CP-Violating Phases in SUSY, Electric Dipole Moments, and Linear Colliders

We reexamine large CP-violating phases in the general Minimal Supersymmetric Standard Model, as well as more restricted models. We perform a detailed scan over parameter space to find solutions which satisfy the current experimental limits on the electric dipole moments of the electron, neutron and $^{199}$Hg atom, exploring the allowed configurations of phases and masses, and we attempt to quantify the level of tuning of the parameters necessary to populate the regions of cancellations. We then consider the measurement of CP-violating phases at a future linear collider. We find that measurements of chargino and neutralino masses and production cross-sections allow for a determination of $\phi_1$(the phase of $M_1$) to a precision of $\pi/30$, while the EDM constraints require that $\theta_\mu$ be too small to be measured. Using the EDM constraints we find that the CP-even model parameters and the phase $\phi_1$ can be determined at a Linear Collider with $400 \gev$ c.m. energy. As long as some information on the size of $|\mu|$ is included in the observables, a measurement of $\phi_1$ is guaranteed for $\phi_1 > \pi/10$. To unambiguously identify CP violation, we construct CP-odd kinematical variables at a linear collider. However, the CP asymmetries are rather small, typically about $0.1-1.5%$, and it will be challenging to experimentally observe the predicted asymmetries.