glue sector might lead to an even better agreement of the three-gluon coupling with the two other couplings. At low momenta, the gap in the gluon propagator becomes important and we find a clear difference between the strength of the various vertices. In particular, the three-gluon vertex drops considerably earlier, which is mainly due to the larger number of gluon legs.

Relative importance of four-fermi channels {#sec:4fermi}
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As mentioned in the discussion of our truncation in Sec. \[sec:truncation\], we include a Fierz-complete basis with all ten basis elements consistent with the $SU(N_c)_c\otimes
SU(N_f)_V\otimes U(1)_B$ symmetry to assess the importance of different four-fermi interaction channels, see App. \[trunc:4f\] for details on the choice of the basis. All four-fermi couplings are shown in Fig. \[fig:fourfermis\_msp\], where in particular $h_{\pi}^2/2
m_{\pi}^2$ corresponds to $\lambda_{(S-P)_+}+\lambda_{(S+P)_-}$ and $\lambda_{\eta'}$ to $\lambda_{(S-P)_+}-\lambda_{(S+P)_-}$. We find that the dynamics of spontaneous chiral symmetry breaking is almost exclusively driven by the chirally symmetric four-fermi channel $\lambda_{(S-P)_+}$, which corresponds to the quantum numbers of the $\sigma,\pi,\eta$ and $a$-mesons. However, this channel is split by the presence of the ’t Hooft determinant coupling, $\lambda_{(S+P)_-}$, such that only the $\sigma$-meson and pions become very light. The dynamically created quark mass is already 