Gaussian sum rules for 0−+ glueball in the instanton vacuum model

Abstract

A semi-classical expansion based on the instanton vacuum model of quantum chromodynamics is taken to obtain the correlation function of the 0−+ pseudoscalar glueball current. Working on the framework of Gaussian sum rules with a Gaussian-tail instantons size distribution, we find the contributions arising from the interaction between the classical instanton fields and quantum fluctuation ones are comparable to the pure classical and quantum ones, and thus impact the sum rule results; whereas the usual condensate contribution turned out to be negligible and may be understood as a small part of the corresponding instanton contributions. In consideration of axial U(1) anomaly, and inspired by the correlation function’s behavior, we assume that the spectral function is saturated by the three zero-width resonances (the mesons η and η′, and the pseudoscalar glueball G) plus continuum, and the corresponding Gaussian sum rules are constructed. The optimal mass and the coupling constant of the lowest pseudoscalar glueball are predicted to be consistent in a series Gaussian sum rules and almost the same as that of our previous Laplace sum rules.