Electric dipole moment of the neutron in two-Higgs-doublet models with flavor changing couplings

I consider contributions to the neutron electric dipole moment within Two Higgs Doublet Models which allow for small flavor changing neutral Higgs couplings. In a previous paper, I considered flavor changing interactions for the Standard Model Higgs boson to first order in the flavor changing coupling. In that paper I found that the obtained value of the neutron electric dipole moment were below the present experimental limit, given previous restrictions on such couplings. Because this was an effective theory, the result depended on an ultraviolet cut off $\Lambda$, parametrized as $ln(\Lambda^2)$. In the present paper I demonstrate that, when going to Two Higgs Doublet Models, the result stays the same as in the previous paper, up to $M_{SM}^2/M_H^2$ corrections, where $M_{SM}$ is the mass of the top-quark or the $W$-boson. $M_H$ is the mass of the heavy neutral scalar Higgs-boson $H$ which is much heavier than the light neutral Higgs boson $h$ with mass $M_h$. In the limit $M_H^2 \gg M_h^2$, the $ln(\Lambda^2)$ behaviour in the previous paper is replaced by $ln(\widetilde{M_H}^2)$, where $\widetilde{M_H}$ is of order $M_H$. I also explain how some divergences due to exchange of the pseudoscalar Higgs $A$ are cancelled by similar contributions from the scalar heavy Higgs $H$, and that these contributions, and finite contributions from $A$-exchange, are suppressed.