Spin decoherence and off-resonance behavior of radio-frequency-driven spin rotations in storage rings

High-frequency driven resonant spin rotators are routinely used as standard instruments in polarization experiments in particle and nuclear physics. Maintaining the continuous exact parametric spin resonance condition of the equality of the spin rotator and the spin precession frequency during operation is one of the challenges. We present a detailed analytical description of the effects of detuning the exact spin resonance on the precessing vertical and in-plane components of the polarization. An important part of the formalism presented here is the consideration of experimentally relevant spin decoherence effects. Within the developed formalism, we address the impact of feedback via pilot-bunch-based comagnetometry on continuous spin flips and on the related interpretation of charged-particle electric dipole moment searches using storage rings. We propose a spin-flip-based tomography of the longitudinal profile of polarization in a bunch, which is important for the evaluation of the polarization-dependent luminosity in collider experiments. We emphasize the potential importance of the previously unexplored phase of the horizontal polarization of the envelope as an indicator of the stability of radio-frequency-driven spin rotations in storage rings and as a testing ground for spin decoherence mechanisms.