to the effective Hamiltonian above with C\_[gb]{}(m\_S) = ( )\^2 f(m\_t\^2/m\_[S\^]{}\^2), where f(x) = + . Running to $\mu \sim m_b$ using [@Boyd:1990bx; @Braaten:1990gq] and estimating the matrix element of the operator with NDA[^8] gives in $\rm e$-$\rm cm$ units d\_n \~2 [Im]{}\[\_U\^ \_D\^\] f(m\_t\^2/m\_[S\^]{}\^2) ( )\^2 10\^[-26]{}.

This is a significantly larger effect on EDM’s than quoted in the general operator analysis [@Blum:2010mj] examining the effects of four Fermi operators on EDM’s as this contribution is not suppressed by small mixing angles or light quark masses. For $m_{S^\pm}=360~{\rm GeV} $ the neutron EDM experimental bound of $d_n < 2.9 \times 10^{-26} \, {\rm e}$-$\rm cm$ implies that $|{\rm Im}[ \eta_U^* \eta_D^*]|<0.26$ We plot the allowed $|{\rm Im}[ \eta_U^* \eta_D^*]|$ as a function of mass for this NDA estimate in Fig. 2.

This suggests that $|{\rm Im}[\eta'^*_U \eta'^*_D]|$ (and the sum of the effect of all other cross terms such as $|{\rm Im}[\eta''^*_U \eta''^*_D]|$ etc.) is also small. However, given the uncertainties from hadronic matrix elements and given the fact that the parameters that enter the contribution to EDM’s are not identical to those in $B_q-{\bar B}_q$ mixing it is difficult to draw precise conclusions on the parameters in the 