limits on electric dipole moments imply that $|{\rm Im}[\eta_U \eta_D]|\lesssim 10^{-1}$. Note that writing this as a constraint just on $\eta_U \eta_D$ depends on truncating a function of $\sqrt{ 2}m_t/v$ at leading order. We also examine the constraint on $ {\rm Re}[\eta_U \eta_D]$ coming from experimental data on weak radiative $B$ decay.

### Neutron Electric Dipole Moment

The large CP violating phases needed in this two scalar doublet model contribute to other CP violating observables. Notable among them are electric dipole moments (EDM’s). We will restrict our discussion here to the dominant contribution that is not suppressed by small quark masses when naive dimensional analysis (NDA) [@Manohar:1983md] is used. It comes about through the colour electric dipole moment of the b quark [@Boyd:1990bx; @Braaten:1990gq] due to the effective Hamiltonian \_[bg]{} = C\_[gb]{} g\_3 m\_b |[b]{} \_[ ]{} T\_a G\^a\_[ ]{} \^[ ]{} b, inducing the dimension six CP violating operator O\_G = g\_3\^3 f\_[ ]{} \^[ ]{} G\_[ ]{} G\_[ ]{}\^ G\_[ ]{}, of Weinberg [@Weinberg:1989dx] when the $b$ quark is integrated out. Our discussion will largely parallel the discussion of [@Manohar:2006ga]. As $\rm S$ couples both to the up and down type quarks it induces a one loop contribution 