SU(5) GUTs with A4 modular symmetry

We propose an A4 modular invariant flavor model of leptons, in which both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus τ. The value of the modulus τ is restricted by the observed lepton mixing angles and lepton masses for the normal hierarchy of neutrino masses. The predictive Dirac CP phase δCP is in the ranges [0°, 50°], [170°, 175°] and [280°, 360°] for Re [τ] < 0, and [0°, 80°], [185°, 190°] and [310°, 360°] for Re [τ] > 0. The sum of three neutrino masses is predicted in [60, 84] meV, and the effective mass for the 0νββ decay is in [0.003, 3] meV. The modulus τ links the Dirac CP phase to the cosmological baryon asymmetry (BAU) via the leptogenesis. Due to the strong wash-out effect, the predictive baryon asymmetry YB can be at most the same order of the observed value. Then, the lightest right-handed neutrino mass is restricted in the range of M1 = [1.5, 6.5] × 1013 GeV. We find the correlation between the predictive YB and the Dirac CP phase δCP. Only two predictive δCP ranges, [5°, 40°] (Re [τ] > 0) and [320°, 355°] (Re [τ] < 0) are consistent with the BAU.

Section: Jhep07(2021)184 4 Numerical Results Of Leptonic Cp Violationmentioning

confidence: 99%

Section: Baryon Asymmetrymentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Modulus τ linking leptonic CP violation to baryon asymmetry in A4 modular invariant flavor model

Okada

Shimizu

Tanimoto

et al. 2021

“…Once the modulus τ acquires its vev, the Yukawa couplings are determined and thus leptonic flavor mixing pattern is obtained. Finite modular groups, such as Γ 2 S 3 [13][14][15], Γ 3 A 4 [12,[16][17][18][19][20][21][22][23][24][25][26][27], Γ 4 S 4 [28][29][30][31][32][33], Γ 5 A 5 [34][35][36], Γ 7…”

Section: Introductionmentioning

confidence: 99%

Explicit perturbations to the stabilizer τ = i of modular $$ {A}_5^{\prime } $$ symmetry and leptonic CP violation

Wang

Zhou

2021

In a class of neutrino mass models with modular flavor symmetries, it has been observed that CP symmetry is preserved at the fixed point (or stabilizer) of the modulus parameter τ = i, whereas significant CP violation emerges within the neighbourhood of this stabilizer. In this paper, we first construct a viable model with the modular $$ {A}_5^{\prime } $$ A 5 ′ symmetry, and explore the phenomenological implications for lepton masses and flavor mixing. Then, we introduce explicit perturbations to the stabilizer at τ = i, and present both numerical and analytical results to understand why a small deviation from the stabilizer leads to large CP violation. As low-energy observables are very sensitive to the perturbations to model parameters, we further demonstrate that the renormalization-group running effects play an important role in confronting theoretical predictions at the high-energy scale with experimental measurements at the low-energy scale.

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

Wang

2023

We propose to generate the flavor structures of the Standard Model plus neutrinos from flipped SU(5) GUT with A4 modular flavor symmetry. Possible way to assign different moduli values for quarks and leptons in modular GUT scheme is discussed. We propose to reduce the multiple modular symmetries to a single modular symmetry in the low energy effective theory with proper boundary conditions. We classify all possible scenarios in this scheme according to the assignments of the modular A4 representations for matter superfields and give the expressions of the quark and lepton mass matrices predicted by our scheme at the GUT scale. After properly selecting the modular weights for various superfields that can lead to better fitting, we can obtain the best-fit points with the corresponding χ2 values for the sample subscenarios. We find that the flavor structures of the Standard Model plus neutrinos can be fitted perfectly in such a A4 modular flavor GUT scheme with single or two modulus fields. Especially, the $$ {\chi}_{\textrm{total}}^2 $$ χ total 2 of our fitting can be as low as 1.558 for sample IX′ of scenario III even if only a single common modulus field for both quark and lepton sectors is adopted. The most predictive scenario III, in which all superfields transform as triplets of A4, can be fitted much better with two independent moduli fields τq, τl for quark sector and lepton sector ($$ {\chi}_{\textrm{total}}^2 $$ χ total 2 ≈ 95) than that with the single modulus case ($$ {\chi}_{\textrm{total}}^2 $$ χ total 2 ≈ 282.4).