QCD Sum Rules and Hadronic Matrix Elements

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In contemporary particle physics research, the fundamental transitions between quarks with different flavour quantum numbers are being intensively investigated in exclusive semileptonic and radiative decays of hadrons containing heavy b- or c-quarks. These processes are especially interesting because they are sensitive to virtual effects of new heavy particles beyond the Standard Model of particle physics. In studies of heavy hadron decays, the theoretical accuracy has to match the high precision of the experimental measurements (at the “Large Hadron Collider” and at future accelerator facilities, the so called “super-flavour factories”). Here, the main challenge lies in the theoretical computation of the strong-interaction effects in Quantum Chromodynamics (QCD). In this project, a combination of theoretical methods aimed at solving this problem will be further developed and applied.The emphasis will be on the so-called light-cone sum rule approach in QCD. Based on analytical calculations, the sum-rule method combines several powerful theory tools: the operator-product expansion in QCD, hadronic dispersion relations and quark-hadron duality. The calculational procedures in QCD will be supplemented by systematic expansions of hadronic amplitudes in QCD-based effective theories, such as the Soft-Collinear Effective Theory. We plan new applications of the sum-rule technique, including: the calculation of semileptonic B- and D-meson decay amplitudes with two pseudoscalar mesons in the final state, the semileptonic transitions of heavy baryons, and the hadronic matrix elements relevant for heavy-hadron decays with flavour-changing neutral currents. In addition to the conventional light-cone sum rules, new sum rules in the effective theories will be obtained to assess the effects of the resummation of higher-order effects in the operator-product expansion.