A CP asymmetry in e^+e^- to chi⁰_ichi⁰_j to chi⁰_j τ stau_k with tau polarization

We propose a CP-odd asymmetry in the supersymmetric process e^+e^- \to \chi^0_i \chi^0_j \to \chi^0_j \tau stau_k by means of the transverse \tau polarization. We calculate the asymmetry and cross sections at a future linear collider in the 500 GeV c.m.s. energy range with longitudinal polarized beams and high luminosity. We work in the Minimal Supersymmetric Standard Model with complex parameters \mu, M_1 and A_\tau. The asymmetry can reach values up to 60 %. We also estimate the sensitivity for measuring the \tau polarization necessary to probe the CP asymmetry.