Comment to: "A note on failure of the ladder approximation to QCD" [Phys. Lett. B 640 (2006) 196 ]

TL;DR

This comment defends the previous proof that the ladder approximation to QCD is inconsistent, clarifying that the counter-claim was based on a mathematical mistake involving divergent integrals.

Contribution

It clarifies the mathematical error in the counter-claim and reaffirms the inconsistency of the ladder approximation to QCD.

Findings

The original proof remains valid.

The counter-claim was based on a mathematical mistake.

The ladder approximation to QCD is inconsistent.

Abstract

In the paper [Hong-Shi Zong, Wei-Min Sun, Phys. Lett. B 640 (2006) 196], the authors claim that our proof of the inconsistency of the ladder approximation to QCD [Phys. Lett. B 611 (2005) 129] was incorrect. However, their claim is based on a derivation which contains a rough mathematical mistake, namely the unjustified change of variables in the divergent (though regularized) integrals. In this comment I will show this explicitly, so our conclusion that the ladder approximation to QCD is inconsistent remains, of course, correct.