A new ratio Q-method analysis for precession frequency measurement in Muon g-2 experiment

In April, 2021, the Fermilab muon g-2 experiment reported its initial, 460 ppb, result for the muon anomalous magnetic moment, ɑ_µ, confirming the findings of the previous BNL experiment. Subsequent runs are underway with the ultimate goal of a 140 ppb determination of ɑ_µ. We discuss a new approach for the measurement of the muon anomalous precession frequency, ω_ɑ, in the g-2 experiment. The approach utilizes the combination of an energy integrating reconstruction(Q-method) of the decay positron time distribution and a ratio histogramming technique for the extraction of the precession frequency. The energy integrating approach offers reduced sensitivity to such systematics as pulse pileup and gain changes. The ratio histogramming technique offers reduced sensitivity to such systematics as muon losses and pedestal variations. This talk will provide an overview and status update of the combined Q-method reconstruction and the ratio method analysis of ω_ɑ for the Run 2 and Run 3 datasets, collected in 2019 and 2020.