Penguin Effects on Kπ and ππ Decays of the B Meson

We give the detailed analyses for the gluonic-penguin effect on the Kπ and ππ decays of the B meson. In the standard model, it is shown that the ratio BR(B → Kπ)/BR(B → ππ) takes the value 0.5 ∼ 3.0 with the strongly depending on the CP violating phase φ and the KM matrix element |Vub|. We obtain the constraint on the form factor by using the experimental branching ratio. It is also found that, in the two-Higgs-doublet model, the charged Higgs contribution which could enhance the B → Xsγ decay does not a sizable effect on our processes. The effect of the final state interaction on these processes is also discussed. E-mail:[email protected] Until now, the rare B decays have been intensively studied in the standpoint of the standard model(SM) and also beyond the standard model. Especially, b → sγ and b → sg sub-processes have attracted one’s attention in the circumstance that the experimental evidence has been found in CLEO [1]. These decays, induced by the flavour changing neutral current, are controlled by the one-loop penguin operators which involve the important SM parameters such as the top-quark mass and the Kobayashi-Maskawa matrix elements Vts and Vtb[2]. In our previous papers [3], we analyzed the inclusive decay B → Xsγ and the exclusive decays B → KXγ, where KX denotes the meson states in the sq(q = u or d) system, as well as the exclusive decays B → KXφ by including the nonstandard physical effects due to the charged Higgs contributions in the two-Higgs-doublet model(THDM) [4][5]. In this paper, we study the B → Kπ and B → ππ decays, which are induced by both tree processes and gluonic penguin ones, in the SM model. Now we take into account QCD corrections, which were not included in the previous calculations[6], since the QCD corrections have been found to give the important contributions to the rare decays of the B meson. Recently, CLEO Collaboration reported the following experimental result [7]: BR(B d → ππ +Kπ) = (2.4 −0.7 ± 0.2)× 10 , (1) where the discrimination between the K meson and the π meson has not been suceeded. We will predict the ratio of the B → Kπ decay width to the B → ππ one, the ratio being almost independent of the form factor. The magnitude of the relevant form factor can be restricted by the experimental branching ratio of eq.(1) as shown later. Furtheremore, we will examine the nonstandard effects due to the charged Higgs contribution in the THDM. Finally, the effect of the phase shifts due to the final state interactions will be discussed as to our numerical results. 2 In the previous paper[5], we give the formulation including the QCD corrections for the rare decays of the B meson. The four-quark operators and the magnetic-transitiontype ones are given for the processes under consideration in the the Hamiltonian [8][9], Heff = 4GF √ 2 [