Gluino and Neutralino contribution to the direct CP violating parameter epsilon'

I present a detailed and complete calculation of the gluino and neutralino contribution to the direct CP violating parameter $\epsilon'$\ within the MSSM. I include the complete mixing matrices of the neutralinos and of the scalar partners of the left and right handed down quarks. I find that the neutralino contribution is generally small but can be larger than the gluino contribution for small values $m_S\le 400$\ GeV of the supersymmetric breaking scale.