content_image/335208.jpg content_image/335209.jpg content_image/335210.jpg content_image/335205.jpg content_image/335206.jpg content_image/335204.jpg content_image/335203.jpg
follows (for r$_{3}$ = 3): 

Note that these systems do not depend on ˆ r$_{i}$ , and so are independent of y$_{b}$ . 

We emphasize the following points: 

<img src='content_image/335208.jpg'>

<img src='content_image/335209.jpg'>

<img src='content_image/335210.jpg'>

• The bound in the D system comes from 〈 δ u 12 〉 and is r$_{3}$ independent. 

• For r$_{3}$ = O (1 − 10), the bound in the B$_{s}$ system comes from 〈 δ d 23 〉 . For r$_{3}$ = O (1 − 7) it scales with 3 /r$_{3}$ ; for r$_{3}$ > 7 it does not scale with r$_{3}$ . 

• For r$_{3}$ = O (1 − 10), the bound in the B$_{d}$ system comes from 〈 δ d 13 〉 . For r$_{3}$ = O (1 − 1 . 5) it scales with 3 /r$_{3}$ ; for r$_{3}$ > 1 . 5 it does not scale with r$_{3}$ . 

As mentioned in Section II, for large tan β and low M$_{A}$ 0 , the B$_{d,s}$ mixing amplitudes can be significantly enhanced. Indeed, comparing the constraints of Eq. (2.4) to Table V, we obtain for r$_{3}$ = 3 (and tan β = 30, M$_{A}$ 0 = 200 GeV): 

<img src='content_image/335205.jpg'>

<img src='content_image/335206.jpg'>

The r$_{3}$ dependence of upper bounds on the supersymmetric contributions to B$_{d}$ and B$_{s}$ mixings is shown in Fig. 1. 

## B. Anarchical A -terms 

We consider scenarios with anarchical A -terms at the messenger scale: 

so that 

<img src='content_image/335204.jpg'>

<img src='content_image/335203.jpg'>

We insert the anarchical structure (5.13) into the expressions of the δ q parameters in Eq. (3.3). We then compare these predictions to the bounds given in the Tables I and II. Note that these bounds are obtained for m$_{˜}$ q = 1 TeV. Recalling that parametrically m 2 ˜ q ∼ r$_{3}$ ˜ m $^{2}$, we use ˜ m ∼ 1 TeV / √ r$_{3}$ . 

