content_image/374981.jpg
Then, one can express all the relevant observables as a function of the two remaining parameters, ρ and η , and check whether there is a range in the ρ − η plane that is consistent with all measurements. The list of observables includes the following: 

• The rates of inclusive and exclusive charmless semileptonic B decays depend on | V$_{ub}$ | 2 ∝ ρ 2 + η $^{2}$; 

• The CP asymmetry in B → ψK$_{S}$ , S$_{B}$$_{→}$$_{ψK}$ = sin 2 β = 2 η (1 − ρ ) (1 − ρ ) $^{2}$+ η 2 ; 

• The rates of various B → DK decays depend on the phase γ , where e iγ = ρ + iη √ ρ $^{2}$+ η $_{2}$; 

• The rates of various B → ππ, ρπ, ρρ decays depend on the phase α = π − β − γ ; 

• The ratio between the mass splittings in the neutral B and B$_{s}$ systems is sensitive to | V$_{td}$/V$_{ts}$ | 2 = λ $^{2}$[(1 − ρ ) 2 + η $^{2}$]; 

• The CP violation in K → ππ decays, ϵ$_{K}$ , depends in a complicated way on ρ and η . 

The resulting constraints are shown in Fig. 1. 

The consistency of the various constraints is impressive. In particular, the following ranges for ρ and η can account for all the measurements [5]: 

One can make then the following statement [7–9]: 

<img src='content_image/374981.jpg'>

Very likely, flavor violation and CP violation in flavor changing processes are domi- nated by the CKM mechanism. 

One can actually go a step further, and allow for arbitrary new physics in all flavor changing processes except for those that have contributions from SM tree diagrams. Then, one can quanti- tatively constrain the size of new physics contributions to processes such as neutral meson mixing. We do so in the next section. 

## III. MODEL INDEPENDENT CONSTRAINTS 

In order to describe NP effects in flavor physics we can follow two main strategies: (i) build an explicit ultraviolet completion of the model, and specify which are the new fields beyond the SM ones, or (ii) analyse the NP effects using a generic effective-theory approach, or integrating-out the new heavy fields. The first approach is more predictive, but also more model dependent. We 

