content_image/358291.jpg content_image/358292.jpg content_image/358293.jpg content_image/358294.jpg
where Y$_{u}$ and Y$_{d}$ denote the up and down quark Yukawa matrices in the flavor basis, and the effect of trilinear soft couplings is included. (The RG-coefficient in front of the A -terms is of order one.) We note the following points: 

1. The factor r$_{3}$ captures the effect of RGE corrections to the diagonal elements of the soft squark mass matrices ( M 2 ˜ $_{q$_{A}$}$)$_{ii}$ via 

with the average diagonal mass-squared defined as 

<img src='content_image/358291.jpg'>

<img src='content_image/358292.jpg'>

For simplicity this factor is taken to be universal among all squarks, as the dominant contribution to the initial squark soft masses and to their RGE is QCD-induced and, in the limit that we neglect the electroweak gauge couplings, is indeed universal. 

2. The coefficients c$_{u}$,c$_{d}$,c$_{uR}$,c$_{dR}$ can be of O (1) for m$_{M}$ ∼ m$_{GUT}$ and are all negative. Yukawa-related contributions to the RGE thus lower the weak scale values of the diagonal ( M 2 ˜ $_{q$_{A}$}$)$_{33}$ entries with respect to the high scale ones. Sub-dominant MFV terms with higher powers of the Yukawa couplings are henceforth neglected. 

3. We use the various ˜ m 2 $_{ij}$( m$_{Z}$ ) to evaluate the denominator of the ( δ q $_{ij}$)$_{A}$ , neglecting D -terms of O ( m 2 $_{Z}$/ ˜ m 2 $_{ij}$) and F -terms of at most O ( m 2 $_{t}$/ ˜ m 2 i $_{3}$). 

4. Eq. (A2) is given in the flavor basis, while the δ q parameters are relevant in the mass basis of the quarks. This rotation of the squarks leaves the parametric pattern of the X$_{ij}$ and Z$_{ij}$ unchanged. 

As concerns the A -terms, we obtain for small to moderate tan β (so that for the purpose of RGE we employ Y$_{d}$ ≪ 1) the following approximate form: 

<img src='content_image/358293.jpg'>

<img src='content_image/358294.jpg'>

where ˜ m represents the typical scale of the SU (3)-related contributions to the gauge- mediated soft masses. The a,b coefficients relate to the MFV part of the trilinear scalar couplings and are irrelevant to our discussion. The dimensionless coefficients d,e can be O (1) and, for our purposes, are taken as such. 

