CP Violating Phases, Nonuniversal Soft Breaking And D-brane Models

The question of CP violating phases and electric dipole moments (EDMs)for the electron ($d_e$) and the neutron ($d_n$) for supergravity models with nonuniversal soft breaking is considered for models with a light ($\stackrel{<}{\sim}$1 TeV) mass spectrum and R-parity invariance. As with models with universal soft breaking (mSUGRA) one finds a serious fine tuning problem generally arises for $\theta_{0B}$ (the phase of the B soft breaking parameter at the GUT scale), if the experimental EDM constraints are obeyed and radiative breaking of $SU(2)_L\times U(1)_Y$ occurs. A D-brane model where $SU(3)_C\times U(1)_Y$ is associated with one set of 5-branes and $SU(2)_L$ with another intersecting set of 5-branes is examined, and the cancellation phenomena is studied over the parameter space of the model. Large values of $\theta_B$ (the phase of B at the electroweak scale) can be accommodated, though again $\theta_{0B}$ must be fine tuned. Using the conventional prescription for calculating $d_n$, one finds the region in parameter space where the experimental EDM constraints on both $d_e$ and $d_n$ hold is significantly reduced, and generally requires tan$\beta\stackrel{<}{\sim}$5 for most of the parameter space, though there are small allowed regions even for tan$\beta\stackrel{>}{\sim}$10. We find the Weinberg three gluon term generally makes significant contributions, and results are sensitive to the values of quark masses.