Abstract
The Fermi National Accelerator Laboratory has measured the anomalous precession frequency $a^{}_\mu = (g^{}_\mu-2)/2$ of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7$^\circ$C. The measured field is weighted by the muon distribution resulting in $\tilde{\omega}'^{}_p$, the denominator in the ratio $\omega^{}_a$/$\tilde{\omega}'^{}_p$ that together with known fundamental constants yields $a^{}_\mu$. The reported uncertainty on $\tilde{\omega}'^{}_p$ for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb.
Highlights
The Muon g−2 Collaboration reports a new measurement of the positive muon magnetic anomaly aμ =/2 [1]
Equation (2) shows that determining aμ from ωa requires precise knowledge of the magnetic-field magnitude experienced by the muons, which we measured with pulsed proton nuclear magnetic resonance (NMR)
The analyses differed in the implementation of the veto window, the interpolation across the missing data, and the usage of other fixed probe stations to account for short-term field fluctuations
Summary
This paper provides data reconstruction, analysis, and systematic uncertainties of the measurement of the magnetic field in the muon storage ring. Loops have been calculated to higher precision [6] This new result, from the Run-1 data set, differs by 3.3 σ from the standard model prediction and agrees with the BNL E821 measurement. The combined experimental average results in a 4.2 σ discrepancy with the theoretical calculation Specific current distributions were used to minimize the field variations across the beam aperture to better than 1 ppm when averaged over the storage ring azimuth, and updated periodically in response to magnetic field drifts. In the cross-section system, it is replaced by z
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