Beam Dynamics Corrections to the Spin Precession Frequency Measurement in the Muon g-2 Experiment*

The Muon g-2 Experiment at Fermilab aims to measure the anomalous magnetic moment of the muon to a record precision of 140 parts per billion (ppb) in order to test the agreement between experiment and the Standard Model. The previous experiment at Brookhaven National Laboratory (BNL) reported a discrepancy of about 3-sigma in 2004. In 2021, the current experiment at Fermilab reported an initial 460-ppb measurement from Run-1 which supported the BNL result, with much more data soon to come.

The experimental method involves positive muon injection into a superconducting magnetic storage ring. While stored, the muon spins precess relative to the beam momentum at a rate which depends on the anomalous magnetic moment. Through parity violation in muon decays, this anomalous spin precession frequency is observable in the energy spectrum of the muons' daughter positrons as a function of time. Combined with a precision measurement of the storage ring's magnetic field, the anomalous spin precession frequency yields the anomalous magnetic moment.

However, there are complications which arise due to beam dynamics within the storage ring, necessitating important corrections. Two effects, known as the electric field and pitch corrections, account for fundamental beam dynamics contributions to the relationship between the spin precession frequency and the magnetic moment. Other corrections arise from biases in the measured spin precession frequency caused by systematic changes in the stored muon ensemble's characteristics over time. This talk will describe the evaluation of these beam dynamics corrections and their uncertainties, with a focus on the electric field and pitch corrections.