Eclectic flavor group ∆(27) ⋊ S3 and lepton model building

Li, Cai-Chang; Ding, Gui-Jun

doi:10.1007/jhep03(2024)054

Cited by 6 publications

(3 citation statements)

References 35 publications

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“…A recent application of this connection for the traditional flavor group ∆( 27) has been discussed in refs. [83,84]. Moreover, BU constructions should avoid the excessive use of modular weights in model building.…”

Section: Discussionmentioning

confidence: 99%

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Flavor’s Delight

Nilles,

Ramos-Sánchez

2024

Entropy

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Discrete flavor symmetries provide a promising approach to understand the flavor sector of the standard model of particle physics. Top-down (TD) explanations from string theory reveal two different types of such flavor symmetries: traditional and modular flavor symmetries that combine to the eclectic flavor group. There have been many bottom-up (BU) constructions to fit experimental data within this scheme. We compare TD and BU constructions to identify the most promising groups and try to give a unified description. Although there is some progress in joining BU and TD approaches, we point out some gaps that have to be closed with future model building.

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Section: Discussionmentioning

confidence: 99%

“…There have been many BU constructions, but only a few take TD considerations into account [82][83][84]. From the presently available TD models, the groups ∆(54) for traditional and T ′ for modular flavor symmetry seem to be the favorite choices.…”

Section: Top-down Does Not Yet Meet Bottom-upmentioning

confidence: 99%

Flavor’s Delight

Nilles,

Ramos-Sánchez

2024

Entropy

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“…As a result, the minimal Kähler potential can be reproduced and the higher order corrections suppressed by powers of ⟨Φ⟩/Λ, where Λ denotes the cutoff scale and ⟨Φ⟩ represents the VEV of flavons breaking the traditional flavor symmetry. See [383,386,387] for model construction with EFG.…”

Section: Eclectic Flavor Symmetrymentioning

confidence: 99%

Neutrino mass and mixing with modular symmetry

Ding,

King

2024

Rep. Prog. Phys.

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This is a review article about neutrino mass and mixing and flavour model building strategies based on modular symmetry. After an introduction to neutrino mass and lepton mixing, we then turn to the main subject of this review, namely a pedagogical introduction to modular symmetry as a candidate for family symmetry, from the bottom-up point of view. After an informal introduction to modular symmetry, we introduce the modular group, and discuss its fixed points and residual symmetry, assuming supersymmetry throughout. We then introduce finite modular groups of level N and modular forms with integer or rational modular weights, corresponding to simple geometric groups or their double or metaplectic covers, including the most general finite modular groups and vector-valued modular forms, with detailed results for N=2,3,4,5. The interplay between modular symmetry and generalized CP symmetry is discussed, deriving CP transformations on matter multiplets and modular forms, highlighting the CP fixed points and their implications. In general, compactification of extra dimensions generally leads to a number of moduli, and modular invariance with factorizable and non-factorizable multiple moduli based on symplectic modular invariance and automorphic forms is reviewed. Modular strategies for understanding fermion mass hierarchies are discussed, including the weighton mechanism, small deviations from fixed points, and texture zeroes. Then examples of modular models are discussed based on single modulus A4 models, a minimal S′4 model of leptons (and quarks), and a multiple moduli model based on three S4 groups capable of reproducing the Littlest Seesaw model. We then extend the discussion to include Grand Unified Theories (GUTs) based on modular (flipped) SU(5) and SO(10). Finally we discuss top-down approaches, including eclectic flavour symmetry and moduli stabilisation.

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Universal predictions of Siegel modular invariant theories near the fixed points

Ding,

Feruglio,

Liu

2024

J. High Energ. Phys.

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We analyze a general class of locally supersymmetric, CP and modular invariant models of lepton masses depending on two complex moduli taking values in the vicinity of a fixed point, where the theory enjoys a residual symmetry under a finite group. Like in models that depend on a single modulus, we find that all physical quantities exhibit a universal scaling with the distance from the fixed point. There is no dependence on the level of the construction, the weights of matter multiplets and their representations, with the only restriction that electroweak lepton doublets transform as irreducible triplets of the finite modular group. Also the form of the kinetic terms, which here are assumed to be neither minimal nor flavor blind, is irrelevant to the outcome. The result is remarkably simple and the whole class of examined theories gives rise to five independent patterns of neutrino mass matrices. Only in one of them, the predicted scaling agrees with the observed neutrino mass ratios and lepton mixing angles, exactly as in single modulus theories living close to τ = i.

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Eclectic flavor group ∆(27) ⋊ S3 and lepton model building

Cited by 6 publications

References 35 publications

Flavor’s Delight

Flavor’s Delight

Neutrino mass and mixing with modular symmetry

Universal predictions of Siegel modular invariant theories near the fixed points

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