Hadronische Matrixelemente mit schweren Quarks aus QCD-Summenregeln

The search for new physics in weak decays is an important subject of modern Particle Physics. At accelerators, e.g. at the Large Hadron Collider (LHC) at CERN, exclusive decays of heavy hadrons with various final states are extensively studied. In theory, these decays are parameterized by hadronic matrix elements which involve nonperturbative quark-gluon dynamics. The calculation of these matrix elements using the technique of QCD sum rules is the main subject of this thesis.

After a general introduction and a discussion of the sum rule technique, the first part of this work is focussed on the derivation and evaluation of various sum rules for a certain kind of hadronic matrix elements called decay constants. In this analysis, for the first time next to leading order corrections to the quark condensate contributions for vector currents are taken into account. In addition to a detailed discussion of uncertainties, the results obtained using the sum rule technique are found to be in good agreement with lattice QCD results.
Furthermore, the previously used QCD sum rules are modified to calculate the decay constants for the first radial excitation of the considered mesons. In the modified sum rule, the hadronic representation of the correlation function is extended to also include the corresponding resonance. Notably, a new fitting procedure is adopted to fix the duality threshold parameter. Despite large uncertainties in the meson masses for the radial excitations, this new procedure provides a satisfactory, and for some channels the first, estimate of the decay constants.
In the last part of the thesis, QCD light-cone sum rules for the calculation of the strong coupling between three mesons, two heavy ones with vector and pseudoscalar spin parity and a pion, are derived. The major purpose of this section is the update and reorganization of the leading order contributions for a smooth implementation in the future next to leading order analysis. Furthermore, the results from the previous sections are used, to provide a first estimate for strong couplings with radial excitations.