Effective Hamiltonian Beyond the Leading Order and their Applications

The thesis consists of four chapters. Chapt.1 summarizes the physics of flavour mixing and CP-violation in the three generation Standard Model. General comments are made about the indirect determination of the unknown top parameters. The discussion is finally restricted to K - and B-systems. Next, the detailed calculation of the NLO evolution of the Effective Hamiltonian for DeltaF = 1 weak decays is given in Chapt.2 and Chapt.3. First the general formalism for the NLO evolution of the Wilson coefficients in presence of QCD and QED corrections is derived. Then we discuss initial conditions for the evolution of the coefficient functions, the origin and the dynamics of operator mixing and the final results for the anomalous dimension matrix. The analytic aspects of the calculation are given in Chapt.3, where we will describe the most important techniques and the results. Chapt.4 is devoted to numerical applications of the analytic results, with an outlook to the possible future implementation in the physics of CP-violation and flavour mixing.