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Based on correction from instanton-gluon interference to correlationfunction, the properties of the $0^{-+}$ pseudoscalar glueball is investigatedin a family of finite-width Gaussian sum rules. In the framework ofsemiclassical expansion for quantum chromodynamics $(\textrm{QCD})$ in theinstanton liquid background, the contribution arising from the the interferencebetween instantons and the quantum gluon fields is calculated, and included inthe correlation function together with pure-classical contribution frominstantons and the perturbative one. The interference contribution is turned tobe gauge-invariant, free of infrared divergence, and has a great role torestore the positivity of the spectra of the full correlation function. Thenegligible contribution from vacuum condensates is excluded in our correlationfunction to avoid the double counting. Instead of the usual zero-widthapproximation for the resonances, the usual Breit-Wigner form with a suitablethreshold behavior for the spectral function of the finite-width resonances isadopted. A consistency between the subtracted and unsubtracted sum rules isvery well justified. The values of the mass, decay width and coupling constantsfor the $0^{-+}$ resonance in which the glueball fraction is dominant areobtained, and agree with the phenomenological analysis.

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