Analysis of CP Violation in Neutralino Decays to Tau Sleptons

In the minimal supersymmetric standard model, tau sleptons $\tilde \tau_{1,2}$ and neutralinos $\tilde \chi^0_{1,2}$ are expected to be among the lightest supersymmetric particles that can be produced copiously at future $e^+e^-$ linear colliders. We analyze $\tilde \tau$ pair and $\tilde \chi_1^0 \tilde \chi_2^0$ production under the assumption $m_{\tilde \chi_1^0} < m_{\tilde \tau_1} < m_{\tilde \chi_2^0}$, allowing the relevant parameters of the SUSY Lagrangian to have complex phases. We show that the transverse and normal components of the polarization vector of the $\tau$ lepton produced in $\tilde \chi_2^0$ decays offer sensitive probes of these phases.