High precision estimates of g − 2 and EDM in general spin precession in storage ring

We analyze the systematic uncertainties on the spin precession of particles in the storage ring, especially in the muon g−2/EDM project. Their particles have both anomalous magnetic moments (g−2) and electric dipole moments (EDM), and their positions and velocity directions have both O(10−3-10−4)≡O(ϵ) extensions. In order to measure these dipole moments up to 0.1 ppm or more we determine the precession frequency up to O(ϵ2). Our analytical formulation includes the Farley's pitch correction in the special case and can be applied to more general experimental setups.