title: Colour Superconductivity and the Equation of State of Dense Matter
Creators: name: Schallmo, Benedikt Paul
Publisher: name: UNSPECIFIED
Year: 2024

description: It is widely accepted that dense strong-interaction matter at low temperatures is governed by a colour-superconducting ground state. To study the emergence of colour superconductivity in dense strong-interaction matter at zero temperature for two massless quark flavours from first principles, we employ a renormalisation group approach. For this purpose, we construct a new class of regulators for functional renormalisation group studies that is designed to handle issues arising from the presence of a Cooper instability governing the dynamics at intermediate and high densities.
We examine the dynamical formation of diquark states in the low-energy regime from the fundamental quark and gluon degrees of freedom that govern the dynamics at high energies. This includes a computation of the (chirally symmetric) diquark condensate, which is associated with a gap in the excitation spectrum of the quarks, and describes pairing of the two-flavour colour-superconducting type. We study the dependence of the gap on the chemical potential and the strong coupling and find a new scaling behaviour of the gap expected to be valid at intermediate densities. Effects of different approximations entering our calculation and possible extensions are discussed. Furthermore, we use the results from our first-principles renormalisation group flows to construct a new simple low-energy model for dense strong-interaction matter.
We demonstrate the application of this low-energy model by computing the zero-temperature thermodynamics of isospin-asymmetric matter with two massless quark flavours at high densities and zero temperature. For trajectories relevant for astrophysical applications, we find indications for a first-order phase transition from a colour-superconducting phase to an ungapped quark-matter phase when the density is increased. This phase transition appears to be absent for isospin-symmetric matter. To provide an estimate for the speed of sound in neutron-star matter, we include constraints from beta equilibrium, electric-charge neutrality, and colour-charge neutrality. Coming from high densities, we find an increase in the speed of sound towards lower densities and that it even exceeds the value associated with the noninteracting quark gas.
In addition to our explicit calculations of the properties of dense strong-interaction matter, we also discuss the thermodynamics at high densities on general grounds. To this end, we consider an expansion of the equation of state of isospin-symmetric matter in the presence of a colour-superconducting gap. This allows us to identify mechanisms underlying qualitatively different behaviours of the speed of sound. For very high densities, we find that the speed of sound approaches its value in the noninteracting limit from below, in agreement with perturbative studies which do not take into account a superconducting gap in the excitation spectrum of the quarks. However, towards lower densities, our general analysis indicates that gap-induced contributions lead to an increase in the speed of sound that eventually exceeds the value associated with a noninteracting quark gas, in agreement with our numerical renormalisation group results. We find that, even for small gap-induced contributions, the existence of a colour-superconducting phase leads to a qualitative change in the behaviour of the speed of sound. Taking into account results from studies based on chiral effective field theory at low densities, these findings suggest the existence of a maximum in the speed of sound at supranuclear densities for densities below ten times the nuclear saturation density.