Incoherent horizontal emittance growth due to the interplay of beam-beam interaction and longitudinal wakefield in crab-waist colliders

In this paper, we investigate incoherent quadrupolar synchrobetatron resonances caused by beam-beam collisions and their interplay with longitudinal wakefields in the context of crab-waist colliders. We present a comprehensive theoretical review of the established theory of synchrobetatron resonances and extend the formalism to explore horizontal synchrobetatron resonances specific to crab-waist colliders. As a case study, we examine incoherent horizontal emittance growth at the SuperKEKB and demonstrate through simulations that the interplay between beam-beam and longitudinal wakefields leads to a horizontal blowup of the bunch size and that the study of the dynamics can be reduced to the horizontal-longitudinal plane, independent of the motion in the vertical dimension. We present extensive simulation results using the codes , y, and , connect our analytical findings with these findings, and propose strategies to mitigate horizontal blowup.