Dense matter in the QCD phase diagram and in compact stars

Sufficiently cold quark matter at asymptotically large chemical potential is a color superconductor in the color- flavor locked (CFL) state. Rigorous first-principle calculations for dense matter can only be applied at densities much larger than present in nature (in compact stars). Only in this case does asymptotic freedom of QCD ensure the validity of perturbative methods. At lower densities matter becomes strongly coupled and the strange quark mass becomes non-negligible. As a consequence, the ground state of matter at this intermediate density (between ordinary nuclear and ultra-dense CFL matter) is very difficult to determine. The goal of this project is to contribute to the understanding of this matter. I am planning to tackle this fundamentally and phenomenologically important problem with different methods, reflected in three project parts. Firstly, I would like to improve the result for the breakdown of CFL within QCD. Currently, we know from a simple calculation which uses the strange quark mass as a small parameter that CFL becomes disfavored compared to unpaired quark matter at a certain value of the strange quark mass. Building on recently improved perturbative calculations for unpaired quark matter, I propose to compute perturbative corrections to this value. Although such an improved value will still not be reliable at densities of astrophysical relevance, it is important to have a tendency from actual QCD suggesting whether or not CFL may persist down to densities where the transition to nuclear matter is expected. Secondly, a model calculation within a Ginzburg-Landau approach is intended to shed light on this question from a different angle. Building on my own recent work about the Ginzburg-Landau phase diagram of dense matter, I would like to include the constraints of electric and color neutrality as well as weak equilibrium into this calculation. These constraints are unavoidable in order to describe realistic dense matter inside a pulsar. They are expected to restrict the allowed Ginzburg-Landau parameter space which has only been considered in full generality in related previous works. Thirdly, I am planning to investigate the superfluid properties of the kaon-condensed CFL phase. This is relevant for astrophysical applications where hydrodynamical simulations usually treat dense matter as a multi-component fluid. It is important to understand whether kaon-condensed CFL has one or two superfluid components. This question is also of fundamental interest since it addresses the problem of an (apparent) superfluid with small explicit symmetry breaking.

Compact stars are after black holes the densest objects in nature. The matter in the interior of a compact star thus probes the fundamental theories of particles and their interactions, in particular the theory of the strong interaction that describes nuclear and quark matter. The main line of research in this project was the study of superfluidity in this kind of matter and its effect on astrophysical observables. The microscopic mechanism of superfluidity (and superconductivity) is very general, and can be applied to particles in high-energy physics such as neutrons, protons, and quarks in the same way as for more conventional systems such as superfluid helium or electronic superconductors. Since the temperature in compact stars is sufficiently cold, it is very likely that stellar superfluidity in nuclear and/or quark matter exists. In this project, we have studied fundamental properties of relativistic superfluids with the help of a quantum field theory for a complex scalar field. In particular, we have derived the two-fluid model from microscopic physics, a model that has been successfully applied in the phenomenology of superfluid helium. In addition, we have computed physical properties of relativistic superfluids, for instance sound velocities. Every superfluid has two distinct modes of sound, and we have worked out their properties for all temperatures below the critical temperature. In these calculations, we have also encountered an instability that manifests itself in an unstable sound mode and that occurs for sufficiently large relative velocities between the superfluid and the normal fluid.The research in this project opens up many questions for future research; for instance it will be very interesting to see whether the above mentioned instability plays a role for the generation of so-called pulsar glitches, which are sudden jumps in the rotation frequency of a pulsar.