a dynamical role only below about $500$ MeV their fluctuations are strongly suppressed in any of the loops by their comparably large mass, see also [@Braun:2014ata].

![Dynamical hadronisation: four-fermi coupling ($\lambda_{\pi}$, see App. \[trunc:4f\]) vs. corresponding coupling from dynamical hadronisation, $(k\,
      h_{\pi})^2/(2m_{\pi}^2)$, in a qualitative approximation.[]{data-label="fig:4fermirebos"}](fourfermi_msp){width="48.00000%"}

Truncation of effective action {#sec:truncation}
------------------------------

![image](mattersystem_diagrams){width="98.00000%"}

In our truncation we consider the momentum dependence of all vertices which include at least one relevant or marginally relevant operator with the help of [@program]. In the pure glue sector we calculate the ghost- and three-gluon vertices in single channel approximations including only the classical tensor structure. Moreover we use modified Slavnov-Taylor identities to fix the momentum dependence of the four-gluon vertex in this channel. This approximation is motivated by results from other methods [@Pelaez:2013cpa; @Blum:2014gna; @Eichmann:2014xya; @Binosi:2014kka; @Gracey:2014mpa; @Cyrol:2014kca], which show non-trivial momentum-dependencies only in momentum regions where the gluon sector already starts to decouple from the system. The matter-glue coupling as the interface between the two subsectors of the system is of crucial importance for the whole system. Therefore we include the full momentum-dependence and all eight tensor structures in the quark-gluon vertex. Furthermore, there are two exceptions from the RG relevance counting, in 