Supersymmetric phases, the electron electric dipole moment and the muon magnetic moment

Abstract

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.