Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL

TL;DR

This work reports the final Brookhaven E821 measurement of the muon anomalous magnetic moment with 0.54 ppm precision, $a_4(expt)=11\,659\,208.0(6.3)\times10^{-10}$. The experiment combines a highly uniform storage-ring field mapped by an array of NMR probes with precise measurements of the muon spin precession frequency via decay electrons, correcting for beam dynamics and detector effects. The Standard Model prediction, dominated by hadronic uncertainties, yields a modest tension with the experimental value, at about 2.2–2.7 sigma depending on hadronic input; this motivates future theory refinements and higher-precision measurements. Plans for an upgraded program (E969) aim to push the precision toward ~0.2 ppm, enhancing sensitivity to possible new physics in the lepton sector.

Abstract

We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a_mu = (g-2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a_mu(Expt) = 11 659 208.0(5.4)(3.3) x 10^-10, where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a_mu includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ~0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e+e- hadronic cross sections, lie 2.2 - 2.7 standard deviations below the experimental result.

Figures (41)

• Figure 1: Relative number and asymmetry distributions versus electron fractional energy $y$ in the muon rest frame (left panel) and in the laboratory frame (right panel). The differential figure-of-merit product $NA^2$ in the laboratory frame illustrates the importance of the higher-energy electrons in reducing the measurement statistical uncertainty.
• Figure 2: Distribution of electron counts versus time for the 3.6 billion muon decays in the R01 $\hbox{$\mu^-$}$ data-taking period. The data is wrapped around modulo $100~\mu$s.
• Figure 3: Plan view of the pion/muon beamline. The pion decay channel is 80 m and the ring diameter is 14.1 m.
• Figure 4: The inflector/storage ring geometry. The downstream end of the inflector is shown, with the beam channel to the left of the storage region (larger radius). The ring center is to the right. Note the limited space between the pole pieces, which has to contain the inflector and its cryostat along with the beam vacuum chamber. The current in the inflector flows into the page in the "C" shaped arrangement of conductors just to the left of the beam channel, and out of the page in the conductors that form a backward "D". The superconductor crosses over the beam channel to connect the two coils.
• Figure 5: The phase space plot for the inflector exit from a beam transport simulation ($x$ is horizontal; $y$ is vertical). Left plot: $p_y/p_z = y'$ vs. $y$. Right plot: $p_x/p_z = x'$ vs. $x$. The inflector center is displaced from the storage ring central orbit by +77 mm. The ellipses represent the storage ring acceptance. After one quarter turn, the distribution in $x$ has rotated through 90 degrees and lies below the ring acceptance. It is then kicked toward more positive $x'$, into the ring acceptance.