The electron electric dipole moment (d_e) and the muon magnetic moment
anomaly (a_{\mu}) recently observed at BNL are analyzed within the framework of
SUGRA models with CP violating phases at the GUT scale. It is seen analytically
that even if d_e were zero, there can be a large Bino mass phase (ranging from
0 to 2 \pi) with a corresponding large B soft breaking mass phase (of size ~<
0.5 with sign fixed by the experimental sign of a_{\mu}). The dependence of the
B phase on the other SUSY parameters, gaugino mass m_{1/2}, \tan \beta, A_0, is
examined. The lower bound of a_{\mu} determines the upper bound of m_{1/2}. It
is shown analytically how the existence of a non-zero Bino phase reduces this
upper bound (which would correspondingly lower the SUSY mass spectra). The
experimental upper bound on d_e determines the range of allowed phases, and the
question of whether the current bound on d_e requires any fine tuning is
investigated. At the electroweak scale, the phases have to be specified to
within a few percent. At the GUT scale, however, the B phase requires fine
tuning below the 1% level over parts of the parameter space for low m_{1/2},
and if the current experimental bound on d_e were reduced by only a factor of
3-4, fine tuning below 1% would occur at both the electroweak and GUT scale
over large regions of the parameter space. All accelerator constraints (m_h >
114 GeV, b -> s \gamma, etc.) and relic density constraints with all
stau-neutralino co-annihilation processes are included in the analysis.Comment: 22 pages, latex, 14 figure
