Constraints on supersymmetric soft phases from renormalization group relations

By using relations derived from renormalization group equations (RGEs), we find that strong indirect constraints can be placed on the top squark mixing phase in $A_t$ from the electric dipole moment of the neutron ${(d}_n$). Since $m_t$ is large, any GUT-scale phase in $A_t$ feeds into other weak scale phases through RGEs, which in turn contribute to $d_n$. Thus CP-violating effects due to a weak-scale $A_t$ are strongly constrained. We find that $|\mathrm{Im}{A}_t^{\mathrm{EW}}|$ must be smaller than or of order |Im ${\mathit{B}}^{\mathrm{EW}}$|, making the electric dipole moment of the top quark unobservably small in most models. Quantitative estimates of the contributions to $d_n$ from $A_u$, $A_d$, and B show that substantial fine-tuning is still required to satisfy the experimental bound on $d_n$. While the low energy phases of the A's are not as strongly constrained as the phase of ${\mathit{B}}^{\mathrm{EW}}$, we note that the phase of a universal ${\mathit{A}}^{\mathrm{GUT}}$ induces large contributions in the phase of ${\mathit{B}}^{\mathrm{EW}}$ through RGEs, and is thus still strongly constrained in most models with squark masses below a TeV.