Modular binary octahedral symmetry for flavor structure of Standard Model

Ding, Gui-Jun; Liu, Xiang-Gan; Lu, Jun-Nan; Weng, Ming-Hua

doi:10.1007/jhep11(2023)083

Cited by 8 publications

(2 citation statements)

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“…The sum of neutrino masses is determined to be 62.9149 meV, this is compatible with the latest bound i m i < 120 meV at 95% confidence level from Planck [349]. Recently a more predictive model for quark and lepton has been constructed with the modular binary octahedral symmetry 2O 30 , and the experimental data can be accommodated by using only 14 real free parameters [353]. It is the minimal modular invariant model for quarks and lepton at present.…”

Section: Extension Of S ′ 4 Modular Model To Quark Sector Without Gutssupporting

confidence: 72%

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: Extension Of S ′ 4 Modular Model To Quark Sector Without Gutssupporting

confidence: 72%

Neutrino mass and mixing with modular symmetry

Ding,

King

2024

Rep. Prog. Phys.

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“…In some orbifolds, only a subgroup of SL(2, Z) is unbroken, even without background fields [88], which opens up the possibility of finite modular flavor symmetries beyond Γ ′ K [65,66,89]. However, a more general discussion has to go beyond SL(2, Z).…”

Section: Discussionmentioning

confidence: 99%

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

Li,

Ding

2024

J. High Energ. Phys.

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We have performed a systematical study of the eclectic flavor group ∆(27) ⋊ S3 which is the extension of the traditional flavor symmetry ∆(27) by the finite modular symmetry S3. Consistency between ∆(27) and S3 requires that the eight nontrivial singlet representations of ∆(27) should be arranged into four reducible doublets. The modular transformation matrices are determined for various ∆(27) multiplets, and the CP-like symmetry compatible with ∆(27) ⋊ S3 are discussed. We study the general form of the Kähler potential and superpotential invariant under ∆(27) ⋊ S3, and the corresponding fermion mass matrices are presented. We propose a bottom-up model for lepton masses and mixing based on ∆(27) ⋊ S3, a numerical analysis is performed and the experimental data can be accommodated.

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Modular binary octahedral symmetry for flavor structure of Standard Model

Cited by 8 publications

References 100 publications

Neutrino mass and mixing with modular symmetry

Neutrino mass and mixing with modular symmetry

Flavor’s Delight

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

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