TABLE V: The order of magnitude estimates for ( δ d,u ij )$_{A}$, A = LL, RR and 〈 δ d,u ij 〉 in the models defined by Eq. (5.3). The numerical estimates are obtained using quark masses at the scale m$_{Z}$ [20] and for r$_{3}$ = 3. All numerical estimates scale as (3 /r$_{3}$ ). q ij ( δ q $_{ij}$)$_{LL}$ ( δ q $_{ij}$)$_{RR}$ 〈 δ q ij 〉 d 12 r/r$_{3}$ ∼ 0 . 3 r r/r$_{3}$ ∼ 0 . 3 r r/r$_{3}$ ∼ 0 . 3 r d 13 ˆ r u $_{1}$/r$_{3}$ ∼ 0 . 3ˆ r u 1 r/r$_{3}$ ∼ 0 . 3 r √ ˆ r u $_{1}$r/r$_{3}$ ∼ 0 . 3 √ ˆ r u $_{1}$r d 23 ˆ r u $_{2}$/r$_{3}$ ∼ 0 . 3ˆ r u 2 r/r$_{3}$ ∼ 0 . 3 r ˆ r u $_{2}$r/r$_{3}$ ∼ 0 . 3 ˆ r u $_{2}$r u 12 r/r$_{3}$ ∼ 0 . 3 r r/r$_{3}$ ∼ 0 . 3 r r/r$_{3}$ ∼ 0 . 3 r u 13 ˆ r$_{1}$/r$_{3}$ ∼ 0 . 3ˆ r$_{1}$ r/r$_{3}$ ∼ 0 . 3 r √$_{ˆ}$ r$_{1}$r/r$_{3}$ ∼ 0 . $_{3}$√$_{ˆ}$ r$_{1}$r u 23 ˆ r$_{2}$/r$_{3}$ ∼ 0 . 3ˆ r$_{2}$ r/r$_{3}$ ∼ 0 . 3 r √$_{ˆ}$ r$_{2}$r/r$_{3}$ ∼ 0 . $_{3}$√$_{ˆ}$ r$_{2}$r q ij ( δ q $_{ij}$)$_{LL}$ ( δ q $_{ij}$)$_{RR}$ 〈 δ q ij 〉 d 12 0 . 006 0 . 006 0 . 006 d 13 max { 0 . 006 , 0 . 003(3 /r$_{3}$ ) } 0 . 006 max { 0 . 006 , 0 . 004 √ 3 /r$_{3}$ } d 23 max { 0 . 006 , 0 . 01(3 /r$_{3}$ ) } 0 . 006 max { 0 . 006 , 0 . 009 3 /r$_{3}$ } u 12 0 . 006 0 . 006 0 . 006 u 13 max { 0 . 006 , 0 . 001 y 2 $_{b}$(3 /r$_{3}$ ) } 0 . 006 max { 0 . 006 , 0 . 003 y$_{b}$ √ 3 /r$_{3}$ } u 23 max { 0 . 006 , 0 . 01 y 2 $_{b}$(3 /r$_{3}$ ) } 0 . 006 max { 0 . 006 , 0 . 009 y$_{b}$ 3 $^{/r$_{3}$}$} TABLE VI: The order of magnitude upper bounds on ( δ d,u ij )$_{LL,RR}$ and 〈 δ d,u ij 〉 corresponding to r/r$_{3}$ ∼ < 0 . 006 and the bounds of Eqs. (5.8,5.9). Entries with an r$_{3}$ dependence are indicated so. and Inserting the bounds (5.7), (5.8) and (5.9) into the predictions of Table V, we obtain the upper bounds on the δ q ij given in Table VI. We learn that the maximal possible effects in the neutral B$_{d}$ , B$_{s}$ and D systems are as ˆ r u 1 = max { r, y 2 $_{t}$V ∗ $_{td}$V$_{tb}$ } ∼ max { r, 0 . 009 } , ˆ r u 2 = max { r, y 2 $_{t}$V ∗ $_{ts}$V$_{tb}$ } ∼ max { r, 0 . 04 } . (5.9) 15