Effect of Electrostatic Deflectors and Fringe Fields on Spin for Hadron Electric Dipole Moment Measurements on Storage Rings

The observed matter-antimatter asymmetry in the universe cannot be explained by the Standard Model. An explanation is a non-vanishing Electric Dipole Moment of subatomic particles. The JEDI (Julich Electric Dipole moment Investigations) collaboration is preparing a direct EDM measurement of protons and deuterons first at the storage ring COSY (COoler SYnchrotron) and later at a dedicated storage ring. To achieve this, one needs a stable polarization, i.e. around 1000 seconds for spin coherence time. One source of decoherence are the electrostatic deflectors, and this must be quantified. We developed an analytical model for cylindrical deflectors, including fringe fields, and the associated beam and spin transfer functions, integrated over the deflector. All boundaries (including ground) are considered, giving a realistic, accurate field map up to any order. We get universal formulas, the only adjustable parameter being the deflector gap/radius ratio, all other terms being numerical. This has been implemented in BMAD. We present the mathematical, physical and numerical developments, as well as results for a proton storage ring.