correction factor, $C^{\rm SM}_q(m_b) =\eta  \, C^{\rm SM}_q(m_t)$.

The models for new physics we discuss generate the effective Hamiltonian at the top scale[^5] $$\label{NPH}
{\cal H}^{\rm NP}_q\simeq (V_{tq}^\star \, V_{tb})^2C^{\rm NP}(m_t) {\bar b}^{\alpha}_R q^{\alpha}_L{\bar b}^{\beta}_R q^{\beta}_L.$$ Running down from $m_b$ operator mixing induces the analogous operator with color indices rearranged. However, its coefficient is very small and we neglect it resulting in the relation, $C^{\rm NP}(m_b) \simeq \eta' C^{\rm NP}(m_t)$, where $\eta'  \simeq 1.45$ [@Bagger:1997gg]. Again using the vacuum insertion approximation at the $b$-quark mass scale we arrive at, $$\left(M_{12}^q\right)^{\rm NP}\simeq(V_{tq}^\star \, V_{tb})^2C^{\rm NP}(m_t)\left(-{5 \over 24}\right) \eta'  f_{B_q}^2 m_{B_q}.$$ Comparing with Eq. (\[hsigma\]) $$\label{key}
 h_q \, e^{2 \, i \, \sigma_q} \simeq-{5 \over 8}\left({C^{\rm NP}(m_t) \over C^{\rm SM}(m_t) }\right) {\eta' \over \eta}.$$

Minimal Two Scalar Doublet Model
================================

We now discuss how the minimal two scalar doublet model with MFV can have enhanced CP violation in $B_q$ mixing due to tree level exchange of neutral scalars.[^6] We denote by $H$ the doublet that gets a vacuum expectation value and by $S$ the doublet that does not. The Lagrangian in the Yukawa sector is \[general\] [L]{}\_Y&=& [|u]{}\^i\_[R]{} g\^[  j]{}\_[U i]{} Q\_[L j]{} H+ [|d]{}\^i\_[R]{} g\^[  j]{}\_[D i]{} Q\_[L j]{} H \^\
