Modular A4 symmetry models of neutrinos and charged leptons

Self Cite

128

In the modular symmetry approach to neutrino models, the flavour symmetry emerges as a finite subgroup Γ N of the modular symmetry, broken by the vacuum expectation value (VEV) of a modulus field τ . If the VEV of the modulus τ takes some special value, a residual subgroup of Γ N would be preserved. We derive the fixed points τ S = i, τ ST = (−1 + i √ 3)/2, τ T S = (1 + i √ 3)/2, τ T = i∞ in the fundamental domain which are invariant under the modular transformations indicated. We then generalise these fixed points to τ f = γτ S , γτ ST , γτ T S and γτ T in the upper half complex plane, and show that it is sufficient to consider γ ∈ Γ N . Focussing on level N = 4, corresponding to the flavour group S 4 , we consider all the resulting triplet modular forms at these fixed points up to weight 6. We then apply the results to lepton mixing, with different residual subgroups in the charged lepton sector and each of the right-handed neutrinos sectors. In the minimal case of two right-handed neutrinos, we find three phenomenologically viable cases in which the light neutrino mass matrix only depends on three free parameters, and the lepton mixing takes the trimaximal TM1 pattern for two examples. One of these cases corresponds to a new Littlest Modular Seesaw based on CSD(n) with n = 1 + √ 6 ≈ 3.45, intermediate between CSD (3) and CSD(4). Finally, we generalize the results to examples with three right-handed neutrinos, also considering the level N = 3 case, corresponding to A 4 flavour symmetry. *

Section: Tri-direct Modular Model With Three Right-handed Neutrinosmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modular S4 and A4 symmetries and their fixed points: new predictive examples of lepton mixing

Ding

King

Liu

et al. 2019

Self Cite

128

“…In the present work we shall adopt the same convention as [16,27,28]. The finite modular group Γ 3 is isomorphic to A 4 which is the symmetry group of the tetrahedron.…”

Section: Modular Symmetrymentioning

confidence: 99%

“…In this subsection we review an example of a model of lepton masses and mixing based on A 4 modular symmetry, first introduced as example 3 in [16] and later reanalysed in the light of current data in [27]. In this example, there is no flavon field other than the modulus τ .…”

Section: The Feruglio Model Of Leptonsmentioning

confidence: 99%

“…The finite modular groups Γ 2 ∼ = S 3 [18][19][20][21], Γ 3 ∼ = A 4 [16,18,19,[22][23][24][25][26][27][28], Γ 4 ∼ = S 4 [28][29][30][31][32] and Γ 5 ∼ = A 5 [32][33][34] have been considered. For example, simple A 4 modular models can reproduce the measured neutrino masses and mixing angles [16,23,27]. The quark masses and mixing angles may also be included together with leptons in an A 4 modular invariant model [35].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fermion mass hierarchies from modular symmetry

King

2020

Self Cite

We show how quark and lepton mass hierarchies can be reproduced in the framework of modular symmetry. The mechanism is analogous to the Froggatt-Nielsen (FN) mechanism, but without requiring any Abelian symmetry to be introduced, nor any Standard Model (SM) singlet flavon to break it. The modular weights of fermion fields play the role of FN charges, and SM singlet fields with non-zero modular weight called weightons play the role of flavons. We illustrate the mechanism by analysing A4 (modular level 3) models of quark and lepton (including neutrino) masses and mixing, with a single modulus field. We discuss two examples in some detail, both numerically and analytically, showing how both fermion mass and mixing hierarchies emerge from different aspects of the modular symmetry.

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).