A Healthy Electron/Neutron EDM in D3/D7 mu-Split-Like SUSY

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Within the framework of N=1 gauged supergravity, using a phenomenological model which can be obtained locally as a Swiss-Cheese Calabi-Yau string-theoretic compactification with a mobile D3-brane localized on a nearly sLag three-cycle in the Calabi-Yau and fluxed stacks of wrapped D7-branes, and which provides a natural realization of mu-Split SUSY, we show that in addition to getting a significant value of electron/neutron EDM dₑ,ₙ/e at two-loop level, one can obtain a sizable contribution of dₑ,ₙ/e even at one-loop level. We obtain dₑ/e O(10⁻²⁹) cm from two-loop diagrams involving heavy sfermions and a light Higgs, and dₑ/e O(10⁻³²) cm from one-loop diagram involving heavy chargino and a light Higgs. Also, dₙ/e O(10⁻³³) cm from one-loop diagram involving SM-like quarks and Higgs. Next, by considering a Barr-Zee diagram involving W bosons and Higgs, and conjecturing that the CP-violating phase can appear from a linear combination of Higgs doublet obtained in the context of mu-split SUSY, we obtain dₑ,ₙ/e O(10⁻²⁷) cm at two-loop level.