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that the projection onto the SU (3) generators has a unit norm ( ∑ $_{i}$a 2 i = 1), we can indentify a unique combination which minimizes the combined bound from top and B constraints. Taking into account the projected LHC sensitivity on t → u i decays, we can expect to reach bounds of O (600 GeV) on the scale Λ$_{t}$ [22], in the absence of a NP signal. 

## IV. MINIMAL FLAVOR VIOLATION 

A very reasonable, although quite pessimistic, set up which avoids the new physics flavor prob- lem is the so-called Minimal Flavor Violation (MFV) hypothesis. Under this assumption, flavor- violating interactions are linked to the known structure of Yukawa couplings also beyond the SM. As a result, non-standard contributions in FCNC transitions turn out to be suppressed to a level consistent with experiments even for Λ ∼ few TeV. One of the most interesting aspects of the MFV hypothesis is that it can naturally be implemented within the generic effective Lagrangian in Eq. (3.1). Furthermore, SM extensions where the flavor hierarchy is generated at a scale much higher than other dynamical scales tend to flow to the MFV class of models in the infra-red. 

The MFV hypothesis consists of two ingredients [23]: (i) a flavor symmetry and (ii) a set of symmetry-breaking terms . The symmetry is nothing but the large global symmetry of the SM Lagrangian in absence of Yukawa couplings shown in Eq. (2.7). Since this global symmetry, and particularly the SU(3) subgroups controlling quark flavor-changing transitions, is already broken within the SM, we cannot promote it to be an exact symmetry of the NP model. Some breaking would appear at the quantum level because of the SM Yukawa interactions. The most restrictive assumption we can make to protect in a consistent way quark-flavor mixing beyond the SM is to assume that Y d and Y u are the only sources of flavor symmetry breaking also in the NP model. To implement and interpret this hypothesis in a consistent way, we can assume that SU (3) 3 q is a good symmetry and promote Y u,d to be non-dynamical fields (spurions) with non-trivial transformation properties under SU (3) 3 $_{q}$: 

<img src='content_image/350495.jpg'>

If the breaking of the symmetry occurs at very high energy scales, at low-energies we would only be sensitive to the background values of the Y , i.e. to the ordinary SM Yukawa couplings. Employing the effective-theory language, an effective theory satisfies the criterion of Minimal Flavor Violation in the quark sector 1 if all higher-dimensional operators, constructed from SM and Y fields, are 

