Colour Superconductivity

Nuclear matter under extreme conditions, such as those generated in heavy-ion collisions and presumably existing in the interior of compact stars, dissolves into the otherwise confined degrees of freedom of quarks and gluons which are described by the fundamental theory of quantum chromodynamics. At high quark chemical potential and comparatively low temperature quantum chromodynamics has been postulated to be in a deconfined phase where the quarks with unequal colour charge form Cooper pairs which spontaneously break colour symmetry, giving rise to the phenomenon of colour superconductivity. This has potentially important consequences for the physics of neutron stars which can be studied by means of pulsar timings and X-ray satellite experiments. Colour superconductivity can be investigated in principle by weak coupling methods and definite results for the first few orders of its parameters have been worked out. Beyond this the systematics of the so-called HDL- resummed perturbation theory has not yet been worked out and also the important question of gauge independence is not completely solved. The aim of this project is to answer these basic questions and, in a second step, to develop practical methods for higher-order calculations, which are of particular importance in view of the size of the coupling constant.

Nuclear matter under extreme conditions, such as those generated in heavy-ion collisions and presumably existing in the interior of compact stars, dissolves into the otherwise confined degrees of freedom of quarks and gluons, which are described by the fundamental theory of quantum chromodynamics. At high quark chemical potential and comparatively low temperature, quantum chromodynamics has been postulated to be in a deconfined phase where the quarks with unequal colour charge form Cooper pairs which spontaneously break colour symmetry, giving rise to the phenomenon of colour superconductivity. This has potentially important consequences for the physics of neutron stars which can be studied by means of pulsar timings and X-ray satellite experiments. Colour superconductivity can be investigated in principle by weak coupling methods, and the aim of this project has been to further develop this methodology and also to answer some outstanding fundamental questions. One important question which could be answered affirmatively was that of the independence of the results obtained so far of unphysical (so-called gauge-fixing) parameters. Another topic that was treated successfully concerned the properties of dense quark matter at temperatures just above the superconductivity phase transition. In this regime there are strong deviations from the behaviour of normal Fermi liquids, which lead in particular to anomalously large specific heat and neutrino emissitivity. These effects have been calculated for the first time quantitatively and have already found applications in the determination of cooling histories of neutron stars with a substantial quark matter core. In the course of this investigation, the systematics of the relevant analytical techniques was unravelled, preparing the ground for further investigations of quark-gluon matter under extreme conditions.