What Does Low Energy Physics Tell Us About The Zero Momentum Gluon Propagator

TL;DR

This paper investigates the gluon propagator in low energy QCD, showing that different theoretical solutions are indistinguishable when matched to experimental data, and confirms the chiral invariance of a nonlocal Nambu--Jona-Lasinio model.

Contribution

It demonstrates that low energy physics cannot distinguish between decoupling and scaling solutions of Dyson-Schwinger equations within a nonlocal Nambu--Jona-Lasinio framework.

Findings

Low energy physics does not differentiate between decoupling and scaling solutions.

The nonlocal model reproduces pion properties and quark condensates accurately.

The model satisfies the GMOR relation at 1% precision.

Abstract

The connection between QCD, a nonlocal Nambu--Jona-Lasinio type model and the Landau gauge gluon propagator is explored. This two point function is parameterized by a functional form which is compatible with Dyson-Schwinger and lattice QCD results. Demanding the nonlocal model to reproduce the experimental values for the pion mass, the pion decay constant, $\Gamma_{\pi \rightarrow \gamma\gamma}$ and the light quark condensate we conclude that low energy physics does not distinguish between the so-called decoupling and scaling solutions of the Dyson-Schwinger equations. This result means that, provided that the model parameters are chosen appropriately, one is free to chose any of the above scenarios. Furthermore, the nonlocal Nambu--Jona-Lasinio quark model considered here is chiral invariant and satisfies the GMOR relation at the 1% level of precision.