CP Violation in the Width Difference of the Scalar Electron Decay due to Complex Gaugino Masses

We calculate the width difference of the scalar electron decay, $\Gamma(\tilde e_L \to e_L\omega) - \Gamma({\bar{\tilde e}}_L \to \bar e_L\omega)$ in the softly broken supersymmetrized standard model. The CP asymmetry is assumed to arise from the complex gaugino masses. Even in limit that the electron mass $m_e$ is vanishing, the difference can be of the order of $\alpha$.