Light mesons in QCD and unquenching effects from the 3PI effective action

TL;DR

This paper studies unquenching effects in QCD by solving coupled Dyson-Schwinger equations with inputs from Lattice QCD, revealing their impact on meson properties and providing insights into scalar meson masses.

Contribution

It introduces a self-consistent approach to include unquenching effects in QCD Green's functions using the 3PI effective action framework, connecting Dyson-Schwinger and Bethe-Salpeter equations.

Findings

Unquenching effects have opposite impacts on the quark-gluon vertex and quark propagator.

The scalar meson mass is predicted to be above 1 GeV.

The vector-axial vector splitting matches experimental data.

Abstract

We investigate the impact of unquenching effects on QCD Green's functions, in the form of quark-loop contributions to both the gluon propagator and three-gluon vertex, in a three-loop inspired truncation of the three-particle irreducible (3PI) effective action. The fully coupled system of Dyson-Schwinger equations for the quark-gluon-, ghost-gluon- and three-gluon vertices, together with the quark propagator, are solved self-consistently; our only input are the ghost and gluon propagators themselves that are constrained by calculations within Lattice QCD. We find that the two different unquenching effects have roughly equal, but opposite, impact on the quark-gluon vertex and quark propagator, with an overall negative impact on the latter. By taking further derivatives of the 3PI effective action, we construct the corresponding quark-antiquark kernel of the Bethe-Salpeter equation for mesons. The leading component is gluon exchange between two fully-dressed quark-gluon vertices, thus introducing for the first time an obvious scalar-scalar component to the binding. We gain access to time-like properties of bound-states by analytically continuing the coupled system of Dyson--Schwinger equations to the complex plane. We observe that the vector axial-vector splitting is in accord with experiment and that the lightest quark-antiquark scalar meson is above 1 GeV in mass.