A progress in inverse matrix method in QCD sum rules

TL;DR

This paper advances the inverse matrix method in QCD sum rules by separating ground state contributions to improve the extraction of physical quantities like decay constants.

Contribution

It develops the inverse matrix method further by incorporating ground state separation, enhancing the accuracy of QCD sum rule analyses.

Findings

Improved extraction of decay constants using the inverse matrix method.

Better handling of spectral density models in QCD sum rules.

Enhanced parameter selection in sum rule analysis.

Abstract

In traditional QCD sum rules, the simple hadron spectral density model of ``delta-function-type ground state + theta-function-type continuous spectrum" determines that there is no perfect parameter selection. In recent years, inverse problem methods, especially the inverse matrix method, have shown better handling of QCD sum rules. This work continues to develop the inverse matrix method. Considering that the narrow-width approximation may still be a good approximation, we separate the contribution of the ground state from the spectral density. Then follow the general steps of the inverse matrix method to extract physical quantities such as decay constants that we are sometimes more interested in.