The axial anomaly, the hadron spectrum, and phases of QCD

In an analysis of recent experimental data from the PHENIX and STAR collaborations at the Relativistic Heavy Ion Collider (RHIC) of the Brookhaven national lab a weakening of the mass splitting between eta`-meson and pions at the temperature of the chiral transition has been reported. The future experiments at the Facility for Antiproton and Ion Research (FAIR) at the GSI Helmholtzzentrum fuer Schwerionenforschung in Darmstadt will extend our knowledge of matter under extreme conditions. Especially high densities will be explored, where effects on this mass splitting are expected as well. The comparatively large mass of the eta`-meson is a consequence of the anomalous breaking of chiral symmetry and also related to the axial U(1) problem. Anomalous chiral symmetry breaking can be described by an effective U(1) violating interaction in terms of a `t Hooft determinant which contributes to the mass splitting between eta`- meson and pions. The main objective of the proposed project is to gain an understanding of the reduction in this mass splitting and the axial anomaly close to the chiral transition from first principle calculations. Within a two flavor effective description in terms of quarks and mesons a drop in the mass of the eta`-meson has been found during the course of the PhD thesis of the applicant. Although such effective descriptions have been successfully applied previously, a quantitative confirmation of these results requires first principle calculations from Quantum Chromodynamics (QCD). This goal will be achieved by deriving the previously used effective description of the axial anomaly in terms of a mesonic `t Hooft determinant from QCD degrees of freedom via the dynamical hadronization technique in the functional renormalization group framework. A side benefit will be a first principle calculation of the mass of the eta`-meson. Additionally, the developed framework will be used to study the curvature of the chiral phase boundary at small quark-densities which depends crucially on a correct description of the chiral anomaly. Finally, this will enable quantitative investigations at intermediate densities, especially of generalized susceptibilities like the kurtosis, relevant in the experimental search for a possible critical endpoint in the QCD phase diagram.

The aim of the project The axial anomaly the hadron spectrum, and phases of QCD were investigations of the properties and phases of strongly-interacting matter. The strong interaction can be described by a relativistic quantum field theory, called Quantum Chromomdynamics (QCD). Together with the electromagnetic and weak interactions, which are described by analogous quantum field theories, it forms the so-called Standard Model of particle physics. As long as the interaction strengths are comparably weak, predictions for the products of particle collisions in particle accelerators can be obtained by applying perturbation theory. This condition is met by the strong interaction due to the asymptotic freedom of quarks at distances smaller than nuclear radii. On the other hand, perturbation theory fails in describing the transition from quarks and gluons to protons, neutrons, pions and other hadrons. In particular, it is incapable of addressing the phenomena of quark confinement and the dynamical creation of most of the proton and neutron mass due to spontaneous chiral symmetry breaking. A method that is better suited for the description of these phenomena is given by lattice gauge theory. Unfortunately, this method is not applicable at large quark densities. Consequently, it cannot tell much about the phase structure of strongly-interacting matter at large densities. Additionally, precise calculations with this approach are computationally very expensive and require often supercomputers.The project The axial anomaly, the hadron spectrum, and phases of QCD uses so-called functional methods, which are not restricted to small quark densities in their applicability. Furthermore, the required computational times are considerably lower than those of lattice gauge theory. On the other hand, applications of functional methods to the calculation of the phase structure and other properties of QCD require often additional assumptions in the form of model parameters. It was possible in this project to eliminate this type of model parameter dependence. This was demonstrated in the publication Chiral symmetry breaking in continuum QCD by calculating the quark propagator, which describes the dynamics of quarks. The resulting quark propagator agrees perfectly with corresponding results for lattice gauge theory. With the help of the dynamical hadronisation technique it was additionally possible to describe the transition from free quarks and gluons al small distances to hadrons at large distances. Therefore the connection between Q-CO and the often used effective models of quarks and mesons could be made, allowing for precise statements about the predictivity of these models. Chiral symmetry breaking in continuum QCD is therefore the necessary prerequisite for model parameter independent investigations of the phase structure of strongly-interacting matter, which are currently being conducted.