CP asymmetries with Longitudinal and Transverse Beam Polarizations in Neutralino Production and Decay into the Z^0 Boson at the ILC

We study neutralino production at the linear collider with the subsequent two-body decays ~chi^0_i -> ~chi^0_n Z^0 and Z^0 -> l^+ l^-, with l=e, mu, tau, or Z^0 -> q q- with q=c,b. We show that transverse electron and positron beam polarizations allow the definition of unique CP observables. These are azimuthal asymmetries in the distributions of the final leptons or quarks. We calculate these CP asymmetries and the cross sections in the Minimal Supersymmetric Standard Model with complex higgsino and gaugino parameters mu and M_1. For final quark pairs, we find CP asymmetries as large as 30%. We discuss the significances for observing the CP asymmetries at the International Linear Collider (ILC). Finally we compare the CP asymmetries with those asymmetries which require unpolarized and/or longitudinally polarized beams only.