a $\rm MFV$ model that has $\eta_U$ small for a symmetry reason. New scalars that transform under flavour [@Arnold:2009ay] can naturally have a small $\eta_U$. Consider a scalar field $S_8$ that transforms the same way as the Higgs doublet under the gauge group but as $({\bf 1},{\bf 8},{\bf 1})$ under the flavor group, S\_8 V\_D S\_8 V\_D\^. We choose to represent the scalar in terms of the Gell-Mann matrices $S_8 = S_8^a \, T^a$ where $a = 1, ...,8$ is a flavour index. The Yukawa couplings are given by \[general\] [L]{}\_Y &=& [|u]{}\_[R]{}\^i \^[ l]{}\_[U i]{} (g\_D\^)\^o\_[ l]{} (T\^[a]{})\^n\_[ o]{} (g\_D)\^j\_[ n]{} Q\_[Lj]{} S\_8\^a,\
&& + [|d]{}\_[R]{}\^i (T\^a)\^m\_[ i]{} (\_D)\^j\_[ m]{} Q\_[Lj]{} S\^[ a]{}\_8+[h.c.]{} where we have made the flavour indices explicit. We use hat superscripts to distinguish this model’s parameters from the two scalar doublet model. Recall that, \[yuk1\] [Y]{}\^[  j]{}\_[U i]{} &=& \_U g\^[  j]{}\_[U i]{} + ’\_U g\^[  j]{}\_[U k]{} \[(g\_U\^)\^[k]{}\_[ l]{} (g\_U)\^[l]{}\_[ i]{}\] + ,\
[Y]{}\^[  j]{}\_[D i]{} &=& \_D g\^[  j]{}\_[D i]{} + ’\_D g\^[  j]{}\_[D k]{} \[(g\_U\^)\^[k]{}\_[ l]{} (g\_U)\^[l]{}\_[ i]{}\] + .

The potential is given by V &=& (H\^[i]{} H\_i - )\^2 + 2 \_1\^2 [Tr]{}\[S\^[ i]{}\_8 S\_[8 i]{}\]\
&+& \_1 H\^[i]{} H\_i 