Recent results in QCD sum rule calculations of heavy meson properties

TL;DR

This paper reviews recent advances in QCD sum rule techniques for determining heavy meson properties, focusing on improved understanding of the effective continuum threshold and its impact on reducing systematic uncertainties.

Contribution

It introduces a new algorithm for fixing the effective continuum threshold in QCD sum rules, enhancing the accuracy of bound-state parameter extraction.

Findings

Improved the control over systematic uncertainties in sum rule calculations.

Demonstrated the impact of new procedures on heavy meson decay constants.

Validated methods using quantum mechanics examples.

Abstract

This talk reviews the recent progress in the extraction of bound-state characteristics from the operator-product expansion (OPE) for field-theory correlators, which constitutes the basis of the method of QCD sum rules. This progress is mainly related to a deeper understanding of one of the key ingredients of the method of sum rules -- the effective continuum threshold. The latter determines to a great extent the numerical values of the bound-state parameters obtained by sum rules. The understanding of properties of the effective continuum threshold allows one to formulate a new algorithm for fixng this quantity for various correlators and in this way gain control over the systematic uncertainties of the bound-state parameters extracted from sum rules. We start with examples from quantum mechanics, where bound-state properties may be calculated independently in two ways: exactly, by solving the Schr\"odinger equation, and approximately, by the method of dispersive sum rules. Knowing the exact solution is crucial as it allows us to control each step of the sum-rule extraction procedure. On the basis of this analysis, we formulate several improvements of the standard procedures adopted in the method of sum rules in QCD. We then show the impact of these modifications on the extraction of the decay constants of heavy mesons.