Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon g-2 Experiment for the positive muon magnetic anomaly a_{μ}≡(g_{μ}-2)/2. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ω_{a} between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ω[over ˜]_{p}^{'} in a spherical water sample at 34.7 °C. The ratio ω_{a}/ω[over ˜]_{p}^{'}, together with known fundamental constants, determines a_{μ}(FNAL)=116 592 040(54)×10^{-11} (0.46 ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both μ^{+} and μ^{-}, the new experimental average of a_{μ}(Exp)=116 592 061(41)×10^{-11} (0.35 ppm) increases the tension between experiment and theory to 4.2 standard deviations.

Muon (g- 2): experiment and theory

A review of the experimental and theoretical determinations of the anomalous magnetic moment of the muon is given. The anomaly is defined bya= (g- 2)/2, where the Landég-factor is the proportionality constant that relates the spin to the magnetic moment. For the muon, as well as for the electron and tauon, the anomalyadiffers slightly from zero (of the order 10^-3) because of radiative corrections. In the Standard Model, contributions to the anomaly come from virtual 'loops' containing photons and the known massive particles. The relative contribution from heavy particles scales as the square of the lepton mass over the heavy mass, leading to small differences in the anomaly fore, μ and τ. If there are heavy new particles outside the Standard Model which couple to photons and/or leptons, the relative effect on the muon anomaly will be ∼ (m_μ/m_e)²≈ 43 × 10³larger compared with the electron anomaly. Because both the theoretical and experimental values of the muon anomaly are determined to high precision, it is an excellent place to search for the effects of new physics or to constrain speculative extensions to the Standard Model. Details of the current theoretical evaluation and of the series of experiments that culminates with E821 at the Brookhaven National Laboratory, are given. At present the theoretical and the experimental values are known with a similar relative precision of 0.5 ppm. There is, however, a 3.4 standard-deviation difference between the two, strongly suggesting the need for continued experimental and theoretical study.