Texture zeros of quark mass matrices at fixed point τ =ω in modular flavor symmetry

We study systematically derivation of the specific texture zeros, that is the nearest neighbor interaction (NNI) form of the quark mass matrices at the fixed point τ =ω τ = ω in modular flavor symmetric models. We present models that the NNI forms of the quark mass matrices are simply realized at the fixed point τ =ω τ = ω in the A₄ A 4 modular flavor symmetry by taking account multi-Higgs fields. Such texture zero structure originates from the ST charge of the residual symmetry Z₃ Z 3 of SL (2, Z ). The NNI form can be realized at the fixed point τ = ω τ = ω in A₄ A 4 and S₄ S 4 modular flavor models with two pairs of Higgs fields when we assign properly modular weights to Yukawa couplings and A₄ A 4 and S₄ S 4 representations to three generations of quarks. We need four pairs of Higgs fields to realize the NNI form in A₅ A 5 modular flavor models.