Supplement: Methods for Data Analysis and Systematic Corrections in the Fermilab E989 Muon g-2 Experiment

A high-precision comparison of measurements and theoretical calculations of the muon's anomalous magnetic moment constitutes a test of the completeness of the Standard Model. In the Brookhaven E821 experiment, which completed data taking in 2001, the muon's anomalous magnetic moment was measured to a precision of 0.54 parts-per-million (ppm). The result from that experiment lies some tantalizing ~3.5 standard deviations from the Standard Model theoretical value. In the Fermilab E989 experiment, which began data taking in 2017, the precision on the anomalous magnetic moment will be improved by nearly a factor of four to the level of 0.14 ppm, thus presenting the possibility for a definitive claim of evidence for new physics, provided the experimental and theoretical central values do not change significantly. In the experiment, relativistic "magic momentum" muons will be stored and subsequently undergo cyclotron orbits within a 1.45 Tesla superconducting magnetic storage ring, with electric fields employed for confinement. This award supports work on systematic corrections to the muon's cyclotron and spin precession frequencies, the difference of which is proportional to the anomalous magnetic moment, resulting from muon transport through the small non-uniformities in the magnetic fields inevitably present over the volume of the storage ring and the magnetic fields resulting from the muons' relativistic motion through the electric fields. Methods for modeling and simulating these systematic effects will be developed by the PI and a graduate student under this award.