Towards the QCD phase diagram with functional methods

The main objective is a realistic description of the dynamics of strongly-interacting matter under extreme conditions, i.e., at non-vanishing temperatures and/or densities. This necessitates to treat the underlying theory of the strong interactions, Quantum Chromodynamics (QCD), beyond perturbation theory. Here, the method of choice, in particular at finite density, is the non-perturbative functional renormalization group (FRG). The degrees of freedom of strongly interacting matter in the low-temperature/low-density phase are baryons and mesons, which are treated as QCD bound states. In contrast, in the high-temperature/high-density phases the underlying degrees of freedom are quarks and gluons. Chiral and deconfinement aspects of the QCD phase structure at finite temperatures and densities are a major focus of this proposal. One target is the qualitative and quantitative improvement of effective models towards full dynamical QCD. The functional renormalization group technique offers a unique way to systematically improve effective QCD models towards ab initio QCD. The theoretical predictions aimed at in this proposal are of significant relevance for the planned experiments at the FAIR and JINR facilities in Darmstadt, Germany, and in Dubna, Russia, respectively and enable a fundamental and conceptual understanding of hadronic matter under extreme conditions from first principles.

The main objective of this project is to provide a realistic description of low-energy hadron physics, while capturing as precisely as possible the complex dynamics of strongly interacting matter necessary for a deeper understanding of heavy-ion collisions. The underlying theory of the strong interaction is Quantum Chromodynamics (QCD) with fundamental quark and gluon degrees of freedom that constitute nuclear matter. QCD generalized to finite temperature and baryon density predicts a phase transition from a hadronic and confined phase with broken chiral symmetry to a deconfined and chirally symmetric quark-gluon plasma phase at high temperatures and moderate densities. The chiral and deconfinement aspects of these QCD phase transitions are central to this project. For a qualitative and quantitative description of such phase transitions - in particular in the vicinity of the phase boundary - a proper inclusion of the relevant quantum and thermal fluctuations that drive the transitions are crucial. The method of choice is given by a version of Wilsons non-perturbative functional renormalization group (FRG) technique that in this context was awarded the Nobel Prize. A version of this non-perturbative FRG approach, based on the Wetterich flow equations, is particularly suited to obtain results beyond the usual mean-field approximations in this research field. In several subprojects of this project various truncation schemata for the effective action are investigated in a systematic manner. Already in a lowest-order derivative expansion of the effective action several universal critical exponents as well as non-universal quantities of different thermodynamic observables could be calculated. Examples are observables such as generalized susceptibilities at finite temperature, densities and finite volumes. They are at least for vanishing densities in excellent agreement with complementary ab-initio non-perturbative QCD simulations on a lattice. Although the FRG approach at finite densities has no sign-problem in contrast to the complementary lattice QCD simulations, the obtained FRG results at moderate baryon densities should be interpreted with caution since at larger densities baryonic degrees of freedom become more and more relevant for the QCD phase structure. Due to inherent complexity, the inclusion of such baryonic degrees of freedom with three quark colors are usually dismissed in functional approaches. This represents an outstanding fundamental issue in the literature. However, a simplified two-color version could be successfully solved and analyzed in this project. Finally, the interplay between the chiral phase transition for two and three quark flavors has been addressed and for the first time the quark mass sensitivity of this phase transition has been established with the FRG method. A scenario with a standard bending of the chiral critical surface as a function of the strange and nonstrange quark masses has been found and hence the existence of a chiral critical endpoint in the QCD phase diagram is realized. In addition, the used FRG approach has also been extended to finite volumes for two and three quark flavors such that the influence of the boundary conditions on the phase structure could be evaluated and compared to recent QCD lattice simulations. All these findings of this project constitute an important contribution to the planned experiments at FAIR and NICA facilities.