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

Abstract

Based on a correction from instanton-gluon interference to the correlation function, the properties of the 0 −+ pseudoscalar glueball are investigated in a family of finite-width Gaussian sum rules. In the framework of a semiclassical expansion for quantum chromodynamics in the instanton liquid background, the contribution arising from the interference between instantons and the quantum gluon fields is calculated, and it is included in the correlation function together with a pure-classical contribution from instantons and the perturbative one. The interference contribution turns out to be gauge-invariant, to be free from an infrared divergence, and to have a great role to play in restoring the positivity of the spectra of the full correlation function. The negligible contribution from vacuum condensates is excluded in our correlation function to avoid 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. 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 they agree with the phenomenological analysis.