The effective continuum threshold in dispersive sum rules

TL;DR

This paper evaluates the accuracy of dispersive sum rules in nonperturbative QCD using a quantum-mechanical model, proposing modifications to improve the extraction of bound-state parameters despite inherent uncertainties.

Contribution

It introduces new procedures for fixing the effective continuum threshold, significantly enhancing the accuracy of bound-state parameter extraction in sum rules.

Findings

Proposed modifications improve the accuracy of sum rule results.

Quantum-mechanical model allows validation against exact solutions.

Systematic uncertainties in sum rules remain challenging to control.

Abstract

We study the accuracy of the bound-state parameters obtained with the method of dispersive sum rules, one of the most popular theoretical approaches in nonperturbative QCD and hadron physics. We make use of a quantum-mechanical potential model since it provides the only possibility to probe the reliability and the accuracy of this method: one obtains the bound-state parameters from sum rules and compares these results with the exact values calculated from the Schr\"odinger equation. We investigate various possibilities to fix the crucial ingredient of the method of sum rules -- the effective continuum threshold -- and propose modifications which lead to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method. Although the rigorous control of systematic uncertainties in the method of sum rules remains unfeasible, the application of the proposed procedures in QCD promises a considerable increase of the actual accuracy of the extracted hadron parameters.