TABLE I: Bounds on representative dimension-six Δ F = 2 operators. Bounds on Λ are quoted assuming an effective coupling 1 / Λ $^{2}$, or, alternatively, the bounds on the respective c$_{ij}$ ’s assuming Λ = 1 TeV. Observables related to CPV are separated from the CP conserving ones with semicolons. In the B$_{s}$ system we only quote a bound on the modulo of the NP amplitude derived from Δ m$_{B}$$_{s}$ (see text). For the definition of the CPV observables in the D system see Ref. [15]. central value for the CP-violating phase, contrary to the SM expectation. The errors are, however, still large and the disagreement with the SM is at about the 2 σ level. If the disagreement persists, becoming statistically significant, this would not only signal the presence of physics beyond the SM, but would also rule out a whole subclass of MFV models (see Sect. IV). (iv) In D − ¯ D mixing we cannot estimate the SM contribution from first principles; however, to a good accuracy this is CP conserving. As a result, strong bounds on possible non-standard CP-violating contributions can still be set. The resulting constraints are only second to those from ϵ$_{K}$ , and unlike in the case of ϵ$_{K}$ are controlled by experimental statistics and could possibly be significantly improved in the near future. A more detailed list of the bounds derived from Δ F = 2 observables is shown in Table I, where we quote the bounds for two representative sets of dimension-six operators: the left-left operators (present also in the SM) and operators with a different chirality, which arise in specific SM extensions. The bounds on the latter are stronger, especially in the kaon case, because of the larger hadronic matrix elements. The constraints related to CPV correspond to maximal phases, and are subject to the requirement that the NP contributions are smaller than 30% (60%) of the total contributions [9] in the B$_{d}$ ( K ) system. Since the experimental status of CP violation in the B$_{s}$ system is not yet settled we simply require that the new physics contributions are smaller than 9 Operator Bounds on Λ in TeV ( c$_{ij}$ = 1) Bounds on c$_{ij}$ (Λ = 1 TeV) Observables Re Im Re Im (¯ s$_{L}$γ $^{µ}$d$_{L}$ ) 2 9 . 8 × 10 2 1 . 6 × 10 4 9 . 0 × 10 − 7 3 . 4 × 10 − 9 Δ m$_{K}$ ; ϵ$_{K}$ (¯ s$_{R}$ d$_{L}$ )(¯ s$_{L}$d$_{R}$ ) 1 . 8 × 10 4 3 . 2 × 10 5 6 . 9 × 10 − 9 2 . 6 × 10 − 11 Δ m$_{K}$ ; ϵ$_{K}$ (¯ c$_{L}$γ $^{µ}$u$_{L}$ ) 2 1 . 2 × 10 3 2 . 9 × 10 3 5 . 6 × 10 − 7 1 . 0 × 10 − 7 Δ m$_{D}$ ; | q/p | , φ$_{D}$ (¯ c$_{R}$ u$_{L}$ )(¯ c$_{L}$u$_{R}$ ) 6 . 2 × 10 3 1 . 5 × 10 4 5 . 7 × 10 − 8 1 . 1 × 10 − 8 Δ m$_{D}$ ; | q/p | , φ$_{D}$ ( ¯ b$_{L}$γ $^{µ}$d$_{L}$ ) 2 5 . 1 × 10 2 9 . 3 × 10 2 3 . 3 × 10 − 6 1 . 0 × 10 − 6 Δ m$_{B}$$_{d}$ ; S$_{ψK}$$_{S}$ ( ¯ b$_{R}$ d$_{L}$ )( ¯ b$_{L}$d$_{R}$ ) 1 . 9 × 10 3 3 . 6 × 10 3 5 . 6 × 10 − 7 1 . 7 × 10 − 7 Δ m$_{B}$$_{d}$ ; S$_{ψK}$$_{S}$ ( ¯ b$_{L}$γ $^{µ}$s$_{L}$ ) 2 1 . 1 × 10 2 7 . 6 × 10 − 5 Δ m$_{B}$$_{s}$ ( ¯ b$_{R}$ s$_{L}$ )( ¯ b$_{L}$s$_{R}$ ) 3 . 7 × 10 2 1 . 3 × 10 − 5 Δ m$_{B}$$_{s}$