Constrained MSSM and the electric dipole moment of the neutron

Solving the renormalization group equations analytically by iterations, we calculate the electric dipole moment (EDM) of the neutron in the MSSM with $\mathrm{CP}$-conserving soft-breaking parameters for the case of three and four generations. For the three-generation case we resolve the apparent discrepancies between order-of-magnitude estimates and numerical calculations existing in the literature. The nonvanishing result arises in first order in the renormalization group coefficient $t=\left(4\mathrm{}\pi {)}^{-2}\ln \right({\Lambda }^2{/M}_W^2).\mathrm{}$ The EDM of the neutron does not exceed ${10}^{-32}e\mathrm{cm}$ in this case. For the four-generation case we show that there is a significant enhancement which renders the EDM of the neutron at a measurable level of ${10}^{-26}e\mathrm{cm}.$