For the computation of processes in the Standard Model of Elementary Particle Physics (SM), so-called effective field theories (EFTs) are used. In this way, it is possible to treat corrections systematically. One EFT is the Heavy Quark Effective Theory (HQET), which exploits the fact that in the heavy quark mass limit m_Q --> infinity, a spin as well as a flavor symmetry appears. In this thesis, three applications of HQET are presented.
First, the ‘1/2 vs. 3/2’ puzzle is addressed. Here, a tension between the theory prediction and the experimental measurement of semileptonic decays of B mesons into orbitally excited D mesons is observed. For the latter, four different states exist that can be arranged into two spin-symmetry doublets, which are classified by the total angular momentum of their light degrees of freedom j = 1/2 and j = 3/2, respectively. Taking into account the spin of the heavy quark, the states in the j = 1/2 doublet can have a total angular momentum of 0 and 1 and the states in the j = 3/2 doublet 1 and 2. From theory, it is expected that the rates for the decays into the states with j = 3/2 are significantly larger than the ones for j = 1/2. In experiments, however, the measured decay rates are roughly the same. In this thesis, it is investigated if a mixing of the two states with a total angular momentum of 1 can ease this tension.
Another aspect of mixing can be observed in the B-anti-B system. Here, the mass difference between the B and anti-B states is determined by the matrix element of the effective local four-quark operator. For the computation of this matrix element a ‘bag parameter’ is introduced which is unity in naive factorization. Any deviation from unity stems from non-factorizable contributions. The bag parameter can be obtained using the established method of sum rules in the context of HQET, which requires the calculation of three-loop diagrams in the case of the non-factorizable contributions. The presented computation completes the next-to-leading order result for the bag parameter.
A further application of HQET is QCD factorization, which has recently been extended to three-body decays. In this thesis, CP violation in the decay B --> pi pi pi is studied in that framework. In experimental data, a rich structure of large local CP asymmetries has been observed. It is investigated if this structure can be explained within the QCD factorization approach. Even though some refinement is required, the rough features of the observed CP asymmetry can be reproduced within this model.