Measurement of the Positive Muon Anomalous Magnetic Moment to 0.7 ppm

A higher precision measurement of the anomalous $g$ value, $a_{\mu }=(g-2)/2$, for the positive muon has been made at the Brookhaven Alternating Gradient Synchrotron, based on data collected in the year 2000. The result $a_{{\mu }^{+}}=11659204(7)(5)\times {10}^{-10}$ (0.7 ppm) is in good agreement with previous measurements and has an error about one-half that of the combined previous data. The present world average experimental value is $a_{\mu }(\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t})=11659203(8)\times {10}^{-10}$ (0.7 ppm).

Figure 1

A two-dimensional multipole expansion of the field averaged over azimuth from 1 out of 22 trolley measurements. Half ppm contours with respect to a central azimuthal average field $B_0=1.451274\mathrm{T}$ are shown. The multipole amplitudes relative to $B_0$ are given at the beam aperture, which has a radius of 4.5 cm and is indicated by the circle.

Figure 2

CBO in the $g-2$ time spectra. The Fourier spectrum was obtained from residuals from a fit based on muon decay and spin precession [Eq. (2)] alone. The horizontal modulation was at ${\omega }_{\mathrm{C}\mathrm{B}\mathrm{O}\mathrm{,}\mathrm{h}}/(2\pi )=466\mathrm{k}\mathrm{H}\mathrm{z}$ in the year 2000, so that the interference frequency ${\omega }_{\mathrm{C}\mathrm{B}\mathrm{O}\mathrm{,}\mathrm{h}}-{\omega }_a$ is numerically close to ${\omega }_a$, as indicated. The frequency ${\omega }_a$ is determined from fits that take CBO into account.

Figure 3

(a) The frequency ${\omega }_a/(2\pi )$ determined from fits to the individual calorimeter time spectra. Data from calorimeters 2 and 20 were discarded, as in the analysis of our 1999 data. (b) The fitted frequency ${\omega }_a/(2\pi )$ versus positron energy. These results come from the analysis described first in the text.

Figure 4

Recent measurements of $a_{\mu }$, together with the standard model prediction using the evaluation in Ref. [9] of $a_{\mu }(\mathrm{h}\mathrm{a}\mathrm{d}\mathrm{,}\mathrm{1})$ from $e^{+}{e}^{-}$ and $\tau$ decay data.