Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 experiment (2104.03247v1)

Abstract: The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has measured the muon anomalous precession frequency $\omega_a$ to an uncertainty of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data collected in four storage ring configurations during its first physics run in 2018. When combined with a precision measurement of the magnetic field of the experiment's muon storage ring, the precession frequency measurement determines a muon magnetic anomaly of $a_{\mu}({\rm FNAL}) = 116\,592\,040(54) \times 10^{-11}$ (0.46 ppm). This article describes the multiple techniques employed in the reconstruction, analysis and fitting of the data to measure the precession frequency. It also presents the averaging of the results from the eleven separate determinations of \omega_a, and the systematic uncertainties on the result.

• The paper achieves a 0.46 ppm precision in measuring the muon’s anomalous precession frequency using a controlled magnetic storage ring.
• The paper employs multiple analysis techniques, including event-based, integrated energy, and ratio methods to accurately determine the muon magnetic anomaly.
• The paper’s results reveal a slight discrepancy with Standard Model predictions, hinting at potential new physics.

Summary of the Fermilab Muon g-2 Experiment Results on Muon Anomalous Precession Frequency

The paper presents a detailed analysis and results from the Fermilab Muon g-2 experiment, aiming to measure the anomalous precession frequency ($\omega_a$) of the muon. This measurement is crucial for determining the muon magnetic anomaly ($a_{\mu}$), which is the difference between the muon's gyromagnetic ratio $g$ and 2, divided by 2. The precise determination of $a_{\mu}$ is a stringent test of the Standard Model (SM) of particle physics and serves as a potential indicator for new physics beyond the SM.

Experimental Design and Methodology

The Fermilab experiment capitalizes on the pioneering techniques of previous muon storage ring experiments at CERN and BNL. It involves the storage of polarized muon beams in a ring with a precisely known and uniform magnetic field. This setup allows for the measurement of the muon's spin precession frequency, which contains contributions from both the normal and anomalous magnetic moments.

The experiment's result for $a_{\mu}$ is derived from the combination of the precession frequency measurement and the accurate determination of the magnetic field within the storage ring. Multiple sophisticated techniques were employed in reconstructing, analyzing, and fitting the data to evaluate $\omega_a$ with a high degree of precision.

Key Results

• The experiment achieved a precision of 0.46 parts per million (ppm) in $\omega_a$.
• The resulting measurement of the muon anomaly was $$a_{\mu}(\text{FNAL}) = 116\,592\,040\, (54) \times 10^{-11}$$, which shows a small discrepancy with respect to the predicted value from the SM.
• This result represents the combination of uncertainties, mostly statistical, with a portion attributed to systematic and beam dynamic effects.

Analysis Techniques

The data analysis involved multiple independent methods, each with different sensitivities and systematic uncertainties. These include:

1. Event-based Methods: These use a threshold or asymmetry-weighted approach for selecting and analyzing decay positron events.
2. Integrated Energy Analysis: This method sums the calorimeter data to deduce the total energy, serving as a cross-check to event-based methods.
3. Ratio Methods: Designed to remove exponential decay and reduce slow-variate effects that may contaminate the data.

Systematic Considerations and Uncertainties

Several factors contribute to the systematic uncertainties in the measurement, such as:

• Detector gain fluctuations corrected through a laser calibration system.
• Calorimeter pileup corrections using multiple estimation methods.
• Residual effects from beam dynamics, such as coherent betatron oscillations (CBO), were modeled extensively.
• Muon losses and the temporal behavior of the muon beam were taken into consideration for precise fitting of precession frequencies.

Implications and Future Directions

The discrepancy between the measured value of $a_{\mu}(\text{FNAL})$ and the SM prediction may point towards new physics beyond the current theoretical models. This experiment represents a vital step in high-precision tests of fundamental physics principles. Future analyses of additional datasets from the Muon g-2 experiment, along with potential new theoretical advancements, will further clarify these discrepancies and refine our understanding of muonic and subatomic physics.

Overall, the results underscore the role of precision experimentation in testing the limits of the Standard Model and exploring the potential for new particles or interactions that could provide insight into unexplained phenomena in physics. Future developments in measurement techniques, theoretical models, or computational methodologies could further elucidate these results, making them a significant point of comparison for ongoing and forthcoming research in high-energy physics.