Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$

Kikuchi, Shota; Kobayashi, Tatsuo; Nasu, Kaito; Takada, Shohei; Uchida, Hikaru

doi:10.1007/jhep04(2024)045

Cited by 6 publications

(1 citation statement)

References 83 publications

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“…For instance, N 2 (H) is isomorphic to (S 3 × S 3 ) ⋊ Z 2 and S 4 × Z 2 respectively for the two-dimensional loci in equation (6.37). Fermion mass models based on symplectic modular symmetry are given in [209,232,236].…”

Section: Siegel Modular Forms and Gcp In Symplectic Modularmentioning

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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Section: Siegel Modular Forms and Gcp In Symplectic Modularmentioning

confidence: 99%

Neutrino mass and mixing with modular symmetry

Ding,

King

2024

Rep. Prog. Phys.

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Finite modular axion and radiative moduli stabilization

Higaki,

Kawamura,

Kobayashi

2024

J. High Energ. Phys.

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We propose a simple setup which can stabilize a modulus field of the finite modular symmetry by the Coleman-Weinberg potential. Our scenario leads to a large hierarchy suppressing instanton-like corrections e2πiτ and to a light axion identified as Reτ, where τ is the modulus field. This stabilization mechanism provides the axion solution to the strong CP problem. The potential has a minimum at a large Imτ which suppresses explicit U(1)PQ violation terms proportional to e−2πImτ, and hence the quality of the axion is ensured by the residual symmetry associated with the T-transformation, τ → τ + 1, around the fixed point τ ∼ i∞.

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Quark and lepton modular models from the binary dihedral flavor symmetry

Arriaga-Osante,

Liu,

Ramos-Sánchez

2024

J. High Energ. Phys.

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Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D3. After building the vector-valued modular forms in the representations of 2D3 with small modular weights, we systematically classify all (Dirac and Majorana) mass textures of fermions with fractional modular weights and all possible 2 + 1-family structures. This allows us to explore the parameter space of fermion models based on 2D3, aiming at a description of both quarks and leptons with a minimal number of parameters and best compatibility with observed data. We consider the separate possibilities of neutrino masses generated by either a type-I seesaw mechanism or the Weinberg operator. We identify a model that, besides fitting all known flavor observables, delivers predictions for six not-yet measured parameters and favors normal-ordered neutrino masses generated by the Weinberg operator. It would be interesting to figure out whether it is possible to embed our model within a top-down scheme, such as $${\mathbb{T}}^{2}/{\mathbb{Z}}_{4}$$ heterotic orbifold compactifications.

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Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$

Cited by 6 publications

References 83 publications

Neutrino mass and mixing with modular symmetry

Neutrino mass and mixing with modular symmetry

Finite modular axion and radiative moduli stabilization

Quark and lepton modular models from the binary dihedral flavor symmetry

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