Theta angle versus CP violation in the leptonic sector

Assuming that the axion mechanism of solving the strong CP problem does not exist and the vanishing of θ at the tree level is achieved by some model-building means, we study the naturalness of having large CP-violating sources in the leptonic sector. We consider the radiative mechanisms which transfer a possibly large CP-violating phase in the leptonic sector to the θ parameter. It is found that a large eθ cannot be induced in the models with one Higgs doublet as at least three loops are required in this case. In the models with two or more Higgs doublets the dominant source of θ is the phases in the scalar potential, induced by CP violation in the leptonic sector. Thus, in the minimal supersymmetric standard model framework the imaginary part of the trilinear soft-breaking parameter A_l generates the corrections to the theta angle already at one loop. These corrections are large, excluding the possibility of large phases, unless the universality in the slepton sector is strongly violated.