The finite-width Laplace sum rules for $0^{++}$ scalar glueball in instanton liquid model

TL;DR

This paper develops finite-width Laplace sum rules within the instanton liquid model to analyze the properties of the $0^{++}$ scalar glueball, incorporating classical, quantum, and interaction effects for more accurate predictions.

Contribution

It introduces a finite-width resonance approach using Brite-Wigner spectral functions in Laplace sum rules, extending previous zero-width approximations for scalar glueballs.

Findings

Estimated mass of the scalar glueball

Determined decay width and coupling constants

Validated consistency between sum rule types

Abstract

In the framework of a semi-classical expansion for quantum chromodynamics in the instanton liquid background, the correlation function of the $0^{++}$ scalar glueball current is given. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluons are taken into account as well. Instead of the usual zero-width approximation for the resonance, the Brite-Wigner form for the spectral function of the finite-width resonance is adopted. The family of the Laplace sum rules for the scalar glueball in quantum chromodynamics with and without light quarks are studed. A consistency between the subtracted and unsubtracted sum rules are very well justified, and the values of the mass, decay width, and the coupling to the corresponding current for the $0^{++}$ resonance in which the glueball fraction is dominant, are obtained.