Systematic Errors in General Spin Precession in Storage Ring

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.