Extraction of ground-state decay constant from dispersive sum rules: QCD vs potential models

We compare the extraction of the ground-state decay constant from the two-point correlator in QCD and in potential models and show that the results obtained at each step of the extraction procedure follow a very similar pattern. We prove that allowing for a Borel-parameter-dependent effective continuum threshold yields two essential improvements compared to employing a Borel-parameter-independent quantity: (i) It reduces considerably the (unphysical) dependence of the extracted bound-state mass and the decay constant on the Borel parameter. (ii) In a potential model, where the actual value of the decay constant is known from the Schrödinger equation, a Borel-parameter-dependent threshold leads to an improvement of the accuracy of the extraction procedure. Our findings suggest that in QCD a Borel-parameter-dependent threshold leads to a more reliable and accurate determination of bound-state characteristics by the method of sum rules.