Theta angle versus CP violation in the leptonic sector - art. no. 116010

Assuming that the axion mechanism of solving the strong CP problem does not exist and the vanishing of theta at the tree level is achieved by some mod el-building means, we study the naturalness of having large CP-violating so urces in the leptonic sector. We consider the radiative mechanisms which tr ansfer a possibly large CP-violating phase in the leptonic sector to the th eta parameter. It is found that a large theta cannot be induced in the mode ls 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 thet a is the phases in the scalar potential, induced by CP violation in the lep tonic 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 a re large, excluding the possibility of large phases, unless the universalit y in the slepton sector is strongly violated.