CP-violating asymmetry in chargino decay into neutralino and W boson

In the MSSM with complex parameters, loop corrections to $\cha_i^\pm \to \neu_j^0 W^\pm$ lead to a CP violating asymmetry $\ACP = (\Gamma(\cha_i^+ \to \neu_j^0 W^+) - \Gamma(\cha_i^- \to \neu_j^0 W^-))/ (\Gamma(\cha_i^+ \to \neu_j^0 W^+) + \Gamma(\cha_i^- \to \neu_j^0 W^-))$. We calculate this asymmetry at full one-loop level. We perform a detailed numerical analysis for $\cha_1^\pm \to \neu_1^0 W^\pm$ and $\cha_2^\pm \to \neu_1^0 W^\pm$ analyzing the dependence on the parameters and phases involved. Asymmetries of several percent are obtained. We also discuss the feasability of measuring these asymmtries at LHC.