Consistent Laplace sum rules for pseudoscalar glueball in the instanton vacuum model

Abstract

Based on the instanton vacuum model of quantum chromodynamics, a systematical analysis on the Laplace sum rules for the 0−+ pseudoscalar glueball is carried out by using a semi-classical expansion. Besides taking the pure-classical contribution from instantons and the pertubative one into account, the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields is included in the correlation function; whereas the usual condensate contribution is understood to be a part of the instanton contribution, and turns out to be negligible. Assuming that the spectral function is saturated by the three lowest resonances (the mesons η and η′, and the pseudoscalar glueball G plus continuum, the corresponding subtracted and unsubtracted Laplace sum rules are constructed. After averaging over the instanton size according to a Gaussian-tail distribution, the optimal mass and the coupling constant of the lowest pseudoscalar glueball are predicted to be almost the same in various Laplace sum rules, and in agreement with the results of the lattice simulations as well.