Finite-width Gaussian sum rules for $0^{-+}$ pseudoscalar glueball based on correction from instanton-gluon interference to correlation function

TL;DR

This paper investigates the properties of the $0^{-+}$ pseudoscalar glueball using finite-width Gaussian sum rules, incorporating instanton-gluon interference effects to improve the accuracy of QCD predictions.

Contribution

It introduces a gauge-invariant, infrared divergence-free interference term in the correlation function, enhancing the sum rule analysis for the pseudoscalar glueball.

Findings

Mass, decay width, and coupling constants consistent with phenomenology.

Interference effects restore positivity of the correlation function spectra.

Finite-width resonance modeling improves upon zero-width approximations.

Abstract

Based on correction from instanton-gluon interference to correlation function, the properties of the $0^{-+}$ pseudoscalar glueball is investigated in a family of finite-width Gaussian sum rules. In the framework of semiclassical expansion for quantum chromodynamics $(\textrm{QCD})$ in the instanton liquid background, the contribution arising from the the interference between instantons and the quantum gluon fields is calculated, and included in the correlation function together with pure-classical contribution from instantons and the perturbative one. The interference contribution is turned to be gauge-invariant, free of infrared divergence, and has a great role to restore the positivity of the spectra of the full correlation function. The negligible contribution from vacuum condensates is excluded in our correlation function to avoid the double counting. Instead of the usual zero-width approximation for the resonances, the usual Breit-Wigner form with a suitable threshold behavior for the spectral function of the finite-width resonances is adopted. A consistency between the subtracted and unsubtracted sum rules is very well justified. The values of the mass, decay width and coupling constants for the $0^{-+}$ resonance in which the glueball fraction is dominant are obtained, and agree with the phenomenological analysis.