Study of systematic effects in the proton EDM experiment with a symmetric-hybrid ring design

The physics and ring design of the storage ring proton electric dipole moment (sr-pEDM) experiment, including the symmetries used to mitigate first-order and second-order systematic effects, are described in [Z. Omarov et al. Comprehensive symmetric-hybrid ring design for a proton edm experiment at below 10^-29 e · cm, Phys. Rev. D 105, 032001 (2022)]. The sr-pEDM experiment leverages a novel symmetric-hybrid, frozen-spin storage ring design using radial electric bending and alternate magnetic focusing to minimize systematic errors, enabling precise measurement of the vertical rotation of the polarization of polarized stored proton beams. In this work, we present a more systematic and detailed analysis of second-order effects, focusing in particular on the interplay between stray radial magnetic fields and electric quadrupole and sextupole fields. We demonstrate how the symmetries of the symmetric-hybrid ring design, including beam reversal and magnetic quadrupole polarity switching, can be used to suppress these effects to below the targeted sensitivity of the sr-pEDM experiment.