Bound-state parameters from dispersive sum rules for vacuum-to-vacuum correlators

TL;DR

This paper evaluates the accuracy of dispersive sum rules for extracting ground-state parameters using a quantum-mechanical model, proposing a new algorithm for the effective continuum threshold that significantly improves precision.

Contribution

It introduces a novel algorithm for fixing the effective continuum threshold, enhancing the accuracy of sum rule methods in quantum mechanics and potentially in QCD.

Findings

The new algorithm improves the accuracy of ground-state parameter extraction.

Application in QCD could significantly increase hadron parameter precision.

Standard procedures are less accurate compared to the proposed method.

Abstract

We study the extraction of the ground-state parameters from vacuum-to-vacuum correlators. We work in quantum-mechanical potential model which provides the only possibility to probe the reliability and the actual accuracy of this method: one obtains the bound-state parameters from the correlators by the standard procedures adopted in the method of sum rules and compares these results with the exact values calculated from the Schroedinger equation. We focus on the crucial ingredient of the method of sum rules - the effective continuum threshold - and propose a new algorithm to fix this quantity. In a quantum-mechanical model, our procedure leads 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. The application of the proposed procedure in QCD promises a considerable increase of the accuracy of the extracted hadron parameters.