Systematic errors of bound-state parameters obtained with SVZ sum rules

TL;DR

This paper investigates the systematic errors in bound-state parameters derived from SVZ sum rules using a harmonic-oscillator model, revealing limitations in controlling uncertainties when the continuum contribution is modeled.

Contribution

It demonstrates the limitations of SVZ sum rules in accurately estimating ground-state parameters when the continuum contribution is not precisely known.

Findings

Sum rules can produce systematic errors in bound-state parameters.

Modeling the continuum contribution affects the accuracy of sum rule results.

Exact solutions in the harmonic oscillator model highlight these limitations.

Abstract

We study 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 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 uncertainties of the extracted ground-state parameters.