\mu>0$, and the SPS 1a$^\prime$ reference point is shown by the big dot. Also shown are the constraints from the Higgs boson and the chargino masses from the direct searches and the charged dark matter ($\tilde{\tau}$ LSP).