Measurement of the anomalous spin precession frequency $\omega_a$ in the Muon $g-2$ experiment at Fermilab

The muon anomaly, $a_\mu=(g_\mu−2)/2$, is a low-energy observable which can be both measured and computed to high precision, making it a sensitive test of the Standard Model (SM) and a probe for new physics. The current discrepancy between the experimental value and the Standard Model calculation from the Muon g−2 Theory Initiative is $a_\mu^{exp} − a_\mu^{SM}=(251±59) \cdot 10^{−11}$, with a significance of 4.2$\sigma$. The Fermilab E989 experiment aims, with the full statistical power, to improve by a factor of four the precision of the measurement. In April 2021 the collaboration published the first measurement, based on the first year of data taking. This paper will present the status of the measurement of the anomalous muon spin precession frequency, $\omega_a$, performed on the datasets collected during Run-2 and Run-3 (2019 and 2020 campaigns), with a preliminary projection of the systematic uncertainties.