Two A5 modular symmetries for Golden Ratio 2 mixing

Self Cite

We extend the littlest modular seesaw to a Grand Unified scenario based on SU (5) endowed with three modular S4 symmetries. We leverage symmetry protected zeroes in the leptonic and down quark sectors to suppress deviations to the littlest modular seesaw predictions, but not contributions to the quark mixing. The model is supplemented by two weighton fields, such that the hierarchical nature of the charged-lepton masses, as well as the quark masses and mixing, stem from the content and symmetries of the model, rather than a hierarchical nature of the Yukawa coefficients.

Section: Jhep05(2024)203mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A modular SU (5) littlest seesaw

de Medeiros Varzielas,

King,

Levy

2024

Self Cite

“…• models with multiple moduli, first considered phenomenologically in [13,24] and further developed in [77,[129][130][131][132][133][134][135][136][137], and…”

Section: Jhep09(2023)196mentioning

confidence: 99%

Quarks at the modular S4 cusp

de Medeiros Varzielas,

Levy,

Penedo

et al. 2023

We analyse the possibility of describing quark masses, mixing and CP violation in $$ {S}_4^{\prime } $$ S 4 ′ modular flavour models without flavons. We focus on the case where the closeness of the modulus to the point of residual $$ {\mathbb{Z}}_3^{ST} $$ ℤ 3 ST symmetry (the cusp) plays a role in generating quark mass hierarchies and discuss the role modular form normalisations play in such constructions. We find that fitting quark data requires explicit CP breaking, unless a second modulus is introduced.

“…To enhance the predictivity of such models, rather than considering the VEV of τ to be a free complex parameter, it is interesting to consider fixed points or stabilizers which are special values for the modulus field τ such as τ = i, ω, i∞ where part of the modular transformations are preserved. However such an approach with one modulus 1 is rather too restrictive and generally calls for additional moduli fields which can be introduced in a straightforward way by considering additional modular groups, with one modulus per modular group, as suggested in [14][15][16][17][18]. A recent example of a model of this kind was based on three finite modular groups S 3 4 broken to its diagonal subgroup S 4 , with three moduli fields in the low energy theory located at three different fixed points, for example τ 1 = i, τ 2 = i + 2, τ 3 = ω, leading to a very predictive and successful phenomenological description of the neutrino and charged lepton masses and lepton mixing based on a version of the littlest seesaw [19].…”

Section: Introductionmentioning

confidence: 99%

Modular flavour symmetry and orbifolds

Anda

King

2023

We develop a bottom-up approach to flavour models which combine modular symmetry with orbifold constructions. We first consider a 6d orbifold 𝕋2/ℤN, with a single torus defined by one complex coordinate z and a single modulus field τ, playing the role of a flavon transforming under a finite modular symmetry. We then consider 10d orbifolds with three factorizable tori, each defined by one complex coordinate zi and involving the three moduli fields τ1, τ2, τ3 transforming under three finite modular groups. Assuming supersymmetry, consistent with the holomorphicity requirement, we consider all 10d orbifolds of the form (𝕋2)3/(ℤN × ℤM), and list those which have fixed values of the moduli fields (up to an integer). The key advantage of such 10d orbifold models over 4d models is that the values of the moduli are not completely free but are constrained by geometry and symmetry. To illustrate the approach we discuss a 10d modular seesaw model with $$ {S}_4^3 $$ S 4 3 modular symmetry based on (𝕋2)3/(ℤ4× ℤ2) where τ1 = i, τ2 = i + 2 are constrained by the orbifold, while τ3 = ω is determined by imposing a further remnant S4 flavour symmetry, leading to a highly predictive example in the class CSD(n) with n = 1 −$$ \sqrt{6} $$ 6 .