[Paper Review] The Phase Diagram of Neutral Quark Matter

Stefan B. Ruester|ArXiv.org|Dec 20, 2006

Pulsars and Gravitational Waves Research3 citations

TL;DR

This thesis investigates the phase diagram of dense, locally neutral three-flavor quark matter using a nine-parameter gap matrix ansatz and a Nambu–Jona-Lasinio (NJL) model with self-consistently generated quark masses. It identifies critical transitions from the color-flavor-locked (CFL) phase to gapless CFL (gCFL) and other phases like metallic CFL (mCFL), uSC, 2SC, and g2SC, showing that neutrino trapping favors 2SC over CFL in protoneutron stars, with implications for quark core stability and strange quark production post-deleptonization.

ABSTRACT

In this thesis, I study the phase diagram of dense, locally neutral three-flavor quark matter as a function of the strange quark mass, the quark chemical potential, and the temperature, employing a general nine-parameter ansatz for the gap matrix. I also study the phase diagram of dense, locally neutral three-flavor quark matter within the framework of a Nambu-Jona-Lasinio (NJL) model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagram in the plane of temperature and quark chemical potential is presented. In addition, I study the effect of neutrino trapping on the phase diagram of dense, locally neutral three-flavor quark matter within the same NJL model. The phase diagrams in the plane of temperature and quark chemical potential, as well as in the plane of temperature and lepton-number chemical potential are presented. The implications of these results for the evolution of protoneutron stars are briefly discussed.

Motivation & Objective

• To map the phase diagram of dense, locally neutral three-flavor quark matter as a function of strange quark mass, quark chemical potential, and temperature.
• To investigate the role of dynamically generated quark masses and diquark coupling strength in determining the ground state phase.
• To analyze the impact of neutrino trapping on the stability of color-superconducting phases in protoneutron stars.
• To assess the implications for the structure and evolution of compact stars, particularly regarding quark core formation and strange quark production.

Proposed method

• Employing a general nine-parameter ansatz for the gap matrix to describe pairing in three-flavor quark matter.
• Using a Nambu–Jona-Lasinio (NJL) model with self-consistent treatment of dynamically generated quark masses.
• Applying mean-field approximation to solve for gap parameters, chemical potentials, and thermodynamic quantities.
• Incorporating neutrino trapping via lepton-number chemical potential in the NJL model to simulate conditions in protoneutron stars.
• Constructing three-dimensional phase diagrams in (T, μ, μ_L) space and analyzing two-dimensional cross-sections.
• Using Matsubara frequency summation and Dirac trace techniques to compute the effective action and pressure.

Experimental results

Research questions

• RQ1 What is the structure of the phase diagram of neutral three-flavor quark matter at zero and finite temperature, varying the strange quark mass and chemical potential?
• RQ2 How does the inclusion of dynamically generated quark masses affect the stability of the CFL and gCFL phases?
• RQ3 What is the effect of neutrino trapping on the competition between the CFL and 2SC phases in protoneutron stars?
• RQ4 How does diquark coupling strength influence the emergence and stability of gapless and metallic color-superconducting phases?
• RQ5 Can the 2SC phase be the ground state in protoneutron stars, and what are the implications for strange quark production?

Key findings

• At zero temperature and small strange quark mass, the ground state is the color-flavor-locked (CFL) phase, transitioning to the gapless CFL (gCFL) phase at a critical strange quark mass.
• The metallic CFL (mCFL) and uSC phases emerge as distinct phases in the phase diagram, with the uSC phase characterized by pairing only in up quark colors.
• Neutrino trapping strongly favors the 2SC phase by reducing the Fermi momentum mismatch between quarks, while disfavoring the CFL phase due to high electron chemical potential.
• The critical line separating the 2SC and normal quark matter phases is only weakly affected by neutrino trapping.
• In protoneutron stars, the CFL phase is unlikely to form before deleptonization is complete, making 2SC the most probable ground state in quark cores.
• Post-deleptonization, a rapid production of strange quarks is expected, potentially leading to observable signatures in compact star evolution.