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sin 2 β and the angle γ in the Presence of New ∆ F = 2 Operators

We present formulae for the mass differences ∆Md and ∆Ms in the B̄ 0 d,s-B 0 d,s systems and for the CP violation parameter ε which are valid in minimal flavour violation models giving rise to new four-fermion ∆F = 2 operators. Short distance contributions to ∆Ms, ∆Md 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 ∆Ms/∆Md, sin 2β and γ that allow to search for the effects of the new operators. We point out that their sizable contributions to the ratio ∆Ms/∆Md would in principle allow γ to be larger than 90◦. Constraints on the functions F i tt imposed by the present (and future) experimental data are also discussed. As an example we show that for large tan β̄ ≡ 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 tan4 β̄ 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. As in this scenario the lower bound on sin 2β following from ε and ∆Md is identical to the SM ones (sin 2β > 0.5), the future low values of the CP asymmetry aψKS may further constrain the stop mixing or rule out this scenario altogether.