CP violation in Semi-Leptonic $\tau$ decays

We study CP violation in semi-leptonic $\tau$ decays and we determine the conditions necessary to be able to define a observable CP asymmetry. We apply these conditions in both models, the standard model for the electroweak interactions and its supersymmetric extensions. In the first case, the leading order contribution to the direct CP asymmetry in $\tau^{\pm} \to K^{\pm}\pi^0 \nu_{\tau}$ decay rates is evaluated. In the second case,we compute the SUSY effective hamiltonian that describes the $|\Delta S|=1$ semileptonic decays of tau leptons. We show that SUSY contributions may enhance the CP asymmetry of $\tau \to K \pi \nu_{\tau}$ decays by several orders of magnitude compared to the standard model expectations.