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

TL;DR

This paper employs Dyson-Schwinger equations and the operator-product expansion to calculate nonlocal quark condensates and analyze their impact on gluon vacuum polarization, revealing finite infrared behavior and positivity violations.

Contribution

It introduces a novel approach combining DSE and OPE to compute nonlocal quark condensates and explores their effects on gluon propagators, including a new method for chemical potential dependence.

Findings

Gluon propagator is finite in the infrared domain.

The ratio m_g/Λ_QCD ranges from 1.33 to 1.39, consistent with previous results.

Evidence of positivity violations in the gluon propagator.

Abstract

The operator-product expansion(OPE) could be employed to obtain the lowest-order, nonlocal quark scalar condensate component of gluon vacuum polarization. In particular, nonlocal quark scalar condensate can be calculated by solving Dyson-Schwinger Equation(DSE) of QCD. Then, field-theoretic aspects of the gluon vacuum polarization and nonperturbative gluon propagator will be considered in the Landau gauge of the Lorentz gauge fixing. The gluon propagator we obtained is finite in the infrared domain where the single gluon mass $m_g$ 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 this ratio. Besides, the analytic structure of the gluon propagators from the OPE's result is explored. Our numerical analysis of the gluon' Schwinger function finds clear evidence of the positivity violations in the gluon propagator. In addition, a new method for obtaining the chemical potential dependence of the gluon vacuum polarization and the dressed gluon propagator is developed.