Stabilization and Consistency for Subtracted and Unsubtracted QCD Sum Rules for 0⁺⁺ Scalar Glueball

Based on a semi-classical expansion for quantum chromodynamics in the instanton liquid background, the correlation function of the 0⁺⁺ scalar glueball current is calculated. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluon ones come into play. It turns out that the latter contributions have a great role not only in making the stabilization of the subtracted and unsubtracted Laplace-transformed QCD sum rules for 0⁺⁺ scalar glueball, but also in bring back the consistency between the two related sum rules, or equivalently between the QCD asymptotic expression and low energy theorem. The result for the scalar glueball mass is predicted to be m_G=1.35GeV.