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Abstract We present details of a high-accuracy absolute scalar magnetometer based on pulsed proton NMR. The B-field magnitude is determined from the precession frequency of proton spins in a cylindrical sample of water after accounting for field perturbations from probe materials, sample shape, and other corrections. Features of the design, testing procedures, and corrections necessary for qualification as an absolute scalar magnetometer are described. The device was tested at B = 1.45 T but can be modified for a range exceeding 1–3 T. The magnetometer was used to calibrate other NMR magnetometers and measure absolute magnetic field magnitudes to an accuracy of 19 parts per billion as part of a measurement of the muon magnetic moment anomaly at Fermilab. 

We present details on a new measurement of the muon magnetic anomaly, $a_{\mu }=(g_{\mu }-2)/2$. The result is based on positive muon data taken at Fermilab’s Muon Campus during the 2019 and 2020 accelerator runs. The measurement uses $3.1\mathrm{GeV}/c$polarized muons stored in a 7.1-m-radius storage ring with a 1.45 T uniform magnetic field. The value of $a_{\mu }$is determined from the measured difference between the muon spin precession frequency and its cyclotron frequency. This difference is normalized to the strength of the magnetic field, measured using nuclear magnetic resonance. The ratio is then corrected for small contributions from beam motion, beam dispersion, and transient magnetic fields. We measure $a_{\mu }=116592057\left(25\right)\times {10}^{-11}$(0.21 ppm). This is the world’s most precise measurement of this quantity and represents a factor of 2.2 improvement over our previous result based on the 2018 dataset. In combination, the two datasets yield $a_{\mu }\left(\mathrm{FNAL}\right)=116592055\left(24\right)\times {10}^{-11}$(0.20 ppm). Combining this with the measurements from Brookhaven National Laboratory for both positive and negative muons, the new world average is $a_{\mu }\left(\exp \right)=116592059\left(22\right)\times {10}^{-11}$(0.19 ppm). Published by the American Physical Society2024 

We present a new measurement of the positive muon magnetic anomaly, 𝑎𝜇≡(𝑔𝜇−2)/2, from the Fermilab Muon 𝑔−2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 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 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, 𝜔𝑝, and of the anomalous precession frequency corrected for beam dynamics effects, 𝜔𝑎. From the ratio 𝜔𝑎/𝜔𝑝, together with precisely determined external parameters, we determine 𝑎𝜇=116 592 057⁢(25)×10−11 (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain 𝑎𝜇⁡(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 2 improvement in precision. 

The ratio of the electric to magnetic form factors of the proton, μpGEp/GMp, has been measured for elastic electron-proton scattering with polarized beam and target up to four-momentum transfer squared Q2=5.66(GeV/c)2 using double spin asymmetry for target spin orientation aligned nearly perpendicular to the beam momentum direction. This measurement of μpGEp/GMp agrees with the Q2 dependence of previous recoil polarization data and reconfirms the discrepancy at high Q2 between the Rosenbluth and the polarization-transfer method with a different measurement technique and systematic uncertainties uncorrelated to those of the recoil-polarization measurements. The form factor ratio at Q2=2.06(GeV/c)2 has been measured as μpGEp/GMp=0.720±0.176stat±0.039sys, which is in agreement with an earlier measurement using the polarized target technique at similar kinematics. The form factor ratio at Q2=5.66(GeV/c)2 has been determined as μpGEp/GMp=0.244±0.353stat±0.013sys, which represents the highest Q2 measurement reached using double spin asymmetries with polarized target to date.