Revisiting light-flavor diquarks in the inverse matrix method of QCD sum rules

TL;DR

This paper applies the inverse matrix method to QCD sum rules to more accurately determine the properties of light-flavor diquarks, avoiding some traditional assumptions and providing consistent results with existing literature.

Contribution

It introduces the inverse matrix method for QCD sum rules, enabling direct spectral density extraction and improved predictions of diquark masses and decay constants.

Findings

Diquark masses with $J^P=0^+$ and $0^-$ are nearly degenerate.

The method yields results consistent with previous theoretical predictions.

Demonstrates the inverse matrix method as a robust tool for nonperturbative QCD analysis.

Abstract

This study reexamines the spectroscopic parameters of light-flavor diquarks within the framework of quantum chromodynamics sum rules (QCDSR) using the inverse matrix method. Conventional QCDSR analyses are based on assumptions such as quark-hadron duality and continuum models, which introduce a degree of systematic uncertainty. The inverse matrix method circumvents these assumptions by reformulating the problem as an inverse integral equation and expanding the unknown spectral density using orthogonal Laguerre polynomials. This method allows for a direct determination of spectral densities, thereby enhancing the precision of predictions regarding resonance masses and decay constants. By employing this methodology with regard to light-flavor diquarks ($sq$ and $ud$), it is possible to extract the associated masses and decay constants. The results indicate that the masses of diquarks with quantum numbers $J^P = 0^+$ and $J^P = 0^-$ are nearly degenerate. We compare our results regarding masses and decay constants with those of other theoretical predictions, which could prove a useful complementary tool in interpretation. Our results are consistent with those in the literature and can be shown as evidence for the consistency of the method. The results achieved in this study highlight the potential of the inverse matrix method as a robust tool for exploring nonperturbative QCD phenomena and elucidating the internal structure of exotic hadronic systems.