ΔM_s/ΔM_d, sin2β and the angle γ in the presence of new ΔF=2 operators

We present formulae for the mass differences ΔM_d and ΔM_s in the B̄_d,s⁰-B_d,s⁰ systems and for the CP violation parameter ε which are valid in minimal flavour violation models giving rise to new four-fermion ΔF=2 operators. Short distance contributions to ΔM_s, ΔM_d and ε are parameterized by three real functions F^s_tt, F^d_tt and F^ε_tt, respectively (F^s_tt=F^d_tt=F^ε_tt holds only if the Standard Model (V-A)⊗(V-A) operators dominate). We present simple strategies involving the ratio ΔM_s/ΔM_d, sin2β and γ that allow to search for the effects of the new operators. We point out that their sizable contributions to the ratio ΔM_s/ΔM_d would in principle allow γ to be larger than 90°. Constraints on the functions Fⁱ_tt imposed by the present (and future) experimental data are also discussed. As an example we show that for large tanβ̄≡v₂/v₁ and H⁺ not too heavy, F^s_tt in the MSSM with heavy sparticles can be substantially smaller than in the SM due the charged Higgs box contributions and in particular due to the growing like tan⁴β̄ contribution of the double penguin diagrams involving neutral Higgs boson exchanges. As a result the bounds on the function F^s_tt can be violated which allows to exclude large mixing of stops. In this scenario the range of sin2β following from ε and ΔM_d is identical to the SM ones (0.5<sin2β<0.8). On the other hand γ following from ΔM_s/ΔM_d is lower.