As a model for nonideal behavior in the equation of state of QCD at high density, we consider cold quark matter in perturbation theory. To second order in the strong coupling constant ␣ s , the results depend sensitively on the choice of the renormalization mass scale. Certain choices of this scale correspond to a strongly first order chiral transition, and generate quark stars with maximum masses and radii approximately half that of ordinary neutron stars. At the center of these stars, quarks are essentially massless.Strongly interacting matter under extreme conditions can reveal new phenomena in quantum chromodynamics ͑QCD͒. Compact stars serve as an excellent observatory to probe QCD at large density, as their interior might be dense enough to allow for the presence of chirally symmetric quark matter, i.e., quark stars ͓1-13͔.The usual model used for quark stars is a bag model, with at most a correction ϳ␣ s from perturbative QCD ͓6͔. In the massless case, the first order correction cancels out in the equation of state, so that one ends up finally with a free gas of quarks modified only by a bag constant. If the bag constant is fit from hadronic phenomenology, then the gross features of quark stars are very similar to those expected for neutron stars: the maximum mass is Ϸ2.M ᭪ , with a radius Ϸ10 km.In this Rapid Communication we consider quark stars, using the equation of state for cold, dense QCD in perturbation theory to ϳ␣ s 2 ͓2,3͔. These results are well known, and our only contribution is to use modern determinations of the running of the QCD coupling constant ͓14͔. At the outset, we stress that we do not suggest that the perturbative equation of state is a good approximation for the densities of interest in quark stars. Rather, we use it merely as a model for the equation of state of QCD.To ϳ␣ s 2 , there is significant sensitivity to the choice of the renormalization mass scale. Under our assumptions, we find that this choice is tightly constrained by the physics. We consider two illustrative values of this parameter. One choice corresponds to a weakly first order chiral transition ͑or no true phase transition͒, and gives maximum masses and radii very similar to that of neutron stars. The second choice corresponds to a strongly first order chiral transition ͓15͔, and generates two types of stars. One type has densities a few times that of nuclear matter, and looks like the stars of a weakly first order chiral transition. In addition, however, there is a new class of star ͓7,12͔, with densities much higher than that of nuclear matter. For this new class, the maximum mass is Ϸ1.M ᭪ , with a radius Ϸ5 km. Other models with nonideal behavior also generate small, dense quark stars ͓8-11͔.Assume that the chiral phase transition occurs at a chemical potential ͓16͔. Our perturbative equation of state is applicable only in the chirally symmetric phase, when the quark chemical potential Ͼ . In this phase, the effects of a strange quark mass, m s Ϸ100 MeV ͓18͔, are small relative to the quark chemical potential...

The structure of the phase diagram for strong interactions becomes richer in the presence of a magnetic background, which enters as a new control parameter for the thermodynamics. Motivated by the relevance of this physical setting for current and future high-energy heavy ion collision experiments and for the cosmological QCD transitions, we use the linear sigma model coupled to quarks and to Polyakov loops as an effective theory to investigate how the chiral and the deconfining transitions are affected, and present a general picture for the temperature-magnetic field phase diagram. We compute and discuss each contribution to the effective potential for the approximate order parameters, and uncover new phenomena such as the paramagnetically-induced breaking of global Z3 symmetry, and possible splitting of deconfinement and chiral transitions in a strong magnetic field.

In recent years, there have been several successful attempts to constrain the equation of state of neutron star matter using input from low-energy nuclear physics and observational data. We demonstrate that significant further restrictions can be placed by additionally requiring the pressure to approach that of deconfined quark matter at high densities. Remarkably, the new constraints turn out to be highly insensitive to the amount -or even presence -of quark matter inside the stars. Subject headings: equation of state -dense matter -stars: neutron