sector we take into account a Fierz-complete basis of all ten tensor structures consistent with a $U(1)_V\times SU(2)_V$ symmetry, see App. \[trunc:4f\], and approximate their momentum dependence using a single ($s$-channel) momentum variable. As discussed previously, we utilize dynamical hadronisation to effectively remove the resonant $\sigma-\pi$ channel from the four-fermi tensor structures via the inclusion of effective (quark-)meson interactions.

In the mesonic sector we include a scale-dependent mesonic wavefunction renormalisation factor, $Z_\pi$, and a Yukawa interaction between quarks and mesons, $h_\pi$. Additionally a scale-dependent effective potential, $U(\rho)$ captures higher mesonic interactions in the non-perturbative regime of spontaneously broken chiral symmetry, see e.g. [@Schaefer:2004en]. This approximation has been shown to be in quantitative agreement with the full momentum dependence [@Helmboldt:2014iya].

Results {#sec:results}
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Quark-gluon interactions {#sec:quark}
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We start by considering the quark-gluon vertex and focus in particular on additional non-classical tensor structures, as they are shown for the symmetric momentum configuration $p_1^2=p_2^2 = p_3^2$ in Fig. \[fig:quarkgluonvertex\_components\_msp\]. To investigate their importance we calculate the full momentum dependence of a basis for the transversally projected Landau-gauge quark-gluon vertex. The resulting eight tensor structures include the classical tensor structure, $$\begin{aligned}
 [{\cal T}^{(1)}_{\bar q A q}]^\mu=\gamma^\mu\,,\end{aligned}$$ three further chirally symmetric tensors $$\begin{aligned}
 {\cal 