Ratio Method to Extract the Anomalous Muon Spin Precession Frequency in the Fermilab Muon g-2 Experiment

The Fermilab Muon g-2 Experiment published its first measurement of the muon magnetic anomaly in April 2021. This measurement, based on Run 1 data, achieved a precision of 0.46 ppm. It confirmed the Brookhaven measurement and pushed the discrepancy with the Standard Model theory prediction to 4.2 sigma. Run 1 accounts for just 6% of the total anticipated data, and analysis of Runs 2 & 3 data is ongoing. The additional statistics from these datasets, as well as improved treatments of systematic effects, is expected to improve the measurement's precision by a factor of two compared to Run 1. One of the measurement's key inputs, the anomalous muon spin precession frequency, is extracted from the time modulation of the decay-positron energy spectrum. One technique for performing this analysis, known as the Ratio Method, time shifts the positron counts to reduce sensitivities to slowly varying effects over the measurement period. This talk will motivate the Ratio Method, describe its methodology, highlight improvements since Run 1, and provide a preliminary look at blinded Runs 2 & 3 data.