A. Chapelain

We present details on a new measurement of the muon magnetic anomaly, $a_{\mu }=(g_{\mu }-2)/2$. The result is based on positive muon data taken at Fermilab’s Muon Campus during the 2019 and 2020 accelerator runs. The measurement uses $3.1\mathrm{GeV}/c$ polarized muons stored in a 7.1-m-radius storage ring with a 1.45 T uniform magnetic field. The value of $a_{\mu }$ is determined from the measured difference between the muon spin precession frequency and its cyclotron frequency. This difference is normalized to the strength of the magnetic field, measured using nuclear magnetic resonance. The ratio is then corrected for small contributions from beam motion, beam dispersion, and transient magnetic fields. We measure $a_{\mu }=116592057(25)\times {10}^{-11}$ (0.21 ppm). This is the world’s most precise measurement of this quantity and represents a factor of 2.2 improvement over our previous result based on the 2018 dataset. In combination, the two datasets yield $a_{\mu }(\mathrm{FNAL})=116592055(24)\times {10}^{-11}$ (0.20 ppm). Combining this with the measurements from Brookhaven National Laboratory for both positive and negative muons, the new world average is $a_{\mu }(\exp )=116592059(22)\times {10}^{-11}$ (0.19 ppm).

We present a new measurement of the positive muon magnetic anomaly, $a_{\mu }\equiv (g_{\mu }-2)/2$, from the Fermilab Muon $g-2$ Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ${\tilde{\omega }}_p^{\prime }$, and of the anomalous precession frequency corrected for beam dynamics effects, ${\omega }_a$. From the ratio ${\omega }_a/{\tilde{\omega }}_p^{\prime }$, together with precisely determined external parameters, we determine $a_{\mu }=116592057(25)\times {10}^{-11}$ (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain $a_{\mu }(\mathrm{FNAL})=116592055(24)\times {10}^{-11}$ (0.20 ppm). The new experimental world average is $a_{\mu }(\exp )=116592059(22)\times {10}^{-11}$ (0.19 ppm), which represents a factor of 2 improvement in precision.