Rescattering E ects in Heavy Quark Decays

Heavy quark decays serve as a powerful tool for testing the Standard Model and, since it probes the quarks of all three generations, provide invaluable possibilities to study CP violation. However, the interpretation of experimental observables in terms of fundamental parameters is often less than clear. Rare hadronic decays of B mesons, for example, proceed through both tree level Cabibbo-suppressed amplitudes and through one loop penguin amplitudes. On the one hand, this situation allows direct CP violating e ects. On the other, these contributions complicate the extraction of Cabibbo-Kobayashi-Maskawa (CKM) angles and, in particular, the angle arg [ VudV ub=VcdV cb] : The decay of a heavy hadron produces quarks in the nal state. Because of their strong QCD interactions they continue to interact after the weak transition took place. Even after they have formed hadrons, there are still strong forces between them, and therefore, the problem of the nal state rescatterings or nal state interactions (FSI) is an important part of the physics of nonleptonic b-decays. The most pronounced e ect of FSI is clearly in direct CPviolation where one compares the rates of a B-meson decay with the charged conjugated process. The corresponding asymmetries between the two decays depend on both a weak (CKM) and a strong rescattering phase provided by the FSI. Furthermore, a non-vanishing asymmetery requires two di erent nal states produced by di erent weak amplitudes which can go into each other by a strong interaction rescattering. Thus, FSI directly a ect the asymmetries and their size can be interpreted in terms of fundamental parameters only if these FSI phases are calculable. As an example, let us rst look at the recently measured combined branching ratios for B ! K and Bd ! K [1]. In the Standard Model, these decays are mediated by the B = 1 Hamiltonian, which takes the form