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where the V$_{i}$ are unitary matrices. The Yukawa interactions (2.5) break the global symmetry, 

<img src='content_image/347053.jpg'>

(Of course, the gauged U (1)$_{Y}$ also remains a good symmetry.) Thus, the transformations of Eq. (2.8) are not a symmetry of L $_{SM}$. Instead, they correspond to a change of the interaction basis. These observations also offer an alternative way of defining flavor physics: it refers to interactions that break the SU (3) 5 symmetry (2.8). Thus, the term “ flavor violation ” is often used to describe processes or parameters that break the symmetry. 

Using the transformation (2.8), one can choose an interaction basis where the number of pa- rameters is minimized. A useful example of such a basis for the quark Yukawa matrices is the following: 

where λ$_{d,u}$ are diagonal, 

<img src='content_image/347055.jpg'>

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while V is a unitary matrix that depends on three real angles and one complex phase. We conclude that there are 10 quark flavor parameters: 9 real ones and a single phase. In the mass basis, one identifies six of the real parameters as the six quark masses, while the remaining three real and one imaginary parameters appear in the CKM matrix [1, 2], V , which describes the couplings of the charged weak-force carriers, the W $^{±}$-bosons, with quark-antiquark pairs. 

Within the standard model, all flavor changing physics comes from the V matrix. There are various ways to choose the four parameters of V . One of the most convenient ways is given by the Wolfenstein parametrization, where the four mixing parameters are ( λ, A, ρ, η ) with λ = | V$_{us}$ | = 0 . 23 playing the role of an expansion parameter and η representing the CP violating phase [3, 4]: 

<img src='content_image/347056.jpg'>

One can assume that flavor changing processes are fully described by the SM, and check the consistency of the various measurements with this assumption. The values of λ and A are known rather accurately [5] from, respectively, K → πℓν and b → cℓν decays: 

<img src='content_image/347057.jpg'>

