Sizable electron/neutron electric dipole moment inD3/D7μ-split supersymmetry

Abstract

Within the framework of $\mathcal{N}=1$ gauged supergravity, using a phenomenological model that can be obtained locally as a Swiss-cheese Calabi-Yau string-theoretic compactification with a mobile $D3$-brane localized on a nearly special Lagrangian three cycle in the Calabi-Yau and fluxed stacks of wrapped $D7$-branes, and which provides a natural realization of $\ensuremath{\mu}$-split supersymmetry (SUSY), we show that in addition to getting a significant value of an [electron/neutron (e/n)] electron dipole moment (EDM) at two-loop level, one can obtain a sizable contribution of (e/n) EDM even at one-loop level due to the presence of heavy supersymmetric fermions nearly isospectral with heavy sfermions. Unlike traditional split SUSY models in which the one-loop diagrams do not give significant contribution to the EDM of the electron/neutron because of very heavy sfermions existing as propagators in the loop, we show that one obtains a ``healthy'' value of the EDM in our model because of the presence of a heavy Higgsino, neutralino/chargino, and gaugino as fermionic propagators in the loops. The independent $CP$-violating phases are generated from nontrivial distinct phase factors associated with four Wilson line moduli [identified with first-generation leptons and quarks and their $SU(2{)}_{L}$-singlet cousins] as well as the $D3$-brane position moduli (identified with two Higgses), and the same are sufficient to produce overall distinct phase factors corresponding to all possible effective Yukawas as well as effective gauge couplings that we discuss in the context of $\mathcal{N}=1$ gauged supergravity action. However, the complex phases responsible to generate a nonzero EDM at one-loop level mainly appear from an off-diagonal contribution of sfermion as well as Higgs mass matrices at the electroweak scale (EW). In our analysis, we obtain a dominant contribution of the electron/neutron EDM around ${d}_{e}/e\ensuremath{\equiv}\mathcal{O}(1{0}^{\ensuremath{-}29})\text{ }\text{ }\mathrm{cm}$ from two-loop diagrams involving heavy sfermions and a light Higgs, and ${d}_{e}/e\ensuremath{\equiv}\mathcal{O}(1{0}^{\ensuremath{-}32})\text{ }\text{ }\mathrm{cm}$ from a one-loop diagram involving a heavy chargino and a light Higgs as propagators in the loop. The neutron EDM gets a dominant contribution of the order ${d}_{n}/e\ensuremath{\equiv}\mathcal{O}(1{0}^{\ensuremath{-}33})\text{ }\text{ }\mathrm{cm}$ from the one-loop diagram involving SM-like quarks and Higgs. To justify the possibility of obtaining a large EDM value in the case of a Barr-Zee diagram which involves ${W}^{\ifmmode\pm\else\textpm\fi{}}$ and the Higgs (responsible to generate the nontrivial $CP$-violating phase) in the two-loop diagrams as discussed by Leigh et al. [Nucl. Phys. B267, 509 (1986)], we provide an analysis of the same in the context of our $D3/D7$ $\ensuremath{\mu}$-split SUSY model at the EW scale. By conjecturing that the $CP$-violating phase can appear from the diagonalization of the Higgs mass matrix obtained in the context of $\ensuremath{\mu}$-split SUSY, we also get an EDM of the electron/neutron around $\mathcal{O}(1{0}^{\ensuremath{-}27})\text{ }\text{ }e\text{ }\mathrm{cm}$ in the case of the two-loop diagram involving ${W}^{\ifmmode\pm\else\textpm\fi{}}$ bosons.