Abstract

We explore the scenario where both the strong CP and Cabbibo-Kobayashi-Maskawa (CKM) phases are determined by the same axion field. Such a scenario is naturally realized in string compactifications. We find that there exists parameter region to realize the tiny strong CP phase and observed CKM phase in magnetized D-brane models.

Highlights

  • From the view point of string theory, the strong CP and CKM phases are not constants, but they are determined by the axion fields originated from the higher-dimensional gauge fields

  • It is natural to ask whether both phases have a common origin and at the same time, the observed value of the CKM phase is compatible with almost vanishing strong CP phase or not

  • We demonstrated that the axiodilaton appearing in the gauge kinetic function and the complex structure moduli in Yukawa couplings on magnetized D7-branes are entangled by certain three-form fluxes which lead to the massless direction in the moduli spaces of the axion-dilaton and one of the complex structure moduli

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Summary

Origin of the QCD and CKM phases

Let us first consider the origin of the QCD phase on gauge fields living on the magnetized D7a-brane wrapping the 4-cycle (T 2)j × (T 2)k with j = k, where the U(1) magnetic fluxes Fa are introduced as mja ls. We discuss the origin of the CKM phase in Yukawa couplings of matter fields living on magnetized D7-branes. Note that a higher-dimensional gauge coupling as well as the Kahler metric of the matter field are involved in the physical Yukawa couplings, but they are real The above calculation can be extended to the T 2/ZN orbifold, where the Yukawa couplings are provided by the linear combination of Yukawa couplings. (For more details, see Ref. [10].) we propose the mechanism to correlate the QCD phase to the CKM phase

Relation between the QCD and CKM phases
Concrete magnetized D-brane model
CP phase from the Yukawa couplings
Suppressed CP phase
Conclusions

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