Seltene semileptonische Zerfälle schwerer Mesonen im QCD-Faktorisierungsansatz

Rare decays of heavy mesons provide an excellent test of the quark flavour sector of the standard model of particle physics. Moreover, precise measurements of corresponding observables in combination with reliable predictions are an important tool to constrain the parameter space of so-called new physics models. In the light of this fact, we analyze in this dissertation the rare semileptonic decays D -> rho l^+ l^- and B -> K pi l^+ l^- in the framework of QCD factorization in a suitable region of phase space.

The main body of this thesis consists of three parts. Object of the first part are the c -> u l^+ l^- Wilson coefficients. We present a consistent two-step running of the coefficients for mass dimension-6 operators from the scale mu = M_W to the scale mu = m_c. The running involves an intermediary scale mu = m_b (with M_W > m_b > m_c), at which the bottom quark is integrated out. The matching coefficients and the anomalous dimensions are taken to the required order by generalizing and extending results from b -> s or s -> d transitions available in the literature.

In the second part of the thesis we consider the rare semileptonic decay D -> rho l^+ l^- in the framework of QCD factorization, where we use our results for the Wilson coefficients from the first part. Our procedure is performed in analogy to the corresponding B decays. Since the decay rate is dominated by non-factorizable effects, e.g. through annihilation topologies, which are especially sensitive to long-distance resonance effects, we pay particular attention to the thourough estimate of the uncertainties connected with these contributions.

The third part of the thesis deals with the rare semileptonic decay B -> K pi l^+ l^- at large invariant dimeson mass. Here it is our goal to make a rough estimate for the decay rates of all possible decay modes in a suitable region of phase space. Therefore we neglect higher-order gluonic corrections and concentrate on the contribution of leading twist of the light cone distribution amplitudes of the light mesons. The numerical analysis reveals a strong supression of the partially integrated branching fraction compared to the resonant decay B -> K^* (-> K pi) l^+ l^- for all decay modes in the considered region of phase space. Still this decay might be important in order to gain additional insight about the decay B -> K^* (-> K pi) l^+ l^- from a proper interpolation between different kinematical regimes.