We study a family of equations of state (EOS) for hybrid neutron star matter. The hybrid EOS are obtained by a Maxwell construction of the first-order phase transition between a hadronic phase described by the relativistic density-functional EOS of the “DD2” class with excluded volume effects and a deconfined quark matter phase modeled by an instantaneous nonlocal version of the Nambu–Jona-Lasinio model in $\text{SU}{\left(2\right)}_f$ with vector interactions and color superconductivity. The form factor in the nonlocal quark matter model is fitted to lattice QCD results in the Coulomb gauge. Owing to strong coupling in the vector meson and diquark channels, a coexistence phase of color superconductivity and chiral symmetry breaking occurs. Our results show an approximately constant behavior for the squared speed of sound with values of 0.4–0.6 in the density region relevant for neutron star interiors. To simultaneously fulfill the constraints from the Neutron Star Interior Composition Explorer radius measurement for PSR $\mathrm{J}0740+6620$ and tidal deformability from GW170817 it is necessary to consider a $\mu$-dependent bag pressure that mimics confinement.

The mass spectrum of ${\pi }^{+}$ and ${\rho }^{+}$ mesons in the presence of a static uniform magnetic field $\overrightarrow{B}$ is studied within a two-flavor Nambu-Jona-Lasinio-like model. We improve previous calculations, taking into account the effect of Schwinger phases carried by quark propagators and using an expansion of meson fields in terms of the solutions of the corresponding equations of motion for nonzero $B$. It is shown that the meson polarization functions are diagonal in this basis. Our numerical results for the ${\rho }^{+}$ meson spectrum are found to disfavor the existence of a meson condensate induced by the magnetic field. In the case of the ${\pi }^{+}$ meson, $\pi$—$\rho$ mixing effects are analyzed for the meson lowest-energy state. The predictions of the model are compared with available lattice QCD results.

We investigate the extension to finite temperatures and neutrino chemical potentials of a recently developed nonlocal chiral quark model approach to the equation of state of neutron star matter. We consider two light quark flavors and current-current interactions in the scalar-pseudoscalar, vector, and diquark pairing channels, where the nonlocality of the currents is taken into account by a Gaussian form factor that depends on the spatial components of the 4-momentum. Within this framework, we analyze order parameters, critical temperatures, phase diagrams, equations of state, and mass-radius relations for different temperatures and neutrino chemical potentials. For parameters of the model that are constrained by recent multimessenger observations of neutron stars, we find that the mass-radius diagram for isothermal hybrid star sequences exhibits the thermal twin phenomenon for temperatures above 30 MeV.

We review the current status of the research on effective nonlocal NJL-like chiral quark models with separable interactions, focusing on the application of this approach to the description of the properties of hadronic and quark matter under extreme conditions. The analysis includes the predictions for various hadron properties in vacuum, as well as the study of the features of deconfinement and chiral restoration phase transitions for systems at finite temperature and/or density. We also address other related subjects, such as the study of phase transitions for imaginary chemical potentials, the possible existence of inhomogeneous phase regions, the presence of color superconductivity, the effects produced by strong external magnetic fields and the application to the description of compact stellar objects.

Mixing effects on the mass spectrum of light neutral pseudoscalar and vector mesons in the presence of an external uniform magnetic field $\overrightarrow{B}$ are studied in the framework of a two-flavor Nambu-Jona-Lasinio (NJL)-like model. The model includes isoscalar and isovector couplings both in the scalar-pseudoscalar and vector sectors, and also incorporates flavor mixing through a ’t Hooft-like term. Numerical results for the $B$ dependence of meson masses are compared with present lattice QCD results. In particular, it is shown that the mixing between pseudoscalar and vector meson states leads to a significant reduction of the mass of the lightest state. The role of chiral symmetry and the effect of the alignment of quark magnetic moments in the presence of the magnetic field are discussed.

We present a physics-informed Bayesian analysis of equation of state constraints using observational data for masses, radii and tidal deformability of pulsars and a generic class of hybrid neutron star equation of state with color superconducting quark matter on the basis of a recently developed nonlocal chiral quark model. The nuclear matter phase is described within a relativistic density functional model of the DD2 class and the phase transition is obtained by a Maxwell construction. We find the region in the two-dimensional parameter space spanned by the vector meson coupling and the scalar diquark coupling, where three conditions are fulfilled: (1) the Maxwell construction can be performed, (2) the maximum mass of the hybrid neutron star is not smaller than 2.0 ${\mathrm{M}}_{\odot }$ and (3) the onset density of the phase transition is not below the nuclear saturation density $n_0=0.15$ fm⁻³. The result of this study shows that the favorable neutron star equation of state has low onset masses for the occurrence of a color superconducting quark matter core between 0.5–0.7 $M_{\odot }$ and maximum masses in the range 2.15–2.22 $M_{\odot }$. In the typical mass range of 1.2–2.0 $M_{\odot }$, the radii of these stars are between 11.9 and 12.4 km, almost independent of the mass. In principle, hybrid stars would allow for larger maximum masses than provided by the hadronic reference equation of state.