Abstract: |
We present simple effective models of flavor and CP, which realize the vanishing \bar\theta in the context of the modular symmetry of level N=3 without the need for an axion. Supposing CP to be a fundamental symmetry of the Lagrangian, the strong CP phase $\bar \theta$ vanish. The vacuum expectation value (VEV) of the modulus $\tau$ leads to the spontaneous breaking of CP, which gives the large value of the CKM phase, while the strong CP phase \bar \theta vanishes or is tiny. This effective model requires three types of texture zeros, which could be realized by assigning both left- and right-handed fermions to A4 singlets 1, 1' and 1'' with relevant weights. The VEV of \tau is restricted to reproduce the observed CKM parameters. In particular, we discuss the cases in which the modulus \tau is close to the fixed points \tau=i, \omega and i \infty, which are consistent with the modulus stabilisation. |