Low-energy limit of the $O(4)$ quark-meson model from the functional renormalization group approach

We compute the low-energy limit of the $O(4)$-symmetric quark-meson model as an effective field theory for Quantum Chromodynamics within the Functional Renormalization Group (FRG) approach. In particular, we analyze the renormalization group flow of momentum-dependent pion self-interactions beyond the local potential approximation. The numerical results for these couplings obtained from the FRG are confronted with a recent tree-level study. Additionally, their effect on the wave-function renormalization and the curvature masses is investigated.