Systematic errors of bound-state parameters extracted by means of SVZ sum rules

TL;DR

This study investigates the systematic errors in extracting bound-state parameters using SVZ sum rules, demonstrating that modeling the continuum contribution leads to uncontrolled errors, even with known exact solutions.

Contribution

The paper provides a detailed analysis of the limitations of standard SVZ sum rule procedures using a harmonic oscillator model with known exact solutions.

Findings

Standard sum rule procedures do not control systematic errors when modeling the continuum.

Exact solutions reveal the inaccuracies in extracted parameters due to continuum modeling.

The method's reliability is compromised without precise knowledge of the continuum contribution.

Abstract

This talk presents the results of our study of systematic errors of the ground-state parameters obtained by Shifman-Vainshtein-Zakharov (SVZ) sum rules. We use the harmonic-oscillator potential model as an example: in this case we know the exact solution for the polarization operator, which allows us to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We extract the parameters of the ground state by making use of the standard procedures of the method of QCD sum rules, and compare the obtained results with their known exact values. We show that if the continuum contribution to the polarization operator is not known and is modelled by some effective continuum threshold, the standard procedures adopted in sum rules do not allow one to gain control over the systematic errors of the extracted ground-state parameters.