Supporting the existence of the QCD critical point by compact star observations

Abstract

In order to prove the existence of a critical end point (CEP) in the QCD phase diagram it is sufficient to demonstrate that at zero temperature $T=0$ a first order phase transition exists as a function of the baryochemical potential $μ$, since it is established knowledge from ab-initio lattice QCD simulations that at $μ=0$ the transition on the temperature axis is a crossover. We present the argument that the observation of a gap in the mass-radius relationship for compact stars which proves the existence of a so-called third family (aka "mass twins") will imply that the $T=0$ equation of state of compact star matter exhibits a strong first order transition with a latent heat that satisfies $Δε/ε_c \gt 0.6$. Since such a strong first order transition under compact star conditions will remain first order when going to symmetric matter, the observation of a disconnected branch (third family) of compact stars in the mass-radius diagram proves the existence of a CEP in QCD. For the equation of state of the twins the quark matter description is based on a QCD-motivated chiral approach with higher-order quark interactions in the Dirac scalar and vector coupling channels. For hadronic matter we select a relativistic mean-field equation of state with density-dependent couplings. Since the nucleons are treated in the quasi-particle framework, an excluded volume has been included for the nuclear equation of state at super-saturation density that takes into account the finite size of the nucleons. Furthermore we show results of a Bayesian analysis (BA) using disjunct M-R constraints for extracting probability measures for cold, dense matter equations of state. This study reveals that measuring the radii of neutron star twins has the potential to support the existence of a first order phase transition for compact star matter.