Hadronic effects in the QCD phase diagram

Abstract

In this thesis, we investigate meson properties at finite chemical potential and vanishing temperature and study the influence of mesonic and baryonic backcoupling effects on the chiral order parameters and different parts of the QCD phase diagram. For this purpose, we solve a coupled set of (truncated) Dyson-Schwinger equations for the Landau gauged quark and gluon propagators with N f = 2 (+1) dynamical quark flavors and the two cases of including and neglecting the backcoupling of hadrons. The corresponding quark-meson Bethe-Salpeter vertices and bound state properties, i.e. the meson masses and decay constants, of multiple light- and strange-quark mesons are explicitly calculated from their homogeneous Bethe- Salpeter equations at finite chemical potential and vanishing temperature. Since the baryon backcoupling is calculated in the quark-diquark approximation, the necessary baryon and diquark wave-functions and properties are approximated by corresponding results explicitly calculated in vacuum. At vanishing temperature, we study the changes of the quark dressing functions and meson Bethe-Salpeter wave-functions with chemical potential and thereby trace charge-conjugation parity breaking. For the light and strange quarks, we observe two separate first-order coexistence regions. From zero chemical potential up to the end of these coexistence regions, we find constant masses and decay constants for every considered meson and the quark condensate. Thereby, we explicitly verify the Silver-Blaze property of QCD. Inside the light- and strange-quark coexistence region, the Pion and the K̄ meson, respectively, become more massive while their decay constants decrease. The corresponding quantities for the (axial-)vector and scalar mesons and the K meson remain (almost) perfectly constant. For the backcoupling of the Pion and/or Sigma meson as well as for the backcoupling of the nucleon and/or scalar diquark, we find similar chiral-restoration effects. Considering backcoupled baryons, oscillations of the quark propagator at finite chemical potential and vanishing temperature prevent a clear statement regarding the liquid-gaseous phase transition. For Pion and Sigma meson backcoupling, we observe a (small) shift of the critical endpoint towards smaller chemical potentials and a reduced curvature of the chiral crossover line. We conclude that the location of the critical endpoint in the phase diagram is mainly determined by microscopic degrees of freedom of QCD (quarks and gluons) while its critical properties are dominated by macroscopic degrees of freedom (especially the Sigma meson).