6 - Effective Hamiltonians for FCNC Processes

Summary

The phenomenological applications of theformulae collected in Chapter 6 require input from lattice QCD (LQCD) and other nonperturbative approches. In particular one needsthe values of hadronic matrix elements of quark currents and those of four-quark operators. In this chapter we will collect all results for hadronic matrix elements, weak decay constants, and other nonperturbative objects in one place so that they can be looked up quickly whenever necessary. But before presenting the results obtained by purely numerical LQCD calculations, we will discuss the application of the so-calleddual QCD approach to weak decays, which was developed by Bardeen, Gerard, and myself over many years. While not as accurate as the lattice QCD method, it offers a better insight in the dominant QCD dynamics at long-distance scales than LQCD itself. The application of LQCD to nonleptonic decays of B mesons is very difficult, and therefore we will devote a section to the QCD factorization approach, stressing its successes and limitations.