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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The electromagnetic calorimeter for the new muon (g − 2) experiment at Fermilab will consist of arrays of PbF 2Č erenkov crystals read out by large-area silicon photo-multiplier (SiPM) sensors. We report here on measurements and simulations using 2.0 -4.5 GeV electrons with a 28-element prototype array. All data were obtained using fast waveform digitizers to accurately capture signal pulse shapes versus energy, impact position, angle, and crystal wrapping. The SiPMs were gain matched using a laser-based calibration system, which also provided a stabilization procedure that allowed gain correction to a level of 10 −4 per hour. After accounting for longitudinal fluctuation losses, those crystals wrapped in a white, diffusive wrapping exhibited an energy resolution σ/E of (3.4 ± 0.1) %/ E/GeV, while those wrapped in a black, absorptive wrapping had (4.6 ± 0.3) %/ E/GeV. The white-wrapped crystals-having nearly twice the total light collection-display a generally wider and impact-position-dependent pulse shape owing to the dynamics of the light propagation, in comparison to the black-wrapped crystals, which have a narrower pulse shape that is insensitive to impact position.

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We have developed a custom amplifier board coupled to a large-format 16-channel Hamamatsu silicon photomulplier device for use as the light sensor for the electromagnetic calorimeters in the Muon g − 2 experiment at Fermilab. The calorimeter absorber is an array of lead-fluoride crystals, which produces short-duration Cherenkov light. The detector sits in the high magnetic field of the muon storage ring. The SiPMs selected, and their accompanying custom electronics, must preserve the short pulse shape, have high quantum efficiency, be non-magnetic, exhibit gain stability under varying rate conditions, and cover a fairly large fraction of the crystal exit surface area. We describe an optimized design that employs the new-generation of thru-silicon via devices. The performance is documented in a series of bench and beam tests.