Phase transition from baryon to quark matter

Abstract

THE equation of state of matter compressed to supernuclear densities is of considerable interest in astrophysics. For example, pulsars are stars compressed to densities greater than the density of atomic nuclei and are thought to be composed primarily of neutrons, based on detailed calculations of the equation of state of baryonic matter assuming that interaction potentials for the baryons (nucleons and hyperons) are derived from low energy nuclear physics¹. There is, however, considerable evidence from high energy physics that baryons have structure, and it is currently believed that this structure is due to the fact that all hadrons consist of quarks bound by vector gluons². The fact that free, isolated quarks have not been observed has led to the speculation that quarks may be permanently bound inside hadrons³. Since the quarks inside the nucleon behave as free particles², the forces confining the quarks apparently become strong only when the distance between quarks exceeds the radius of a nucleon, ∼ 10⁻¹³ cm. When the density of matter is increased beyond the point that the mean distance between quarks in different baryons is ≪ 10⁻¹³ cm the description of matter as interacting baryons becomes invalid, and instead, a description of matter composed of quarks becomes relevant. At sufficiently high densities matter will behave like a relativistic gas of free quarks⁴ with P ≃ ρ/3, where P is the pressure and ρ is the energy density of matter. The density at which the baryon to quark transition occurs is of crucial importance to the structure of pulsars. General relativity implies that for a given equation of state there is a maximum energy density for stable stars¹. It is therefore of considerable interest to know whether the energy density of baryon matter at the baryon–quark phase transition is less than this maximum value. Indeed, it has recently been suggested⁵ that the existence of quark matter inside pulsars would allow larger masses for pulsars than was previously thought possible. We will show, however, that there are reasons to doubt this.