the lack of additional model input, the computation only depends on the fundamental parameters of QCD, the strong coupling $\alpha_s$ and the current quark masses which are set at a large, perturbative momentum scales. We implement a systematic vertex expansion scheme that is fully capable of taking the non-perturbative physics at low momenta into account. Gauge invariance is implemented and tested in the form of modified Slavnov-Taylor identities (mSTIs). In the present work we focus on the matter system as one of the two subsectors of the full calculation. Using results for the Yang-Mills propagators [@Fischer:2008uz; @FP], we solve the matter sector in a quenched approximation and assess the quality of our results in comparison to lattice QCD, see Fig. \[fig:main\_result\]. A separate analysis of the fully coupled system is presented elsewhere.

The paper is organised as follows. In Sec. \[sec:setup\] we describe our approach to QCD, in particular we briefly introduce the dynamical hadronisation procedure within the functional renormalisation group approach and describe the used truncation scheme. In Sec. \[sec:results\], we present our results and comment on the mechanism of chiral symmetry breaking in the light of our investigations. Technical details on modified Slavnov-Taylor identities and on our truncation 