Magnetic Field Measurement and Analysis for the Muon g-2 Experiment at Fermilab

TL;DR

This paper details the precise measurement and analysis of the magnetic field in the Fermilab Muon g-2 experiment, crucial for determining the muon's anomalous magnetic moment with high accuracy.

Contribution

It provides a comprehensive methodology for magnetic field measurement, calibration, and uncertainty analysis in the Muon g-2 experiment at Fermilab.

Findings

Measured magnetic field with 114 ppb uncertainty

Calibrated magnetic field using nuclear magnetic resonance

Quantified contributions to measurement uncertainty

Abstract

The Fermi National Accelerator Laboratory has measured the anomalous precession frequency $a^{}_\mu = (g^{}_\mu-2)/2$ of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7$^\circ$C. The measured field is weighted by the muon distribution resulting in $\tilde{\omega}'^{}_p$, the denominator in the ratio $\omega^{}_a$/$\tilde{\omega}'^{}_p$ that together with known fundamental constants yields $a^{}_\mu$. The reported uncertainty on $\tilde{\omega}'^{}_p$ for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb.