Infrared behaviour of propagators and running coupling in the conformal window of QCD

TL;DR

This study uses Dyson-Schwinger equations to analyze how increasing quark flavors affects the infrared behavior of propagators and the running coupling in QCD, revealing a conformal window with power-law behavior.

Contribution

It provides a self-consistent Dyson-Schwinger analysis of unquenching effects in Landau gauge QCD with many quark flavors, identifying the critical flavor number for conformal behavior.

Findings

The non-perturbative running coupling exhibits a plateau above the critical flavor number.

Propagators show power-law behavior indicating conformality in this regime.

Critical flavor number $N_f^{crit}=4.5$ is sensitive to the quark-gluon vertex details.

Abstract

Using the Dyson-Schwinger approach we investigate Landau gauge QCD with a relatively large number of chiral quark flavours. A self-consistent treatment on the propagator level enables us to study unquenching effects via the quark loop diagram in the gluon equation. Above the critical number of fermion flavours the non-perturbative running coupling develops a plateau over a wide momentum range. Correspondingly, the propagators follow a power law behaviour in this momentum range indicating conformal behaviour. Our value $N_f^{crit}=4.5$ is strongly sensitive to the details of the quark-gluon vertex calling for more detailed investigations in future studies.