Imperfections in the Crab-Waist Scheme

The crab-waist collision scheme has been the baseline choice for SuperKEKB and future circular $e^+e^-$ colliders. Achieved through properly phased sextupoles, the crab-waist transform is essential in suppressing beam-beam resonances, thereby enabling high luminosity in these colliders. In this paper, we explore potential sources of imperfections that may compromise the effectiveness of the crab-waist transform. We begin by reviewing the theoretical framework of the ideal crab-waist scheme and the associated weak-strong beam-beam resonances. Following this, we analyze how machine imperfections could amplify these resonances, thereby impacting collider performance. Finally, we briefly address the connections between theoretical models, simulations, and beam experiments, with a particular focus on the use of weak-strong beam experiments to identify and diagnose potential imperfections in machine settings.