CPviolating phases, nonuniversal soft breaking, and D-brane models

Abstract

The question of $\mathrm{CP}$ 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 $(\ensuremath{\lesssim}1\mathrm{TeV})$ mass spectrum and R-parity invariance. As with models with universal soft breaking (MSUGRA) one finds that a serious fine-tuning problem generally arises for ${\ensuremath{\theta}}_{0B}$ (the phase of the B soft breaking parameter at the GUT scale), if the experimental EDM constraints are obeyed and radiative breaking of ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{U(1)}_{Y}$ occurs. A D-brane model where ${\mathrm{SU}(3)}_{C}\ifmmode\times\else\texttimes\fi{}{U(1)}_{Y}$ is associated with one set of 5-branes and ${\mathrm{SU}(2)}_{L}$ 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 ${\ensuremath{\theta}}_{B}$ (the phase of B at the electroweak scale) can be accommodated, though again ${\ensuremath{\theta}}_{0B}$ 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 $\mathrm{tan}\ensuremath{\beta}\ensuremath{\lesssim}5$ for most of the parameter space, though there are small allowed regions even for $\mathrm{tan}\ensuremath{\beta}\ensuremath{\gtrsim}10.$ We find that the Weinberg three gluon term generally makes significant contributions, and the results are sensitive to the values of the quark masses.