Abstract
We study Froggatt-Nielsen (FN) like flavor models with modular symmetry. The FN mechanism is a convincing solution to the flavor puzzle in the quark sector. The FN mechanism requires an extra U(1) gauge symmetry which is broken at high energies. Alternatively, in the framework of modular symmetry the modular weights can play the role of the FN charges of the extra U(1) symmetry. Based on the FN-like mechanism with modular symmetry we present new flavor models for the quark sector. Assuming that the three generations have a common representation under the modular symmetry, our models simply reproduce the FN-like Yukawa matrices. We also show that the realistic mass hierarchy and mixing angles, which are related to each other through the modular parameters and a scalar vev, can be realized in models with several finite modular groups (and their double covering groups) without unnatural hierarchical parameters.
Highlights
The Froggatt-Nielsen (FN) mechanism is another well-known possible solution for the flavor puzzle [46]
The Yukawa coupling itself is controlled by the modular weights of the fermion fields, since the modular forms are classified by modular weights
We present new flavor models for the quark sector based on the FN-like mechanism with modular symmetry
Summary
We briefly review the modular symmetry and the Froggatt-Nielsen mechanism. To construct a modular invariant action, coupling constants should form representations of the modular group, and such functions are known as the modular forms. The modular forms of level N and weight k are holomorphic functions satisfying the following transformation f (γτ ) = (cτ + d)kf (τ ),. Throughout this paper, we assume global supersymmetry The matter fields such as quarks are denoted by chiral superfields. We assume that they transform as the modular forms of level N and weight k, γ : Φi → (cτ + d)ki ρΦ(γ)ijΦj,. In order to be invariant under modular symmetry, the allowed Yukawa couplings are given in term of the modular forms, which are classified by modular weights.
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