Extraction of bound-state parameters from dispersive sum rules

TL;DR

This paper introduces a new algorithm for determining the effective continuum threshold in dispersive sum rules, significantly improving the accuracy of extracting ground-state parameters in quantum mechanics models and QCD.

Contribution

A novel algorithm for fixing the effective continuum threshold in sum rules, validated in a quantum-mechanical model and applicable to QCD for better accuracy.

Findings

The new algorithm improves ground-state parameter accuracy in models.

Application to QCD suggests similar accuracy improvements.

Quantum-mechanical tests validate the method's reliability.

Abstract

The procedure of extracting the ground-state parameters from vacuum-to-vacuum and vacuum-to-hadron correlators within the method of sum rules is considered. The emphasis is laid on the crucial ingredient of this method - the effective continuum threshold. A new algorithm to fix this quantity is proposed and tested. First, a quantum-mechanical potential model which provides the only possibility to probe the reliability and the actual accuracy of the sum-rule method is used as a study case. In this model, our algorithm is shown to lead to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method and used in all previous applications of dispersive sum rules in QCD. As a next step, it is demonstrated that the procedures of extracting the ground-state decay constant in the potential model and in QCD are quantitatively very close to each other. Therefore, the application of the proposed algorithm in QCD promises a considerable increase of the accuracy of the extracted hadron parameters.