breaking in quenched QCD was put forward. In their analysis the IR fixed points in the four-fermi interactions are destabilised if the gauge coupling exceeds a critical coupling $\alpha_\text{crit}$ and as a result the four-fermi coupling becomes singular. Although the argument is qualitatively correct, in quenched QCD the picture is not so simple, as the drop of the gauge coupling at small momenta, see Fig. \[fig:alpha\_msp\], lets the quark sector become subcritical again. This was discussed as one possible scenario in [@Braun:2006jd], but is confirmed here as the actual physical situation. In Fig. \[fig:alpha\_msp\], we show the different running couplings and the critical gauge coupling. Since the gauge coupling decreases below the critical coupling for decreasing momenta, it is merely the area above the critical value line which is decisive for the occurrence of chiral symmetry breaking.

Our findings indicate that an approach where the vertex strength of all tensor structures of the quark-gluon vertex is subsummed in an enhanced strength of the classical tensor structure lacks quantitative precision. Using such an enhanced quark-gluon vertex in our calculation would lead to much too large contributions in the four-fermi sector, from gluonic box diagrams which grow like $\alpha^2_{\bar q A q}$. 