ΔMs/ ΔMd, sin2 β and the angle γ in the presence of new ΔF=2 operators

Abstract

We present formulae for the mass differences ΔM d and ΔM s in the B ̄ d,s 0 – B d, s 0 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 , sin2 β 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 F i tt imposed by the present (and future) experimental data are also discussed. As an example we show that for large tan β ̄ ≡v 2/v 1 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 tan 4 β ̄ 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 sin2 β following from ε and ΔM d is identical to the SM ones (0.5<sin2 β<0.8). On the other hand γ following from ΔM s / ΔM d is lower.