where ϵ denotes a generic MFV-invariant U(1)$_{PQ}$-breaking source. Even if ϵ ≪ 1, the product ϵ × tan β can be O (1), inducing large corrections to the down-type Yukawa sector: Since the b -quark Yukawa coupling becomes O (1), the large-tan β regime is particularly in- teresting for helicity-suppressed observables in B physics. One of the clearest phenomenological consequences is a suppression (typically in the 10 − 50% range) of the B → ℓν decay rate with re- spect to its SM expectation [35]. Potentially measurable effects in the 10 − 30% range are expected also in B → X$_{s}$γ [36] and Δ M$_{B}$$_{s}$ [37]. Given the present measurements of B → ℓν , B → X$_{s}$γ , and Δ M$_{B}$$_{s}$ , none of these effects seems to be favored by data. However, present errors are still sizable compared to the estimated NP effects. The most striking signature could arise from the rare decays B$_{s,d}$ → ℓ $^{+}$ℓ $^{−}$, whose rates could be enhanced over the SM expectations by more than one order of magnitude [38]. An enhancement of both B$_{s}$ → ℓ $^{+}$ℓ − and B$_{d}$ → ℓ $^{+}$ℓ − respecting the MFV relation Γ( B$_{s}$ → ℓ $^{+}$ℓ $^{−}$) / Γ( B$_{d}$ → ℓ $^{+}$ℓ $^{−}$) ≈ | V$_{ts}$/V$_{td}$ | 2 would be an unambiguous signature of MFV at large tan β [27]. The breaking of the SU (3) 3 q flavor group and the breaking of the discrete CP symmetry are not necessarily related, and we can add flavor-diagonal CPV phases to generic MFV models [39–41]. Because of the experimental constraints on electric dipole moments (EDMs), which are generally sensitive to such flavour-diagonal phases [40], in this more general case the bounds on the scale of new physics are substantially higher with respect to the “minimal” case, where the Yukawa couplings are assumed to be the only breaking sources of both symmetries [23] If tan β is large, the inclusion of flavor-diagonal phases has interesting effects also in flavour- changing processes. The main consequences, derived in a model independent manner, can be summarized as follows [30]: (i) extra CPV can only arise from flavor diagonal CPV sources in the UV theory; (ii) the extra CP phases in B$_{s}$ − ¯ B$_{s}$ mixing provide an upper bound on the amount of CPV in B$_{d}$ − ¯ B$_{d}$ mixing; (iii) if operators containing right-handed light quarks are sub-dominant then the extra CPV is equal in the two systems, and is negligible in transitions between the first two generations to the third one. Conversely, these operators can break the correlation between CPV in the B$_{s}$ and B$_{d}$ systems, and can induce significant new CPV in ϵ$_{K}$ . 17 B. MFV with additional flavor-diagonal phases ϵ Q$_{L}$Y $^{d}$D$_{R}$ ˜ φ$_{U}$ vev −→ ϵ Q$_{L}$Y $^{d}$D$_{R}$ 〈 ˜ φ$_{U}$ 〉 = ( ϵ × tan β ) Q$_{L}$Y $^{d}$D$_{R}$ 〈 φ$_{D}$ 〉 . (4.8)