Study On B�'sYY Decay In Standard Model

As well known, flavor-changing neutral-currents (FCNC) induced B-meson rare de-cays provide an ideal opportunity for extracting information about the fundamental parameters of the standard model (SM) and some hadronic parameters in QCD, such as the CKM matrix elements,the meson decay constant fB, providing information on heavy meson wavefunctions. And since these decays occur in the SM only through loops, they also play an important role in testing higher-order effects in the SM and in searching for the physics beyond the SM.Theoretical predictions for inclusive decays B→X_sγ(γ), B→X_sl~+l~-(γ)and exclusive decays B_s→γγ, B_s→l~+l~-(γ) and B→K(K*)l~+l~- have been studied extremely by many authors in the framework of the SM and new physics. Among these works, obtaining effective Hamiltonians for b→sγ, b→sl~+l~- is regarded as the fundamental research with following assumption: i) The effective Hamiltonians for b→sγ, b→sl~+l~- can be used directly to the processes as Bs→γγ, Bs→l~+l~-(γ) and ii) the operators included in the effective Hamiltonians are sufficient to describe the processes in model without particles much lighter thanW boson. It is clear that these two assumptions are proble-matic. Therefore, we propose the following questions:Whether the effective Hamiltonians are obtained entirely from the on-shell quark contribution? Clearly, in the process b→sγγ, b quark or s quark can be not on-shell. It means that the assumption i) seems inconsistent unless that the off-shell quarks effects on b→sγ, b→sl~+l~- are small and can be neg-lected;Whether the diagrams without b→sγeffective vertex also contribute to b→sγγand b→sl~+l~-γ? Even contributions coming from the diagrams with another photon attached to internal lines are do strongly suppressed by a factor m_b~2/m_w~2 as stated in some previous works, contribution from the di-agrams with WWγγinteraction in the SM is surely comparable to others.Based on the above two questions , we will present a comprehensive calculation for b→sγγat matching scale in this paper. Based on the calculation, we proved the following three conclusions, (1) The off-shell quark effect in the diagrams with b→sγeffective vertex is ap-parent and can't be neglected.(2) The contribute of the diagrams without b→sγeffective vertex also can't be neglected.(3) The off-shell quarks effect and the contributions from diagrams without b→sγvertex cancel each other exactly so that the operators of b→sγcan be used safely to describe b→sγγ.Although the conclusion can be drawn by using Low's low energy theorem, this work is useful in deepening our understanding of B physics and thus valuable.