Abstract
We discuss a minimal flavour model with twin modular symmetries, leading to trimaximal TM$_1$ lepton mixing in which the first column of the tri-bimaximal lepton mixing matrix is preserved. The model involves two modular $S_4$ groups, one acting in the neutrino sector, associated with a modulus field value $\tau_{SU}$ with residual $Z^{SU}_2$ symmetry, and one acting in the charged lepton sector, associated with a modulus field value $\tau_{T}$ with residual $Z^{T}_3$ symmetry. Apart from the predictions of TM$_1$ mixing, the model leads to a new neutrino mass sum rule which implies lower bounds on neutrino masses close to current limits from neutrinoless double beta decay experiments and cosmology.
Highlights
The discovery of neutrino masses and lepton mixing opened up a new direction in physics beyond Standard Model (SM) focused on understanding their theoretical origin
III, we propose a model based on Sν4 × Sl4 with two moduli fields, which is broken to a single diagonal S4 with two independent moduli fields at low energies, whose stabilizers lead to different remnant symmetry in the different sectors, which may be used to enforce trimaximal TM1 mixing with the new neutrino mass sum rule
We have discussed a minimal model of trimaximal mixing in which the first column of the tribimaximal lepton mixing matrix is achieved via two modular S4 groups, namely Sl4 × Sν4
Summary
The discovery of neutrino masses and lepton mixing opened up a new direction in physics beyond Standard Model (SM) focused on understanding their theoretical origin. In a recent paper [59], two of us extended the formalism of finite modular symmetry to the case of multiple moduli fields τJ (J 1⁄4 1; ...M) associated with the finite modular symmetry Γ1N1 × Γ2N2 × Á Á Á × ΓMNM This is motivated by superstring theory which involves six compact extra dimensions, suggesting the introduction of three modular symmetries associated with three different factorized tori in the simplest compactifications. The considered model involved three finite modular symmetries SA4 , SB4 , and SC4 , associated with two right-handed neutrinos and the charged lepton sector, respectively, broken by two bi-triplet scalars to their diagonal subgroup.
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