Soft modes in hot QCD matter

The chiral crossover of QCD at finite temperature and vanishing baryon density turns into a second-order phase transition if lighter than physical quark masses are considered. If this transition occurs sufficiently close to the physical point, its universal critical behavior would largely control the physics of the QCD phase transition. We quantify the size of this region in QCD using the functional renormalization group. This allows us to study both critical and noncritical effects on equal footing, facilitating a precise determination of the scaling regime. We find that the physical point is far away from the critical region. Importantly, we show that the physics of the chiral crossover is dominated by soft modes even far beyond the critical region. While scaling functions determine all thermodynamic properties of the system in the critical region, the order parameter potential is the relevant quantity away from it. We compute this potential in QCD using the functional renormalization group and Dyson-Schwinger equations and provide a simple parametrization for phenomenological applications.