We discuss the phase structure of QCD for N f = 2 and N f = 2 + 1 dynamical quark flavours at finite temperature and baryon chemical potential. It emerges dynamically from the underlying fundamental interactions between quarks and gluons in our work. To this end, starting from the perturbative high-energy regime, we systematically integrate-out quantum fluctuations towards low energies by using the functional renormalisation group. By dynamically hadronising the dominant interaction channels responsible for the formation of light mesons and quark condensates, we are able to extract the phase diagram for µB/T 6. We find a critical endpoint at (TCEP, µB CEP ) = (107, 635) MeV. The curvature of the phase boundary at small chemical potential is κ = 0.0142(2), computed from the renormalised light chiral condensate ∆ l,R . Furthermore, we find indications for an inhomogeneous regime in the vicinity and above the chiral transition for µB 417 MeV. Where applicable, our results are in very good agreement with the most recent lattice results. We also compare to results from other functional methods and phenomenological freeze-out data. This indicates that a consistent picture of the phase structure at finite baryon chemical potential is beginning to emerge. The systematic uncertainty of our results grows large in the density regime around the critical endpoint and we discuss necessary improvements of our current approximation towards a quantitatively precise determination of QCD phase diagram.

We present an analysis of the dynamics of two-flavour QCD in the vacuum. Special attention is paid to the transition from the high energy quark-gluon regime to the low energy regime governed by hadron dynamics. This is done within an functional renormalisation group approach to QCD amended by dynamical hadronisation techniques. The latter allow us to describe conveniently the transition from the perturbative high-energy regime to the nonperturbative low-energy limit without suffering from a fine-tuning of model parameters. In the present work, we apply these techniques to two-flavour QCD with physical quark masses and show how the dynamics of the dominant low-energy degrees of freedom emerge from the underlying quark-gluon dynamics.

We study the impact of higher order quark-meson scattering processes on the chiral phase structure of two-flavour QCD at finite temperature and quark density. Thermal, density and quantum fluctuations are included within a functional renormalisation group approach to the quark-meson model. We present results on the chiral phase boundary, the critical endpoint, and the curvature of the phase transition line at vanishing density.

We investigate baryon number fluctuations for finite temperature and density in two-flavor QCD. This is done within a QCD-improved low-energy effective theory in an extension of the approach put forward in [1,2]. In the present work we aim at improving the predictive power of this approach for large temperatures and density, that is, for small collision energies. This is achieved by taking into account the full frequency dependence of the quark dispersion. This ensures the necessary Silver Blaze property of finite density QCD for the first time, which so far was only implemented approximately. Moreover, we show that Polyakov loop fluctuations have a sizeable impact at large temperatures and density. The results for the kurtosis of baryon number fluctuations are compared to previous effective theory results, lattice results and recent experimental data from STAR.

In this work we present first results on vector and axial-vector meson spectral functions as obtained by applying the non-perturbative functional renormalization group approach to an effective lowenergy theory motivated by the gauged linear sigma model. By using a recently proposed analytic continuation method, we study the in-medium behavior of the spectral functions of the ρ and a1 mesons in different regimes of the phase diagram. In particular, we demonstrate explicitly how these spectral functions degenerate at high temperatures as well as at large chemical potentials, as a consequence of the restoration of chiral symmetry. In addition, we also compute the momentum dependence of the ρ and a1 spectral functions and discuss the various time-like and space-like processes that can occur.

We study the chiral dynamics of vector mesons in two-flavor QCD in vacuum by utilizing a functional renormalization group approach. This allows us to capture the dynamical transition from the quark-gluon phase at high energies to the hadronic phase at low energies without the necessity of model parameter tuning. We use this to analyze the scaling of vector meson masses towards the chiral symmetry breaking scale, the decoupling of the mesons at high energies and the validity of vector meson dominance.

The low-energy sector of QCD with N f = 2+1 dynamical quark flavors at non-vanishing chemical potential and temperature is studied with a non-perturbative functional renormalization group method. The analysis is performed in different truncations in order to explore fluctuation-induced modifications of the quark-meson correlations as well as quark and meson propagators on the chiral phase transition of QCD. Depending on the chosen truncation significant quantitative implications on the phase transition are found. In the chirally symmetric phase, the quark flavor composition of the pseudoscalar (η, η )-meson complex turns out to be drastically sensitive to fluctuation-induced modifications in the presence of the axial U(1) A anomaly. This has important phenomenological consequences for the assignment of chiral partners to these mesons.

We calculate chiral susceptibilities in (2 þ 1)-flavor QCD for different masses of the light quarks using the functional renormalization group (fRG) approach to first principles QCD. We follow the evolution of the chiral susceptibilities with decreasing masses as obtained from both the light-quark and the reduced quark condensate. The latter compares very well with recent results from the HotQCD Collaboration for pion masses m π ≳ 100 MeV. For smaller pion masses, fRG and lattice results are still consistent. In particular, the estimates for the chiral critical temperature are in very good agreement. We close by discussing different extrapolations to the chiral limit.