Flavor structures of quarks and leptons from flipped SU(5) GUT with A4 modular flavor symmetry

Du, Xiao Kang; Wang, Fei

doi:10.1007/jhep01(2023)036

Cited by 12 publications

(2 citation statements)

References 85 publications

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“…One could use the modular symmetry to avoid the complicated vacuum alignment, the three generations of chiral matter fields of the flipped SU (5) would be arranged to be multiplets of Γ N (or Γ ′ N ) with certain modular weights. Then all the Yukawa couplings y D ij , y U ij , y E ij , y S ij and (M S ) ij would be modular forms of level N [359,360], the quark and lepton mass matrices would depend on a smaller number of free parameters.…”

Section: Modular Flipped Su(5)mentioning

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: Modular Flipped Su(5)mentioning

confidence: 99%

Neutrino mass and mixing with modular symmetry

Ding,

King

2024

Rep. Prog. Phys.

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“…• models of quark-lepton unification [20,22,79,98,101,108,[111][112][113][114][115][116][117][118][119][120][121][122][123][124][125][126][127][128],…”

Section: Jhep09(2023)196mentioning

confidence: 99%

Quarks at the modular S4 cusp

de Medeiros Varzielas,

Levy,

Penedo

et al. 2023

J. High Energ. Phys.

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We analyse the possibility of describing quark masses, mixing and CP violation in $$ {S}_4^{\prime } $$ S 4 ′ modular flavour models without flavons. We focus on the case where the closeness of the modulus to the point of residual $$ {\mathbb{Z}}_3^{ST} $$ ℤ 3 ST symmetry (the cusp) plays a role in generating quark mass hierarchies and discuss the role modular form normalisations play in such constructions. We find that fitting quark data requires explicit CP breaking, unless a second modulus is introduced.

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

Kikuchi,

Kobayashi,

Nasu

et al. 2024

J. High Energ. Phys.

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We study an approach to construct Siegel modular forms from Sp(6, Z). Zero-mode wave functions on T6 with magnetic flux background behave Siegel modular forms at the origin. Then T-symmetries partially break depending on the form of background magnetic flux. We study the background such that three T-symmetries TI, TII and TIII as well as the S-symmetry remain. Consequently, we obtain Siegel modular forms with three moduli parameters (ω1, ω2, ω3), which are multiplets of finite modular groups. We show several examples. As one of examples, we study Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$ in detail. Then, as a phenomenological applicantion, we study quark flavor models using Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$. Around the cusp, ω1 = i∞, the Siegel modular forms have hierarchical values depending on their TI-charges. We show the deviation of ω1 from the cusp can generate large quark mass hierarchies without fine-tuning. Furthermore CP violation is induced by deviation of ω2 from imaginary axis.

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Flavor structures of quarks and leptons from flipped SU(5) GUT with A4 modular flavor symmetry

Cited by 12 publications

References 85 publications

Neutrino mass and mixing with modular symmetry

Neutrino mass and mixing with modular symmetry

Quarks at the modular S4 cusp

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

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