[Paper Review] Density functional approach to quark matter with confinement and color superconductivity

O. Ivanytskyi, D. Blaschke|arXiv (Cornell University)|Apr 7, 2022

Pulsars and Gravitational Waves ResearchPhysics and Astronomy76 references56 citations

TL;DR

This paper develops a relativistic density functional approach to quark matter that incorporates confinement via a mean-field quark self-energy and color superconductivity through diquark pairing. It constructs a hybrid equation of state for neutron stars, showing that selected parametrizations can support hybrid stars with masses up to 2.67 M⊙, consistent with the massive component in GW190814 and the NICER radius measurement of PSR J0740+6620.

ABSTRACT

We present a novel relativistic density-functional approach to modeling quark matter with a mechanism to mimic confinement. The quasiparticle treatment of quarks provides their suppression due to a large quark selfenergy already at the mean-field level. We demonstrate that our approach is equivalent to a chiral quark model with medium-dependent couplings. The dynamical restoration of the chiral symmetry is ensured by construction of the density functional. Supplemented with the vector repulsion and diquark pairing the model is applied to construct a hybrid quark-hadron EoS of cold compact-star matter. We study the connection of such a hybrid EoS with the stellar mass-radius relation and tidal deformability. The model results are compared to various observational constraints including the NICER radius measurement of PSR J0740+6620 and the tidal deformability constraint from GW170817. The model is shown to be consistent with the constraints, still allowing for further improvement by adjusting the vector repulsion and diquark pairing couplings.

Motivation & Objective

• To develop a relativistic density functional framework that incorporates quark confinement via a medium-dependent self-energy at the mean-field level.
• To include dynamical chiral symmetry restoration through a self-consistent density functional formalism.
• To incorporate vector repulsion and diquark pairing to model color superconductivity in cold quark matter.
• To construct a hybrid quark-hadron equation of state (EoS) for compact star matter and test its consistency with observational constraints.
• To assess whether the model can reproduce the mass and radius of PSR J0740+6620 and the tidal deformability from GW170817, and to explore the possibility of very massive hybrid stars.

Proposed method

• Formulates a relativistic density functional Lagrangian with scalar, pseudoscalar, vector, and diquark pairing interactions, using chirally symmetric quark bilinears as the interaction argument.
• Applies a second-order Taylor expansion of the interaction potential around mean-field values to include mesonic correlations beyond mean field, ensuring correct pion mass and decay constant.
• Uses a confining mean-field potential inspired by the string-flip model to suppress quark degrees of freedom and mimic confinement.
• Introduces medium-dependent effective couplings (GS and GPS) in scalar and pseudoscalar channels derived from second derivatives of the potential.
• Incorporates vector interaction (GV) and diquark pairing (GD) to model repulsion and color superconductivity, respectively.
• Constructs a hybrid equation of state by matching the quark matter EoS to a hadronic EoS at a transition density, using Gibbs conditions and pasta phase considerations.

Experimental results

Research questions

• RQ1 Can a density functional approach with confinement and color superconductivity reproduce the observed mass and radius of PSR J0740+6620?
• RQ2 To what extent does the inclusion of diquark pairing and vector repulsion affect the maximum mass of hybrid neutron stars?
• RQ3 Can the model produce a hybrid equation of state consistent with the tidal deformability constraint from GW170817?
• RQ4 What parametrizations of the model allow for hybrid stars with masses in the range 2.5–2.67 M⊙, as suggested by GW190814?
• RQ5 How does the dynamical restoration of chiral symmetry manifest in the model’s thermodynamic potential and medium-dependent quark masses?

Key findings

• The model successfully reproduces the pion mass and decay constant through a second-order expansion of the density functional, ensuring consistency with QCD vacuum phenomenology.
• The inclusion of diquark pairing and vector repulsion leads to a stiffened equation of state, enabling the formation of massive hybrid stars.
• Selected parametrizations of the model predict hybrid star sequences with maximum masses in the range 2.5–2.67 M⊙, consistent with the inferred mass of the lighter component in GW190814.
• The model’s hybrid equation of state satisfies the NICER radius constraint for PSR J0740+6620, with predicted radii in the 11.2–12.5 km range.
• The tidal deformability predicted by the model is compatible with the GW170817 constraint, supporting the viability of the hybrid EoS.
• The approach is equivalent to a chiral quark model with medium-dependent couplings, and the quasiparticle treatment ensures quark suppression via large self-energies at the mean-field level.