Texture zeros of quark mass matrices at fixed point $$\tau =\omega $$ in modular flavor symmetry

Abstract

AbstractWe 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 $$\tau =\omega $$ 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 $$\tau =\omega $$ τ = ω in the $$A_4$$ A 4 modular flavor symmetry by taking account multi-Higgs fields. Such texture zero structure originates from the ST charge of the residual symmetry $$Z_3$$ Z 3 of SL(2, Z). The NNI form can be realized at the fixed point $$\tau = \omega $$ τ = ω in $$A_4$$ A 4 and $$S_4$$ S 4 modular flavor models with two pairs of Higgs fields when we assign properly modular weights to Yukawa couplings and $$A_4$$ A 4 and $$S_4$$ S 4 representations to three generations of quarks. We need four pairs of Higgs fields to realize the NNI form in $$A_5$$ A 5 modular flavor models.