We present a new measurement of the positive muon magnetic anomaly, a µ ≡ (gµ − 2)/2, from the Fermilab Muon g −2 Experiment based on data collected in 2019 and 2020. We have analyzed more than four 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 two due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω′ p , and of the anomalous precession frequency corrected for beam dynamics effects, ωa. From the ratio ωa/ω ′ p , together with precisely determined external parameters, we determine a µ = 116 592 057(25) × 10 −11 (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a µ (FNAL) = 116 592 055(24) × 10 −11 (0.20 ppm). The new experimental world average is aµ(Exp) = 116 592 059(22) × 10 −11 (0.19 ppm), which represents a factor of two improvement in precision.

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A single calorimeter station for the Muon g − 2 experiment at Fermilab includes the following subsystems: a 54-element array of PbF 2 Cherenkov crystals read out by large-area SiPMs, bias and slow-control electronics, a suite of 800 MSPS waveform digitizers, a clock and control distribution network, a gain calibration and monitoring system, and a GPU-based frontend read out through a MIDAS data acquisition environment. The entire system performance was evaluated using 2.5 − 5 GeV electrons at the End Station Test Beam at SLAC. This paper includes a description of the individual subsystems and the results of measurements of the energy response and resolution, energy-scale stability, timing resolution, and spatial uniformity. All measured performances meet or exceed the g − 2 experimental requirements. Based on the success of the tests, the complete production of the required 24 calorimeter stations has been made and installation into the main experiment is complete. Furthermore, the calorimeter response measurements determined here informed the design of the reconstruction algorithms that are now employed in the running g − 2 experiment. to determine the anomalous magnetic moment a µ ≡ (g − 2)/2 of the muon to a relative precision of 140 parts per billion (ppb). The measurement is made by observing the spin precession frequency ω s relative to the cyclotron frequency ω c for muons orbiting a highly uniform magnetic storage ring with