Equation for spin decoherence rate in an all-electric ring

Abstract: There is a quantitative error in the derivation for the spin decoherence rate by Talman in IPAC2012. The crucial point is a subtle confusion between the concept of longitudinal' as inalong the reference orbit' and `parallel to the particle velocity.' They are $\it not$ the same direction, and the distinction is significant for high-precision experiments to search for a possible nonzero electric dipole moment (EDM) of a charged particle in a storage ring.