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.

We have measured the spin structure functions g p 2 and g d 2 and the virtual photon asymmetries A p 2 and A d 2 over the kinematic range 0.02 ≤ x ≤ 0.8 and 0.7 ≤ Q 2 ≤ 20 GeV 2 by scattering 29.1 and 32.3 GeV longitudinally polarized electrons from transversely polarized NH3 and 6 LiD targets. Our measured g2 approximately follows the twist-2 Wandzura-Wilczek calculation. The twist-3 reduced matrix elements d p 2 and d n 2 are less than two standard deviations from zero. The data are inconsistent with the Burkhardt-Cottingham sum rule if there is no pathological behavior as x → 0. The Efremov-Leader-Teryaev integral is consistent with zero within our measured kinematic range. The absolute value of A2 is significantly smaller than the A2 < R(1 + A1)/2 limit.

Among the most fundamental observables of nucleon structure, electromagnetic form factors are a crucial benchmark for modern calculations describing the strong interaction dynamics of the nucleon's quark constituents; indeed, recent proton data have attracted intense theoretical interest. In this Letter, we report new measurements of the proton electromagnetic form factor ratio using the recoil polarization method, at momentum transfers Q2=5.2, 6.7, and 8.5  GeV2. By extending the range of Q2 for which G(E)(p) is accurately determined by more than 50%, these measurements will provide significant constraints on models of nucleon structure in the nonperturbative regime.

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