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where there is no summation over i, j, k and where ˜ m 2 q$_{j}$q$_{i}$ = ˜ m 2 q$_{j}$ − ˜ m 2 $_{q$_{i}$}$. Then, the contribution of the intermediate ˜ q$_{k}$ can be neglected and, furthermore, to a good approximation, K$_{ii}$K ∗ $_{ji}$+ K$_{ij}$K ∗ jj = 0. For these cases, we obtain 

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It is further useful to use instead of ˜ m$_{q}$ the mass scale ˜ m q ij = 1 $_{2}$( ˜ m$_{q}$$_{i}$ + ˜ m$_{q}$$_{j}$ ) [43]. We also define 

<img src='content_image/368370.jpg'>

The new sources of flavor and CP violation contribute to FCNC processes via loop diagrams involving squarks and gluinos (or electroweak gauginos, or higgsinos). If the scale of the soft supersymmetry breaking is below TeV, and if the new flavor violation is of order one, and/or if the phases are of order one, then these contributions could be orders of magnitude above the experimental bounds. Imposing that the supersymmetric contributions do not exceed the phe- nomenological constraints leads to constraints of the form ( δ q $_{ij}$)$_{MM}$ ≪ 1. Such constraints imply that either quasi-degeneracy (Δ ˜ m 2 q$_{j}$q$_{i}$ ≪ ˜ m q 2 $_{ij}$) or alignment ( | K q ij | ≪ 1) or a combination of the two mechanisms is at work. 

Table IV presents the constraints obtained in Refs. [44–47] as appear in [42]. Wherever relevant, a phase suppression of order 0.3 in the mixing amplitude is allowed, namely we quote the stronger between the bounds on R e ( δ q $_{ij}$) and 3 I m ( δ q $_{ij}$). The dependence of these bounds on the average squark mass m$_{˜}$ $_{q}$, the ratio x ≡ m 2 ˜ $_{g}$/m 2 ˜ q as well as the effect of arbitrary strong CP violating phases can be found in [42]. 

For large tan β , some constraints are modified from those in Table IV. For instance, the effects of neutral Higgs exchange in B$_{s}$ and B$_{d}$ mixing give, for tan β = 30 and x = 1 (see [42, 48] and references therein for details): 

<img src='content_image/368369.jpg'>

where M$_{A}$ 0 denotes the pseudoscalar Higgs mass, and the above bounds scale roughly as (30 / tan β ) $^{2}$. 

The experimental constraints on the ( δ q $_{ij}$)$_{LR}$ parameters in the quark-squark sector are presented in Table V. The bounds are the same for ( δ q $_{ij}$)$_{LR}$ and ( δ q $_{ij}$)$_{RL}$ , except for ( δ d $_{12}$)$_{MN}$ , where the bound 

