The minimal seesaw model with a modular S4 symmetry

Wang, Xin; Zhou, Shun

doi:10.1007/jhep05(2020)017

Cited by 99 publications

(60 citation statements)

References 102 publications

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“…The experimental values corresponding to the lepton sectors, the masses of charged leptons, neutrino mass-square differences, three mixing angles, and the CP phase can be reproduced in models with modular symmetries of Γ 2 ≅ S 3 [10][11][12], Γ 3 ≅ A 4 [12][13][14][15][16], Γ 4 ≅ S 4 [17,18], and Γ 5 ≅ A 5 [19]. Modular symmetry is also applied to other physics beyond the standard model such as leptogenesis and inflation [20][21][22][23], and relationships between generalized CP symmetry [24,25] and the modular symmetry are also pointed out [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Modular flavor symmetry on a magnetized torus

2020

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We study the modular invariance in magnetized torus models. The modular invariant flavor model is a recently proposed hypothesis for solving the flavor puzzle, where the flavor symmetry originates from modular invariance. In this framework, coupling constants such as Yukawa couplings are also transformed under the flavor symmetry. We show that the low-energy effective theory of magnetized torus models is invariant under a specific subgroup of the modular group. Since Yukawa couplings as well as chiral zero modes transform under the modular group, the above modular subgroup (referred to as modular flavor symmetry) provides a new type of modular invariant flavor models with D 4 × Z 2 , ðZ 4 × Z 2 Þ ⋊ Z 2 , and ðZ 8 × Z 2 Þ ⋊ Z 2. We also find that conventional discrete flavor symmetries which arise in magnetized torus model are noncommutative with the modular flavor symmetry. Combining both symmetries, we obtain a larger flavor symmetry, which is the semidirect product of the conventional flavor symmetry and the modular flavor symmetry for the nonvanishing Wilson line. For the vanishing Wilson line, we have additional Z 2 symmetry, i.e., parity, which is the unique common element between the conventional flavor symmetry and the modular flavor symmetry.

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Section: Introductionmentioning

confidence: 99%

Modular flavor symmetry on a magnetized torus

2020

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“…Modular invariant flavor models have been also proposed on the Γ 2 S 3 [24], Γ 4 S 4 [25] and Γ 5 A 5 [26]. Phenomenological discussions of the neutrino flavor mixing have been done based on A 4 [27][28][29], S 4 [30][31][32] and A 5 [33]. A clear prediction of the neutrino mixing angles and the CP violating phase was given in the simple lepton mass matrices with the A 4 modular symmetry [28].…”

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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“…The finite modular groups Γ 2 ∼ = S 3 [3][4][5][6], Γ 3 ∼ = A 4 [1,3,4,[7][8][9][10][11][12][13][14], Γ 4 ∼ = S 4 [13,[15][16][17][18][19]] and Γ 5 ∼ = A 5 [18,20,21] have been considered. For example, simple A 4 modular models can reproduce the measured neutrino masses and mixing angles [1,8,12].…”

Section: Jhep08(2020)164mentioning

confidence: 99%

Modular invariant models of leptons at level 7

Ding

King

et al. 2020

J. High Energ. Phys.

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We consider for the first time level 7 modular invariant flavour models where the lepton mixing originates from the breaking of modular symmetry and couplings responsible for lepton masses are modular forms. The latter are decomposed into irreducible multiplets of the finite modular group Γ 7 , which is isomorphic to PSL(2, Z 7), the projective special linear group of two dimensional matrices over the finite Galois field of seven elements, containing 168 elements, sometimes written as PSL 2 (7) or Σ(168). At weight 2, there are 26 linearly independent modular forms, organised into a triplet, a septet and two octets of Γ 7. A full list of modular forms up to weight 8 are provided. Assuming the absence of flavons, the simplest modular-invariant models based on Γ 7 are constructed, in which neutrinos gain masses via either the Weinberg operator or the type-I seesaw mechanism, and their predictions compared to experiment.

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The minimal seesaw model with a modular S4 symmetry

Cited by 99 publications

References 102 publications

Modular flavor symmetry on a magnetized torus

Modular flavor symmetry on a magnetized torus

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

Modular invariant models of leptons at level 7

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