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.

A new measurement of the magnetic anomaly a μ of the positive muon is presented based on data taken from 2020 to 2023 by the Muon g − 2 Experiment at Fermi National Accelerator Laboratory (FNAL). This dataset contains over 2.5 times the total statistics of our previous results. From the ratio of the precession frequencies for muons and protons in our storage ring magnetic field, together with precisely known ratios of fundamental constants, we determine a μ = 1 165 920 710 ( 162 ) × 10 − 12 (139 ppb) for the new datasets, and a μ = 1 165 920 705 ( 148 ) × 10 − 12 (127 ppb) when combined with our previous results. The new experimental world average, dominated by the measurements at FNAL, is a μ ( exp ) = 1 165 920 715 ( 145 ) × 10 − 12 (124 ppb). The measurements at FNAL have improved the precision on the world average by over a factor of 4.

We observe a deuteron beam polarization lifetime near 1000 s in the horizontal plane of a magnetic storage ring (COSY). This long spin coherence time is maintained through a combination of beam bunching, electron cooling, sextupole field corrections, and the suppression of collective effects through beam current limits. This record lifetime is required for a storage ring search for an intrinsic electric dipole moment on the deuteron at a statistical sensitivity level approaching ${10}^{-29}e\mathrm{cm}$.

A new method to determine the spin tune is described and tested. In an ideal planar magnetic ring, the spin tune—defined as the number of spin precessions per turn—is given by ${\nu }_{\mathrm{s}}=\gamma G$ ($\gamma$ is the Lorentz factor, $G$ the gyromagnetic anomaly). At $970\mathrm{MeV}/c$, the deuteron spins coherently precess at a frequency of $\approx 120\mathrm{kHz}$ in the Cooler Synchrotron COSY. The spin tune is deduced from the up-down asymmetry of deuteron-carbon scattering. In a time interval of 2.6 s, the spin tune was determined with a precision of the order ${10}^{-8}$, and to $1\times {10}^{-10}$ for a continuous 100 s accelerator cycle. This renders the presented method a new precision tool for accelerator physics; controlling the spin motion of particles to high precision is mandatory, in particular, for the measurement of electric dipole moments of charged particles in a storage ring.

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).

This Letter reports the successful use of feedback from a spin polarization measurement to the revolution frequency of a $0.97\mathrm{GeV}/c$ bunched and polarized deuteron beam in the Cooler Synchrotron (COSY) storage ring in order to control both the precession rate ($\approx 121\mathrm{kHz}$) and the phase of the horizontal polarization component. Real time synchronization with a radio frequency (rf) solenoid made possible the rotation of the polarization out of the horizontal plane, yielding a demonstration of the feedback method to manipulate the polarization. In particular, the rotation rate shows a sinusoidal function of the horizontal polarization phase (relative to the rf solenoid), which was controlled to within a 1 standard deviation range of $\sigma =0.21\mathrm{rad}$. The minimum possible adjustment was 3.7 mHz out of a revolution frequency of 753 kHz, which changes the precession rate by $26\mathrm{mrad}/\mathrm{s}$. Such a capability meets a requirement for the use of storage rings to look for an intrinsic electric dipole moment of charged particles.