Internal Nucleon Properties and the Equation of State of Ultra-Dense Matter

Abstract

The question of the link between the nucleon properties and the equation of state of ultra-dense matter, both being composed of quarks and gluons, is investigated by adopting a soliton model to describe internal nucleon properties and a direct mapping between nucleon and quark matter to obtain the equation of state of ultra-dense matter. We compare $π+ω$ and $π+ω+ρ$ soliton models and analyze the presence of a pressure singularity at the nucleon center due to the $ρ$ field. This singularity impacts the equation of state in ultra-dense matter. Only the pressure derived from the canonical energy-momentum tensor has a singularity, while the Belinfante pseudo-gauge transformation of the energy-momentum tensor generates an internal pressure without a singularity. We then investigate predictions for the equation of state of ultra-dense matter based on different prescriptions for the nucleon pressure. It is shown that none of the prescriptions agree with the thermodynamical pressure defined in uniform matter. The mismatch between any equation of state and the thermodynamical one questions the simplicity of the direct mapping between finite-size nucleon properties and uniform matter as well as the role of the nucleon surface in the internal energy density and the pressure.