Large evolution of the bilinear Higgs coupling parameter in supersymmetric models and reduction of phase sensitivity

The phases in a generic low-energy supersymmetric model are severely constrained by the experimental upper bounds on the electric dipole moments of the electron and the neutron. Coupled with the requirement of radiative electroweak symmetry breaking, this results in a large degree of fine tuning of the phase parameters at the unification scale. In supergravity type models, this corresponds to very highly tuned values for the phases of the bilinear Higgs coupling parameter $B$ and the universal trilinear coupling $A_0$. We identify a cancellation/enhancement mechanism associated with the renormalization group evolution of $B$, which, in turn, reduces such fine-tuning quite appreciably without taking recourse to very large masses for the supersymmetric partners. We find a significant amount of reduction of this fine-tuning in nonuniversal gaugino mass models that do not introduce any new phases.
Comment: Version to appear in Phys.Rev.D. Insignificant changes like a few typos corrected. 26 pages, 7 figures, LaTex