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.

Large experimental programmes in the fields of nuclear and particle physics search for evidence of physics beyond that explained by current theories. The observation of the Higgs boson completed the set of particles predicted by the standard model, which currently provides the best description of fundamental particles and forces. However, this theory's limitations include a failure to predict fundamental parameters, such as the mass of the Higgs boson, and the inability to account for dark matter and energy, gravity, and the matter-antimatter asymmetry in the Universe, among other phenomena. These limitations have inspired searches for physics beyond the standard model in the post-Higgs era through the direct production of additional particles at high-energy accelerators, which have so far been unsuccessful. Examples include searches for supersymmetric particles, which connect bosons (integer-spin particles) with fermions (half-integer-spin particles), and for leptoquarks, which mix the fundamental quarks with leptons. Alternatively, indirect searches using precise measurements of well predicted standard-model observables allow highly targeted alternative tests for physics beyond the standard model because they can reach mass and energy scales beyond those directly accessible by today's high-energy accelerators. Such an indirect search aims to determine the weak charge of the proton, which defines the strength of the proton's interaction with other particles via the well known neutral electroweak force. Because parity symmetry (invariance under the spatial inversion (x, y, z) → (-x, -y, -z)) is violated only in the weak interaction, it provides a tool with which to isolate the weak interaction and thus to measure the proton's weak charge . Here we report the value 0.0719 ± 0.0045, where the uncertainty is one standard deviation, derived from our measured parity-violating asymmetry in the scattering of polarized electrons on protons, which is -226.5 ± 9.3 parts per billion (the uncertainty is one standard deviation). Our value for the proton's weak charge is in excellent agreement with the standard model and sets multi-teraelectronvolt-scale constraints on any semi-leptonic parity-violating physics not described within the standard model. Our results show that precision parity-violating measurements enable searches for physics beyond the standard model that can compete with direct searches at high-energy accelerators and, together with astronomical observations, can provide fertile approaches to probing higher mass scales.

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The Jefferson Lab Q weak experiment determined the weak charge of the proton by measuring the parityviolating elastic scattering asymmetry of longitudinally polarized electrons from an unpolarized liquid hydrogen target at small momentum transfer. A custom apparatus was designed for this experiment to meet the technical challenges presented by the smallest and most precise ep asymmetry ever measured. Technical milestones were achieved at Jefferson Lab in target power, beam current, beam helicity reversal rate, polarimetry, detected rates, and control of helicity-correlated beam properties. The experiment employed 180 µA of 89% longitudinally polarized electrons whose helicity was reversed 960 times per second. The electrons were accelerated to 1.16 GeV and directed to a beamline with extensive instrumentation to measure helicitycorrelated beam properties that can induce false asymmetries. Møller and Compton polarimetry were used to measure the electron beam polarization to better than 1%. The electron beam was incident on a 34.4 cm liquid hydrogen target. After passing through a triple collimator system, scattered electrons between 5.8• and 11.6• were bent in the toroidal magnetic field of a resistive copper-coil magnet. The electrons inside this acceptance were focused onto eight fused silicaČerenkov detectors arrayed symmetrically around the beam axis. A total scattered electron rate of about 7 GHz was incident on the detector array. The detectors were read out in integrating mode by custom-built low-noise pre-amplifiers and 18-bit sampling ADC modules. The momentum transfer Q 2 = 0.025 GeV 2 was determined using dedicated low-current (∼100 pA) measurements with a set of drift chambers before (and a set of drift chambers and trigger scintillation counters after) the toroidal magnet.