Quark-Hadron Duality and Effective Continuum Thresholds in Dispersive Sum Rules

Full text: We consider the extraction of ground-state parameters within the framework of QCD sum rules, with emphasis on the crucial ingredient of this approach, viz., the effective continuum threshold, which governs the accuracy of the duality approximation. We propose a new algorithm to fix this quantity and probe both reliability and actual accuracy of sum-rule predictions at the example of quantum mechanical potential models, which allow for comparison with the exact solutions. Our procedure yields a significant improvement of the accuracy of resulting ground state parameters compared with standard sum-rule techniques used in all previous applications of dispersive sum rules in QCD. Moreover, the procedures of extracting ground-state decay constants in potential models and in QCD prove to be quantitatively very similar. Thus, the application of the proposed algorithm in QCD promises to result in a considerable increase of the accuracy of the extracted hadron parameters. (author)