function as well via the relation $\partial_t\Delta M_q(0)\varpropto \langle
\sigma\rangle \partial_t\Delta h_\pi $. Momentum dependencies are very important in $\partial_t\Delta M_q(p)$, since we expect this term to be approximately zero for momenta larger than the chiral symmetry breaking scale, see App. \[sec:dynhad\] for details. Similarly, we had to include momentum dependencies in the remaining four-fermi interactions that appear in the tadpole diagram. In the language of dynamical hadronisation, chiral symmetry breaking in terms of the quark mass function is then triggered by the additional term, $\partial_t\Delta M_q$, see . This, however, is just due to the chosen parameterisation of the four-fermi interaction in terms of mesons. Without dynamical hadronisation, chiral symmetry breaking would be driven by the tadpole diagrams containing the resonant (momentum-dependent) four-fermi channel, which in turn is driven by quark-gluon interactions.

Gluonic vertices and running couplings {#sec:runningcouplings}
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From our calculated momentum-dependent QCD vertices, namely from the quark-gluon, the ghost-gluon and the three-gluon vertex we can extract running couplings. Following the detailed discussion in App. \[app:mSTI\], these running couplings are required to be degenerate at (semi-) perturbative momenta by means of Slavnov-Taylor identities, whereas they will start to deviate in the non-perturbative regime below momenta $\mathcal{O}(1$ GeV$)$. Additionally, 