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 conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 µm, probing distances less than the dark-energy length scale λ d = 4 hc/ρ d ≈ 85 µm. We find with 95% confidence that the inverse-square law holds (|α| ≤ 1) down to a length scale λ = 56 µm and that an extra dimension must have a size R ≤ 44 µm.PACS numbers: 95.36.+x,04.80.Cc,12.38.Qk Recent cosmological observations [1,2,3] have shown that 70% of all the mass and energy of the Universe is a mysterious "dark energy" with a density ρ d ≈ 3.8 keV/cm 3 and a repulsive gravitational effect. This darkenergy density corresponds to a distance λ d = 4 hc/ρ d ≈ 85 µm that may represent a fundamental length scale of gravity [4,5]. Although quantum-mechanical vacuum energy should have a repulsive gravitational effect, the observed ρ d is between 10 60 to 10 120 times smaller than the vacuum energy density computed according to the standard laws of quantum mechanics. Sundrum [6] has suggested that this huge discrepancy (the "cosmological constant problem") could be resolved if the graviton were a "fat" object with a size comparable to λ d that would prevent it from "seeing" the short-distance physics that dominates the vacuum energy. His scenario implies that the gravitational force would weaken for objects separated by distances s < ∼ λ d . Dvali, Gabadaze and Senjanovíc [7] argue that a similar weakening of gravity could occur if there are extra time dimensions. In their scenario, the standard model particles are localized in "our" time, while the gravitons propagate in the extra time dimension(s) as well. Other scenarios predict the opposite behavior: the extra space dimensions of Mtheory would cause the gravitational force to get stronger for s < ∼ R where R is the size of the largest compactified dimension [8]. These considerations, plus others involving new forces from the exchange of proposed scalar or vector particles[9] motivated the tests of the gravitational inverse-square law we report in this Letter.Our tests were made with a substantially upgraded version of the "missing mass" torsion-balance instrument used in our previous inverse-square-law tests [10,11]. The instrument used in this work [12], shown in Fig. 1, consisted of a torsion-pendulum detector suspended by a thin ≈ 80-cm-long tungsten fiber above an attractor that was rotated with a uniform angular velocity ω by a geared-down stepper motor. The detector's 42 test bodies were 4.767-mm-diameter cylindrical holes machined into a 0.997-mm-thick molybdenum detector ring. The hole centers were arrayed in two circles, each of which had 21-fold azimuthal symmetry. The attractor had a similar 21-fold azimuthal symmetry and consisted of a 0.997 mm thick molybdenum disc with 42 3.178-mm-diameter holes mounted atop a thicker tantalum disc containing 21 6.352-mm-diameter holes. The gravitational interaction between the missing masses of the detector and attractor holes applied a torque on the detector that oscillated 21 times for eac...

Motivated by higher-dimensional theories that predict new effects, we tested the gravitational 1/r(2) law at separations ranging down to 218 microm using a 10-fold symmetric torsion pendulum and a rotating 10-fold symmetric attractor. We improved previous short-range constraints by up to a factor of 1000 and find no deviations from Newtonian physics.

Motivated by a variety of theories that predict new effects, we tested the gravitational 1/r 2 law at separations between 10.77 mm and 137 µm using two different 10-fold azimuthally symmetric torsion pendulums and rotating 10-fold symmetric attractors. Our work improves upon other experiments by up to a factor of about 100. We found no deviation from Newtonian physics at the 95% confidence level and interpret these results as constraints on extensions of the Standard Model that predict Yukawa or power-law forces. We set a constraint on the largest single extra dimension (assuming toroidal compactification and that one extra dimension is significantly larger than all the others) of R * ≤ 160 µm, and on two equal-sized large extra dimensions of R * ≤ 130 µm. Yukawa interactions with |α| ≥ 1 are ruled out at 95% confidence for λ ≥ 197 µm. Extra-dimensions scenarios stabilized by radions are restricted to unification masses M * ≥ 3.0 TeV/c 2 , regardless of the number of large extra dimensions. We also provide new constraints on power-law potentials V (r) ∝ r −k with k between 2 and 5 and on the γ5 couplings of pseudoscalars with m ≤ 10 meV/c 2 .

We present new measurements of the 7 Be(p,γ) 8 B cross section fromĒcm = 116 to 2460 keV, that incorporate several improvements over our previously published experiment, also discussed here. Our new measurements lead to S17(0) = 22.1 ± 0.6(expt) ± 0.6(theor) eV b based on data from Ecm = 116 to 362 keV, where the central value is based on the theory of Descouvemont and Baye. The theoretical error estimate is based on the fit of 12 different theories to our low energy data. We compare our results to other S17(0) values extracted from both direct ( 7 Be(p,γ) 8 B) and indirect (Coulomb dissociation and heavy-ion reaction) measurements, and show that the results of these 3 types of experiments are not mutually compatible. We recommend a "best" value, S17(0) = 21.4 ± 0.5(expt) ± 0.6(theor) eV b, based on the mean of all modern direct measurements below the 1 + resonance. We also present S-factors at 20 keV which is near the center of the Gamow window: the result of our measurements is S17(20) = 21.4 ± 0.6(expt) ± 0.6(theor) eV b, and the recommended value is S17(20) = 20.7 ± 0.5(expt) ± 0.6(theor) eV b.PACS numbers: 26.20+f, 26.65+t, 25.40Lw