Scaling, decoupling and transversality of the gluon propagator

TL;DR

This paper discusses technical issues in solving the Dyson-Schwinger equation for the gluon propagator in Landau gauge Yang-Mills theory, highlighting the coexistence of decoupling and scaling solutions and their implications.

Contribution

It clarifies the conditions under which both decoupling and scaling solutions can exist, emphasizing that the scaling solution cannot be dismissed by certain technical arguments.

Findings

Both decoupling and scaling solutions are possible in the infrared.

The scaling solution exhibits conformal behavior as a limiting case.

Technical issues do not exclude the scaling solution.

Abstract

In this note we discuss a couple of technical issues relevant to solving the Dyson-Schwinger equation for the gluon propagator in Landau gauge Yang-Mills theory. In the deep infrared functional methods extract a one-parameter family of solutions generically showing a massive behavior referred to as 'decoupling' but also including the so-called 'scaling' solution with a conformal infrared behavior as a limiting case. We emphasize that the latter cannot be ruled out by technical arguments related to the removal of quadratic divergencies and transversality.