Nonlocal quark scalar condensate from the Dyson–Schwinger equation and the gluon vacuum polarization based on the OPE approach

Abstract

Operator-product expansion (OPE) can be employed to obtain the lowest-order, nonlocal quark scalar condensate component of gluon vacuum polarization. In particular, the nonlocal quark scalar condensate can be calculated by solving the Dyson–Schwinger equation (DSE) of QCD. Then, field-theoretical aspects of the gluon vacuum polarization and nonperturbative gluon propagator are considered in the Landau gauge. The gluon propagator we obtained is finite in the infrared domain, where the single gluon mass [Formula: see text] can be determined. Our results for the [Formula: see text] ratio range of that from 1.32 to 1.36, which agrees with previous determinations for this ratio. Then, the analytic structure of the gluon propagators from the OPE results is explored. The analysis of the gluon Schwinger function finds clear evidence of the positivity violations in the gluon propagator. In addition, the results of replacing the OPE simplified quark loop with the full quark one-loop are calculated in vacuum to investigate how good the OPE approximation approach is. The results demonstrate that the OPE approach provides a good approximate method to calculate the full light [Formula: see text] quark loop in vacuum. In particular, the OPE approach can well approximate the approach with full quark one-loop in a specific model. Finally, a new method for obtaining the chemical potential dependence of the gluon vacuum polarization and the dressed gluon propagators is developed.