Can one control systematic errors of QCD sum rule predictions for bound states?

TL;DR

This paper investigates the limitations of QCD sum rules in accurately determining ground-state parameters, using a harmonic oscillator model to compare known exact solutions with sum rule predictions.

Contribution

It demonstrates that when the continuum contribution is modeled rather than known, QCD sum rules cannot reliably control systematic errors in parameter extraction.

Findings

Sum rules fail to control errors when the continuum is unknown.

Exact solutions reveal limitations of the sum rule method.

Modeling the continuum introduces significant uncertainties.

Abstract

We study the possibility to control systematic errors of the ground-state parameters obtained by Shifman-Vainshtein-Zakharov (SVZ) sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator, which allows one to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We determine the parameters of the ground state making use of the standard procedures of the method of QCD sum rules, and compare the obtained results with the known exact values. We show that in the situation when the continuum contribution to the polarization operator is not known and is modelled by an effective continuum, the method of sum rules does not allow to control the systematic errors of the extracted ground-state parameters.