Systematic Errors in General Spin Precession in Storage Ring

TL;DR

This paper analyzes systematic errors affecting spin precession measurements in storage rings, crucial for precise muon g-2 and EDM experiments, by developing an analytical framework that accounts for small positional and velocity deviations.

Contribution

It provides a comprehensive analytical formulation for systematic errors in spin precession, including the Farley's pitch correction, applicable to various experimental configurations.

Findings

Quantifies the impact of small positional and velocity deviations on spin precession.

Develops an analytical model including the Farley's pitch correction.

Enhances precision in measuring muon g-2 and EDM by accounting for systematic errors.

Abstract

We analyse the systematic errors on the spin precession of particles in the storage ring, especially in the muon g-2/EDM project. There particles have both anomalous magnetic moments (g-2) and elctric dipole moments(EDM), and their positions and velocity directions have both $O(10^{-3}-10^{-4})\equiv O(\epsilon)$ extensions. In order to measure these dipole moments up to $0.1$ppm or more we determine the precession frequency up to $O(\epsilon^2)$. Our analytical formulation includes the Farley's pitch correction in the special case and can be applied to more general experimental setups.