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The operator-product expansion(OPE) could be employed to obtain thelowest-order, nonlocal quark scalar condensate component of gluon vacuumpolarization. In particular, nonlocal quark scalar condensate can be calculatedby solving Dyson-Schwinger Equation(DSE) of QCD. Then, field-theoretic aspectsof the gluon vacuum polarization and nonperturbative gluon propagator will beconsidered in the Landau gauge of the Lorentz gauge fixing. The gluonpropagator we obtained is finite in the infrared domain where the single gluonmass $m_g$ can be determined. Our results of the ratio $m_{g}/\Lambda_{QCD}$the range of that from 1.33 to 1.39 agree with previous determinations for thisratio. Besides, the analytic structure of the gluon propagators from the OPE'sresult is explored. Our numerical analysis of the gluon' Schwinger functionfinds clear evidence of the positivity violations in the gluon propagator. Inaddition, a new method for obtaining the chemical potential dependence of thegluon vacuum polarization and the dressed gluon propagator is developed.

nonlocal quark condensate from Dyson-Schwinger Equation and its contributions to the gluon vacuum polarization based on OPE approach