How reliable are bound-state parameters obtained from QCD sum rules?

TL;DR

This paper evaluates the reliability of QCD sum rules in extracting bound-state parameters by comparing sum rule results with exact values in a quantum-mechanical model, revealing significant uncontrolled uncertainties especially in form factors.

Contribution

It introduces a quantum-mechanical potential model to test the accuracy of sum rule methods for bound-state parameters, highlighting their limitations.

Findings

Uncontrollable uncertainties in sum rule results are significant.

Systematic errors in form factors are larger than in decay constants.

Estimated errors in form factors can exceed 10%.

Abstract

We discuss the extraction of ground-state parameters, such as decay constants and form factors, from two- and three-point dispersive sum rules, making use of a quantum-mechanical potential model. This model provides a unique possibility to probe the reliability and the accuracy of the method of sum rules: one obtains the bound-state parameters by the standard procedures adopted in sum rules, and compares these results with the exact values, known in the potential model. We demonstrate the presence of uncontrollable uncertainties in the ground-state parameters obtained from sum rules and estimate their magnitude. The uncontrolled uncertainties in ground-state form factors are shown to be typically much larger than those in the decay constants. In the example presented, the uncontrolled systematic error in the extracted form factor is found to exceed the 10% level.