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 violation in modular invariant flavor models

Kobayashi, Tatsuo; Shimizu, Yusuke; Takagi, Kenta; Tanimoto, Morimitsu; Tatsuishi, Takuya H.; Uchida, Hikaru

doi:10.1103/physrevd.101.055046

Cited by 80 publications

(43 citation statements)

References 73 publications

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“…The approach to unify CP and modular symmetries is recently developed in Refs. [8][9][10][11], and the relationship between the strong CP and CKM phases is also pointed out in Ref. [12].…”

Section: Introductionmentioning

confidence: 79%

Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes

Kobayashi

Otsuka

2020

Phys. Rev. D

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We systematically investigate the possibilities of realizing the spontaneous CP violation in Type IIB flux compactifications on toroidal orientifolds. Our detailed analysis for a generic choice of three-form fluxes leads to the presence of flat directions, where CP-breaking and-conserving vacua are degenerate, indicating that flux compactifications are not sufficient to realize the spontaneous CP violation. Furthermore, the four-dimensional CP can be embedded into the duality symmetries, namely modular symmetries for a particular choice of fluxes.

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“…The approach to unify CP and modular symmetries is recently developed in Refs. [8][9][10][11], and the relationship between the strong CP and CKM phases is also pointed out in Ref. [12].…”

Section: Introductionmentioning

confidence: 79%

Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes

Kobayashi

Otsuka

2020

Phys. Rev. D

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“…The same transformation of τ was also derived from the higher dimensional theories [94]. The four-dimensional CP symmetry can be embedded into (4 + d) dimensions as higher dimensional proper Lorentz symmetry with positive determinant.…”

Section: Jhep03(2021)010mentioning

confidence: 65%

“…It can predict the CP violating phase [92]. The modular invariance has been also studied combining with the generalized CP symmetry in flavor theories [93,94]. It provides a powerful framework to predict CP violating phases of quarks and leptons.…”

Section: Jhep03(2021)010mentioning

confidence: 99%

Spontaneous CP violation by modulus τ in A4 model of lepton flavors

Okada

Tanimoto

2021

J. High Energ. Phys.

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We discuss the modular A4 invariant model of leptons combining with the generalized CP symmetry. In our model, both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus τ. The source of the CP violation is a non-trivial value of Re[τ] while other parameters of the model are real. The allowed region of τ is in very narrow one close to the fixed point τ = i for both normal hierarchy (NH) and inverted ones (IH) of neutrino masses. The CP violating Dirac phase δCP is predicted clearly in [98°, 110°] and [250°, 262°] for NH at 3 σ confidence level. On the other hand, δCP is in [95°, 100°] and [260°, 265°] for IH at 5 σ confidence level. The predicted ∑mi is in [82, 102] meV for NH and ∑mi = [134, 180] meV for IH. The effective mass 〈mee〉 for the 0νββ decay is predicted in [12.5, 20.5] meV and [54, 67] meV for NH and IH, respectively.

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“…[19], shall be briefly mentioned below.) We focus first on modular transformations that are not CP-like and assume that the corresponding Kähler modulus T has been stabilized [55,56] at a self-dual point in moduli space. In other words, we suppose that T is stabilized at a vacuum expectation value (vev) T , at which there exists a nontrivial finite [57] subgroup H T ⊂ SL(2, Z) T that leaves T invariant.…”

Section: Local Flavor Unificationmentioning

confidence: 99%

Eclectic flavor scheme from ten-dimensional string theory – I. Basic results

2020

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String theory leads to a flavor scheme where modular symmetries play a crucial role. Together with the traditional flavor symmetries they combine to an eclectic flavor group, which we determine via outer automorphisms of the Narain space group. Unbroken flavor symmetries are subgroups of this eclectic group and their size depends on the location in moduli space. This mechanism of local flavor unification allows a different flavor structure for different sectors of the theory (such as quarks and leptons) and also explains the spontaneous breakdown of flavor-and CP-symmetries (via a motion in moduli space). We derive the modular groups, including CP and R-symmetries, for different sub-sectors of sixdimensional string compactifications and determine the general properties of the allowed flavor groups from this top-down perspective. It leads to a very predictive flavor scheme that should be confronted with the variety of existing bottom-up constructions of flavor symmetry in order to clarify which of them could have a consistent top-down completion.

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CP violation in modular invariant flavor models

Cited by 80 publications

References 73 publications

Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes

Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes

Spontaneous CP violation by modulus τ in A4 model of lepton flavors

Eclectic flavor scheme from ten-dimensional string theory – I. Basic results

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