Neutrality and phases of color-superconducting quark matter

When matter is compressed to the highest densities imaginable, what will it look like, and what will its properties be? The densest matter in the observable universe is in neutron stars, which are more massive than the sun, while possessing a radius of only about 12 km. Astrophysicists are trying to learn about ultra-dense matter by making astronomical observations of neutron stars, and we hope that with better telescopes we will learn more. To make the most of these observations, we need to compare them with theoretical predictions of how different forms of ultra-dense matter are expected to behave, and this project seeks to improve our theoretical understanding and allow us to make better predictions. To predict the properties of ultra-dense matter we use the best-confirmed theory of particle physics, the "Standard Model". According to the Standard Model, all matter is made of quarks and electrons. Quarks bind together via the strong force to form protons and neutrons, which make up the nuclei of atoms. Electrons are guided by the electromagnetic force to arrange themselves in a cloud around the nucleus, forming an atom. However, at the densities we are interested in, atoms no longer exist. At the density of a neutron star the electrons are squeezed into the nuclei, and matter becomes a liquid of neutrons and protons ("nuclear matter"), and ultimately a liquid of quarks ("quark matter") whose behavior is mainly governed by the strong interaction. The standard model contains a theory of the strong interaction: Quantum Chromodynamics, often abbreviated as QCD. Our goal is to use QCD to understand and predict the properties of matter at and beyond the highest densities that occur in the universe. The difficulty with doing this is that QCD is an intractable theory: it is very difficult to solve the mathematical equations and integrals to obtain predictions. Previous work used general arguments to suggest that ultra-dense matter might form itself into phases analogous to those we see on materials on earth: superconductors, superfluids, insulators, and so on. We aim to make predictions based on QCD, the theory that has been shown to accurately describe the behavior of quarks in particle accelerators. We will use functional integral equations (Dyson-Schwinger equations) to clarify several questions. We will address the role of electrons in the densest form of quark matter, which is currently unclear. We will also investigate which possible phases might be realized as the density increases from nuclear matter up through quark matter. Our goal is to obtain predictions of how those phases behave, and this could be used with astronomical observations of neutron stars to confirm our understanding of matter at extreme density.

When matter is compressed to the highest densities imaginable, what will it look like, and what will its properties be? The densest matter in the observable universe is in neutron stars, which are more massive than the sun, while possessing a radius of only about 12 km. Astrophysicists are trying to learn about ultra-dense matter by making astronomical observations of neutron stars, and we hope that with better telescopes we will learn more. To make the most of these observations, we need to compare them with theoretical predictions of how different forms of ultra-dense matter are expected to behave, and this project seeks to improve our theoretical understanding and allow us to make better predictions. To predict the properties of ultra-dense matter we use the best-confirmed theory of particle physics, the Standard Model. According to the Standard Model, all matter is made of quarks and electrons. Quarks bind together via the strong force to form protons and neutrons, which make up the nuclei of atoms. Electrons are guided by the electromagnetic force to arrange themselves in a cloud around the nucleus, forming an atom. However, at the densities we are interested in, atoms no longer exist. At the density of a neutron star the electrons are squeezed into the nuclei, and matter becomes a liquid of neutrons and protons (nuclear matter), and ultimately a liquid of quarks (quark matter) whose behavior is mainly governed by the strong interaction. The standard model contains a theory of the strong interaction: Quantum Chromodynamics, often abbreviated as QCD. Our goal is to use QCD to understand and predict the properties of matter at and beyond the highest densities that occur in the universe. The difficulty with doing this is that QCD is an intractable theory: it is very difficult to solve the mathematical equations and integrals to obtain predictions. Previous work used general arguments to suggest that ultra-dense matter might form itself into phases analogous to those we see on materials on earth: superconductors, superfluids, insulators, and so on. The main motiviation for the central question in this project was a study that suggested the presence of electrons in the color-superconducting quark matter phase. This statement is against the established opinion, according to which the presence of electrons in that phase is very unlikely. By using a theoretical model, we could shed light on this question. Our findings not only confirm the presence of electrons in that phase, but also isolate a mechanism that is responsible for this phenomenon. The main findings of the project have been published in Physical Review Letters, one of the worlds leading physics journals.