A note on the predictions of models with modular flavor symmetries

Chen, Mu‐Chun; Ramos‐Sánchez, Saúl; Ratz, Michael

doi:10.1016/j.physletb.2019.135153

Cited by 121 publications

(106 citation statements)

References 29 publications

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“…In ref. [33] it was pointed out that general terms in the Kähler potential reduce the predictivity of models based on finite modular symmetries. This problem could be solved within the eclectic flavor picture with more restrictions on the Kähler potential due to the nontrivial combination of finite modular groups and traditional flavor groups.…”

Section: Discussionmentioning

confidence: 99%

“…The full eclectic flavor group is a nontrivial product of the traditional flavor group, a corresponding finite modular group and a CP-like transformation. We cannot treat these symmetries separately (as mostly done in the BU-approach) and have to be aware of restrictions (for superpotential and Kähler potential [33]) from all of these components.…”

Section: Introductionmentioning

confidence: 99%

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Eclectic flavor groups

Nilles¹,

Ramos‐Sánchez

Vaudrevange

2020

J. High Energ. Phys.

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The simultaneous study of top-down and bottom-up approaches to modular flavor symmetry leads necessarily to the concept of eclectic flavor groups. These are nontrivial products of modular and traditional flavor symmetries that exhibit the phenomenon of local flavor enhancement in moduli space. We develop methods to determine the eclectic flavor groups that can be consistently associated with a given traditional flavor symmetry. Applying these methods to a large family of prominent traditional flavor symmetries, we try to identify potential candidates for realistic eclectic flavor groups and show that they are relatively rare. Model building with finite modular flavor symmetries thus appears to be much more restrictive than previously thought.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Eclectic flavor groups

Nilles¹,

Ramos‐Sánchez

Vaudrevange

2020

J. High Energ. Phys.

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“…In modular invariant models, the Yukawa couplings transform nontrivially under the modular symmetry and they are modular forms which are holomorphic functions of τ [12]. Models with modular flavour symmetry can be highly predictive, the neutrino masses and mixing parameters can be predicted in terms of few input parameters, although the predictive power of this framework may be reduced by the Kähler potential which is less constrained by modular symmetry [13].…”

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

J. High Energ. Phys.

128

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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. *

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“…ref. [26]. On the other hand, it turns out that the superpotential is also modular invariant since e.g.…”

Section: Modular Symmetries Of Orbifold Compactificationsmentioning

confidence: 99%

Eclectic flavor scheme from ten-dimensional string theory – I. Basic results

2020

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String theory leads to a flavor scheme where modular symmetries play a crucial role. Together with the traditional flavor symmetries they combine to an eclectic flavor group, which we determine via outer automorphisms of the Narain space group. Unbroken flavor symmetries are subgroups of this eclectic group and their size depends on the location in moduli space. This mechanism of local flavor unification allows a different flavor structure for different sectors of the theory (such as quarks and leptons) and also explains the spontaneous breakdown of flavor-and CP-symmetries (via a motion in moduli space). We derive the modular groups, including CP and R-symmetries, for different sub-sectors of sixdimensional string compactifications and determine the general properties of the allowed flavor groups from this top-down perspective. It leads to a very predictive flavor scheme that should be confronted with the variety of existing bottom-up constructions of flavor symmetry in order to clarify which of them could have a consistent top-down completion.

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A note on the predictions of models with modular flavor symmetries

Cited by 121 publications

References 29 publications

Eclectic flavor groups

Eclectic flavor groups

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

Eclectic flavor scheme from ten-dimensional string theory – I. Basic results

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