Charming penguin and direct CP-violation in charmless B decays

In the study of two-body charmlessB decays as a mean of looking for direct CP-violation and measuring the CKM mixing parameters in the Standard Model, the short-distance penguin contribution with its absorptive part generated by charm quark loop seems capable of producing sufficient B → Kπ decays rates, as obtained in factorization and QCD-improved factorization models. However there are also long-distance charming penguin contributions which could give rise to a strong phase due to the rescattering D∗D∗ s → Kπ etc. In this talk, I would like to discuss recent works on the charming penguin contribution as a different approach to the calculation of these contributions in two-body charmless B decays. We find that the charming penguin contribution is significant for B → Kπ decays and, together with the tree and penguin terms, produces large branching ratios in agreement with data, though the analysis is affected by large theoretical uncertainties. The absorptive part due to the charmed meson intermediate states is found to produce large CP asymmetries for B → Kπ, ππ decays. PC073.1002 October 2002 † Talk given at the QCD Euroconference 2002, Montpellier 2-9 July 2002 In nonleptonic charmless two-body B decays, the interference between the tree-level and penguin terms make it possible to look for direct CP-violation and to determine the CP-violating weak CKM phase angle γ from these decays [1, 2, 3]. It is known that the top quark penguin amplitude is insufficient to produce a large B → Kπ decay rates. When the effects of charm quark loop are included, the decay rate is enhanced [4, 5, 6, 7, 8] and are in qualitative agreement with data [8, 9, 10, 11]. The effects of charm quark loop is contained in QCD-improved factorization as shown recently [12, 13, 14]. One can also take the view that these charm quark loop contributions are basically long-distance effects, essentially due to charmed meson rescattering processes, such as, e.g. B → DsD → Kπ. These contributions, first discussed in [15], have been more recently stressed by [16, 17] where they are called the charming penguin contributions. In [18, 19] , we have evaluated these contributions and found that both the absorptive and the real part of the charming penguin are large, comparable to the short-distance part and is capable of generating large CP asymmetries in charmless B decays. In this talk I would like to discuss these calculations and stress the importance of the charming penguin in charmless B decays, especially the large absorptive part generated by the charmed meson rescattering effects and the CP asymmetries obtained. That the charmed meson rescatterings could generate a large charming penguin is easily seen from the unitarity of the S–matrix. For example, the absorptive part of the B → Kπ decays amplitude would get the main contribution from the DsD and D ∗ sD ∗ intermediate states since the color-favored, Cabibbo-allowed B → DsD and B → D∗ sD decays which are governed by the large coefficient a2 = 1.03 have branching ratios of the order 10−2 compared with the penguin-dominated B → Kπ decays with branching ratios a few 10−5. Without the suppression of the process DsD → Kπ and D∗ sD ∗ → Kπ, we would have a very large B → Kπ decay rates. In the standard model, the effective Hamiltonian for B → Kπ decays are given by Heff = GF √ 2 [VubV ∗ us(c1O u 1 + c2O u 2 ) + VcbV ∗ cs(c1O c 1 + c2O c 2)− V ∗ tbVts 10