Modular flavor symmetry and vector-valued modular forms

Liu, Xiang-Gan; Ding, Gui-Jun

doi:10.1007/jhep03(2022)123

Cited by 18 publications

(31 citation statements)

References 94 publications

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“…Since their introduction in BU constructions [8], most of the attempts for a description of flavor with modular flavor symmetries have concentrated on the lepton sector alone, see e.g. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and references therein. Even though apparently more difficult to accomodate, there have been some fits of the flavor parameters that include the quark sector, see e.g.…”

Section: Jhep09(2022)224mentioning

confidence: 99%

The first string-derived eclectic flavor model with realistic phenomenology

Baur

Nilles²,

Ramos‐Sánchez

et al. 2022

J. High Energ. Phys.

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Eclectic flavor groups arising from string compactifications combine the power of modular and traditional flavor symmetries to address the flavor puzzle. This top-down scheme determines the representations and modular weights of all matter fields, imposing strict constraints on the structure of the effective potential, which result in controlled corrections. We study the lepton and quark flavor phenomenology of an explicit, potentially realistic example model based on a 𝕋6/ℤ3× ℤ3 orbifold compactification of the heterotic string that gives rise to an Ω(2) eclectic flavor symmetry. We find that the interplay of flavon alignment and the localization of the modulus in the vicinity of a symmetry-enhanced point leads to naturally protected fermion mass hierarchies, favoring normal-ordered neutrino masses arising from a see-saw mechanism. We show that our model can reproduce all observables in the lepton sector with a small number of parameters and deliver predictions for so far undetermined neutrino observables. Furthermore, we extend the fit to quarks and find that Kähler corrections are instrumental in obtaining a successful simultaneous fit to the quark and lepton sectors.

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Section: Jhep09(2022)224mentioning

confidence: 99%

The first string-derived eclectic flavor model with realistic phenomenology

Baur

Nilles²,

Ramos‐Sánchez

et al. 2022

J. High Energ. Phys.

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“…Here, k is the so-called modular weight, which is sometimes taken to be an integer, but in top-down models often happens to be a rational number. 2 In order to understand how this story is related to finite groups, the perhaps most direct way is to consider the theory of vector-valued modular forms [114]. The latter transform under (5.3) as…”

Section: Modular Formsmentioning

confidence: 99%

“…A relevant pending question is what kind of neutrino phenomenology can be obtained from these symmetries. Further, it is clear now that more general eclectic flavor symmetries can be constructed, especially including vector-valued modular forms [114], which might open new avenues of relating neutrino data to possible UV completions of the SM.…”

Section: Eclectic Flavor Symmetriesmentioning

confidence: 99%

Neutrino Flavor Model Building and the Origins of Flavor and CP Violation: A Snowmass White Paper

Almumin¹,

Chen²,

Cheng³

et al. 2022

Preprint

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The neutrino sector offers one of the most sensitive probes of new physics beyond the Standard Model of Particle Physics (SM). The mechanism of neutrino mass generation is still unknown. The observed suppression of neutrino masses hints at a large scale, conceivably of the order of the scale of a Grand Unified Theory (GUT), a unique feature of neutrinos that is not shared by the charged fermions. The origin of neutrino masses and mixing is part of the outstanding puzzle of fermion masses and mixings, which is not explained in the SM. Flavor model building for both quark and lepton sectors is important in order to gain a better understanding of the origin of the structure of mass hierarchy and flavor mixing, which constitute the dominant fraction of the SM parameters.Recent activities in neutrino flavor model building based on non-Abelian discrete flavor symmetries and modular flavor symmetries have been shown to be a promising direction to explore. The emerging models provide a framework that has a significantly reduced number of undetermined parameters in the flavor sector. In addition, such framework affords a novel origin of CP violation from group theory, due to the intimate connection between physical CP transformation and group theoretical properties of non-Abelian discrete groups.Model building based on non-Abelian discrete flavor symmetries and their modular variants enables the particle physics community to interpret the current and anticipated upcoming data from neutrino experiments. Non-Abelian discrete flavor symmetries and their modular variants can result from compactification of a higher-dimensional theory. Pursuit of flavor model building based on such frameworks thus also provides the connection to possible UV completions, in particular to string theory. We emphasize the importance of constructing models in which the uncertainties of theoretical predictions are smaller than, or at most compatible with, the error bars of measurements in neutrino experiments. While there exist proof-of-principle versions of bottom-up models in which the theoretical uncertainties are under control, it is remarkable that the key ingredients of such constructions were discovered first in top-down model building. We outline how a successful unification of bottom-up and top-down ideas and techniques may guide us towards a new era of precision flavor model building in which future experimental results can give us crucial insights in the UV completion of the SM.

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“…Modular invariance constrains the Yukawa couplings to be level N modular forms which are specific holomorphic functions of τ . To be more general, one can use any normal subgroup of Γ rather than Γ(N ) such that the Yukawa couplings are vector-valued modular forms of SL(2, Z) [7]. The modular invariance approach to the flavor puzzle, especially for the lepton flavor structure have been extensively exploited, and various modular invariant models have been constructed in past years with the groups Γ 2 ∼ = S 3 [8][9][10][11], Γ 3 ∼ = A 4 [6,8,9,, Γ 4 ∼ = S 4 [25,[39][40][41][42][43][44][45][46][47], Γ 5 ∼ = A 5 [44,48,49] and Γ 7 ∼ = P SL(2, Z 7 ) [50].…”

Section: Introductionmentioning

confidence: 99%

Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry

Ding,

King,

et al. 2022

Preprint

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We study the prediction for leptogenesis in two renormalizable supersymmetric SO(10) × A 4 modular models in which the neutrino mass is dominantly generated by the type I seesaw mechanism. The evolution of the lepton asymmetries are described in terms of the three-flavored density matrix equations for three heavy Majorana neutrinos, where both vanishing initial condition and thermal initial condition of the right-handed neutrinos are considered. We also present an analytical approximation based on the Boltzmann equations. We find regions of parameter space compatible with the measured fermion masses and mixing parameters as well as the baryon asymmetry of the Universe. The predictions for the light neutrino masses, the effective mass in neutrinoless doble beta decay and the leptonic CP violation phases are discussed.

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Modular flavor symmetry and vector-valued modular forms

Cited by 18 publications

References 94 publications

The first string-derived eclectic flavor model with realistic phenomenology

The first string-derived eclectic flavor model with realistic phenomenology

Neutrino Flavor Model Building and the Origins of Flavor and CP Violation: A Snowmass White Paper

Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry

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