Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm (2308.06230v2)

Abstract: We present a new measurement of the positive muon magnetic anomaly, $a_\mu \equiv (g_\mu - 2)/2$, 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, $\tilde{\omega}'^{}_p$, and of the anomalous precession frequency corrected for beam dynamics effects, $\omega_a$. From the ratio $\omega_a / \tilde{\omega}'^{}_p$, together with precisely determined external parameters, we determine $a_\mu = 116\,592\,057(25) \times 10^{-11}$ (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain $a_\mu\text{(FNAL)} = 116\,592\,055(24) \times 10^{-11}$ (0.20 ppm). The new experimental world average is $a_\mu (\text{Exp}) = 116\,592\,059(22)\times 10^{-11}$ (0.19 ppm), which represents a factor of 2 improvement in precision.

• The paper achieves a precise measurement of the muon anomalous magnetic moment at 0.20 ppm, significantly improving upon previous results.
• It employs a refined methodology using polarized muons in a storage ring with advanced calibration, reducing systematic uncertainties by over 50%.
• The findings, including a 5.0σ discrepancy with Standard Model predictions, underscore potential new physics beyond established theories.

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm

The paper "Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm" presents a significant advancement in the precise measurement of the muon anomaly, $a_\mu$, achieved by the Fermilab Muon $g-2$ Experiment. This effort builds upon the foundations laid by previous experiments, refining both the methodology and instrumentation to deliver a result with enhanced precision.

Content and Methodology

The paper describes the use of polarized muons at 3.1 GeV/c, injected into a storage ring at Fermilab, to measure $a_\mu$ through the detection of decay positrons. The number of detected positrons in the data analyzed from 2019 and 2020 is more than four times that of earlier runs. Critical improvements in the experimental setup and analysis methods have led to a reduction in systematic uncertainties by more than a factor of two.

The experiment relied on precise control and measurement of the storage ring conditions. Improvements included enhanced temperature stability and refined magnetic field measurements. Data were blinded to avoid bias, with the true value of the digitization clock altered during the analysis phase, necessitating sophisticated calibration and correction procedures.

Numerical Results

The primary result presented in the paper is: $$a_\mu (\text{FNAL}) = 116,592,055(24) \times 10^{-11} ~~~ (0.20~\text{ppm})$$

Notably, this result represents a significant tightening of precision compared to previous efforts. The experimental world average, combining results from this effort and the Brookhaven National Laboratory (BNL) in the past, is: $$a_\mu (\text{exp}) = 116,592,059(22)\times 10^{-11} ~~~ (0.19~\text{ppm})$$

Implications and Future Directions

From a theoretical standpoint, the paper highlights the critical role of $a_\mu$ as a stringent test of the Standard Model (SM). Any observed deviation from SM predictions could indicate new physics beyond the established theories. The comparison of the Fermilab results with SM predictions shows a 5.0 $\sigma$ discrepancy. However, a recent lattice QCD calculation and other emerging data on hadronic contributions may require an adjustment of the theoretical predictions.

On the experimental front, the work demonstrates a successful model for increasing measurement precision through both enhanced statistical analysis and systematic error reduction. As the collaboration proceeds with further data analysis, additional refinements are anticipated to further lower the uncertainties, possibly doubling the current precision.

Conclusion

This paper articulates a meticulously conducted experiment that reinforces Fermilab's standing in precision physics. The incrementally tighter constraints offered by $a_\mu$ measurements represent both a technical triumph in experimental physics and an enduring challenge in theoretical physics, signalling the possible necessity for refined or novel theories to accommodate these and future findings. Future prospects are bright as the ongoing analysis seeks to further dissect and interpret the intriguing anomalies posed by $a_\mu$.