Abstract
The predicted Standard Model (SM) electric dipole moments (EDMs) of electrons and quarks are tiny, providing an important window to observe new physics. Theories beyond the SM typically allow relatively large EDMs. The EDMs depend on the relative phases of terms in the effective Lagrangian of the extended theory, which are generally unknown. Underlying theories, such as string/M-theories compactified to four dimensions, could predict the phases and thus EDMs in the resulting supersymmetric (SUSY) theory. Earlier one of us, with collaborators, made such a prediction and found, unexpectedly, that the phases were predicted to be zero at tree level in the theory at the unification or string scale ∼ $$ \mathcal{O} $$ (1016 GeV). Electroweak (EW) scale EDMs still arise via running from the high scale, and depend only on the SM Yukawa couplings that also give the CKM phase. Here we extend the earlier work by studying the dependence of the low scale EDMs on the constrained but not fully known fundamental Yukawa couplings. The dominant contribution is from two loop diagrams and is not sensitive to the choice of Yukawa texture. The electron EDM should not be found to be larger than about 5 × 10−30 e cm, and the neutron EDM should not be larger than about 5 × 10−29 e cm. These values are quite a bit smaller than the reported predictions from Split SUSY and typical effective theories, but much larger than the Standard Model prediction. Also, since models with random phases typically give much larger EDMs, it is a significant testable prediction of compactified M-theory that the EDMs should not be above these upper limits. The actual EDMs can be below the limits, so once they are measured they could provide new insight into the fundamental Yukawa couplings of leptons and quarks. We comment also on the role of strong CP violation. EDMs probe fundamental physics near the Planck scale.
Highlights
Extensively [4]–[18]
Since we are interested in the size of the detectable electric dipole moments (EDMs), we look for the largest contributions from the Yukawa couplings, which will have the smallest powers of ǫ
Since generically in the M-theory framework we expect the trilinears to not be aligned with the Yukawas, we compute how large a phase one could get at the low scale given O(1) phases in the trilinear via the Yukawa matrix, and how this would enter into the expressions for the EDMs
Summary
We summarize the arguments from reference [19] that the high-scale soft-breaking supersymmetry Lagangian from the compactified M-theory leads to the prediction that the dominant CP-violation generating EDMs arises from the phases in the superpotential Yukawas, and has the same source as the CKM phase. The Kahler potential only depends on the real moduli fields, and the meson condensation φφ, so it introduces no explicit phases By removing overall phases one can see that ∂J K and ∂J Wand F − terms are real It is argued in [19] that higher order corrections to the Kahler potential exist, they do not give rise to new CP-violating phases. The conical singularities associated with different flavors do not carry the same charges under the U(1)’s in a given basis, which forbids the existence of off-diagonal terms Such terms can arise when the symmetries are spontaneously broken, but that should be suppressed.
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