Fluctuations in Cold and Dense QCD Matter with Functional Methods

Abstract

This work is aimed at the study of fluctuation effects in cold and dense strong-interaction matter. In Nature, such matter exists in the cores of neutron stars and its properties are largely unknown. Utilizing an effective quark-meson truncation to quantum chromodynamics with two and three quark flavors, we integrate out quantum fluctuations by means of the functional renormalization group (FRG) method and study their impact on the properties of compact stars. The required thermodynamic equation of state (EoS) is hereby calculated for beta-equilibrated and neutral quark matter. We find significant differences to conventional EoS obtained from simple mean-field approximations. Pure quark-matter stars based on the nonperturbative EoS have larger radii and masses than their mean-field counterparts. Furthermore, the EoS obtained with the FRG allows for the construction of hybrid stars, i.e., neutron stars with a quark-matter core, as long as the utilized nucleonic equation of state is not too stiff. The underlying Maxwell construction assumes a sharp interface between nucleonic and quark matter and leads to a single continuous branch in the mass-radius diagram. However, with the inclusion of strangeness the popular two-solar-mass limit for the experimentally observed maximum mass cannot be reached anymore. With the additional inclusion of repulsive vector-meson interactions on a mean-field level, we find a sufficient increase in the EoS's stiffness to permit hybrid stars with masses over 2$M_\odot$. However, a Maxwell construction with nucleonic equations of state that lead to smaller overall radii and tidal deformabilities in better agreement with experiment is still not possible. Moreover, we investigate the origin of the strange back-bending of the chiral phase transition line at low temperatures in the quark-meson model in local potential approximation. We observe that the back-bending depends on the regulator function used by the FRG. For Callan-Symanzik-type regulators, it vanishes along with the associated negative entropy densities. This hints at the existence of strong cutoff-scheme-dependent truncation artifacts in local potential approximation at finite density and low temperatures.