TABLE III: The order of magnitude estimates for ( δ d,u ij )$_{LL,RR}$ and 〈 δ d,u ij 〉 in the hybrid gauge-gravity models with FN structure [7]. The numerical estimates are obtained using quark masses at the scale m$_{Z}$ [20], and taking r$_{3}$ = 3. All results scale as (3 /r$_{3}$ ). For 〈 δ d i 3 〉 we use | V$_{i}$$_{3}$ | ∼ | V$_{ti}$ | . q ij ( δ q $_{ij}$)$_{LL}$ ( δ q $_{ij}$)$_{RR}$ 〈 δ q ij 〉 d 12 ( r/r$_{3}$ ) | V$_{12}$ | ∼ 0 . 08 r ( r/r 3 )( m$_{d}$/m$_{s}$ ) | V 12 | ∼ 0 . 08 r ( r/r$_{3}$ ) √ m$_{d}$/m$_{s}$ ∼ 0 . 08 r d 13 y 2 t | V ∗ $_{td}$V$_{tb}$ | /r$_{3}$ ∼ 0 . 003 ( r/r 3 )( m$_{d}$/m$_{b}$ ) | V 13 | ∼ 0 . 08 r y$_{t}$ √ rm$_{d}$/m$_{b}$/r$_{3}$ ∼ 0 . $_{01}$√$_{r}$ d 23 y 2 t | V ∗ $_{ts}$V$_{tb}$ | /r$_{3}$ ∼ 0 . 01 ( r/r 3 )( m$_{s}$/m$_{b}$ ) | V 23 | ∼ 0 . 2 r y$_{t}$ rm$_{s}$/m$_{b}$/r$_{3}$ ∼ 0 . $_{05}$√$_{r}$ u 12 ( r/r$_{3}$ ) | V$_{12}$ | ∼ 0 . 08 r ( r/r 3 )( m$_{u}$/m$_{c}$ ) | V 12 | ∼ 0 . 003 r ( r/r$_{3}$ ) √ m$_{u}$/m$_{c}$ ∼ 0 . 02 r u 13 (ˆ r/r$_{3}$ ) | V$_{13}$ | ∼ 0 . 001ˆ r ( r/r 3 )( m$_{u}$/m$_{t}$ ) | V 13 | ∼ 0 . 0006 r √ r ˆ rm$_{u}$/m$_{t}$/r$_{3}$ ∼ 0 . $_{0009}$√$_{r}$$_{ˆ}$ r u 23 (ˆ r/r$_{3}$ ) | V$_{23}$ | ∼ 0 . 01ˆ r ( r/r 3 )( m$_{c}$/m$_{t}$ ) | V 23 | ∼ 0 . 03 r r ˆ rm$_{c}$/m$_{t}$/r$_{3}$ ∼ 0 . $_{02}$√$_{r}$$_{ˆ}$ r q ij ( δ q $_{ij}$)$_{LL}$ ( δ q $_{ij}$)$_{RR}$ 〈 δ q ij 〉 d 12 0 . 007 0 . 007 0 . 007 d 13 [0 . 003] 0 . 007 0 . 003 d 23 [0 . 01] 0 . 01 0 . 01 u 12 0 . 007 0 . 0003 0 . 001 u 13 0 . 001 0 . 00005 0 . 0003 u 23 0 . 01 0 . 003 0 . 006 TABLE IV: The order of magnitude upper bounds on ( δ d,u ij )$_{LL,RR}$ and 〈 δ d,u ij 〉 for r/r$_{3}$ ∼ < 0 . 03 in hybrid FN models [7]. Entries in parentheses are independent of r , therefore representing estimates rather than upper bounds, and scale as (3 /r$_{3}$ ). The bounds on 〈 δ d 13 , 23 〉 scale as √ 3 /r$_{3}$ . The bounds on ( δ u i $_{3}$)$_{LL}$ [ 〈 δ u i 3 〉 ] correspond to ˆ r ∼ 1 and scale as (3 /r$_{3}$ ) [ √ 3 /r$_{3}$ ]; if ˆ r = r , these bounds are a $_{factor of 10 [}$√$_{10] stronger and do not scale with}$ r$_{3}$ . For small values of tan β , ˆ r = r and Eq. (4.3) applies to ˆ r . Inserting r/r$_{3}$ ∼ < 0 . 03 and r ≤ ˆ r ∼ < 1 into the predictions of Table III, we obtain the upper bounds on the δ q ij presented in Table IV. The maximal possible effects in the neutral B$_{d}$, B$_{s}$ and D systems are thus as follows 11