We reconsider the problem of the hyperon puzzle and its suggested solution by quark deconfinement within the two-phase approach to hybrid compact stars with recently obtained hadronic and quark matter equations of state. For the hadronic phase we employ the hypernuclear equation of state from the lowest order constrained variational method and the quark matter phase is described by a sufficiently stiff equation of state based on a color superconducting nonlocal Nambu-Jona-Lasinio model with constant (model A) and with density-dependent (model B) parameters. We study the model dependence of phase transition obtained by a Maxwell construction. Our study confirms that also with the present set of modern equations of state the quark deconfinement presents a viable solution of the hyperon puzzle even for the new constraint on the lower limit of the maximum mass from PSR J0740+6620. In this work we provide with model B for the first time a hybrid star EoS with an intermediate hypernuclear matter phase between the nuclear and color superconducting quark matter phases, for which the maximum mass of the compact star reaches 2.2 M , in accordance with most recent constraints. In model A such a phase cannot be realised because the phase transition onset is at low densities, before the hyperon threshold density is passed. We discuss possible consequences of the hybrid equation of state for the deconfinement phase transition in symmetric matter as it will be probed in future heavy-ion collisions at FAIR, NICA and corresponding energy scan programs at the CERN and RHIC facilities.

We analyze the nuclear matter correlation properties in terms of the pair correlation function. To this aim we systematically compare the results for the variational method in the lowest-order constrained variational (LOCV) approximation and for the Bruekner-Hartree-Fock (BHF) scheme. A formal link between the Jastrow correlation factor of LOCV and the defect function (DF) of BHF is established and it is shown under which conditions and approximations the two approaches are equivalent. From the numerical comparison it turns out that the two correlation functions are quite close, which indicates in particular that the DF is approximately local and momentum independent. The equations of state (EOS) of nuclear matter in the two approaches are also compared. It is found that once the three-body forces (TBF) are introduced, the two EOS are fairly close, while the agreement between the correlation functions holds with or without TBF.

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The two-body correlation functions, obtained in a lowest-order constrained variational calculation for hot nuclear and neutron matter, with the Reid potential and the explicit inclusion of (1234), are state averaged and used to calculate the three-body cluster energy. The three-body cluster energy is found to vary between about 1 and 2 MeV through and beyond twice the nuclear-matter saturation density for temperatures between 5 and 20 MeV. However, the inclusion of a three-body cluster reduces the nuclear-matter flashing and critical temperatures. A critical temperature of 15.8 MeV and a critical exponent of 0.35 is found. The results of entropy calculations are in good agreement with experimental prediction and other theoretical results. Finally it is shown that by allowing an explicit (1234) degree of freedom through the Reid potential up to and including the three-body clusters, the lowest-constrained variational calculation yields other nuclear-and neutron-matter properties close to the available semi-empirical and experimental data at zero and finite temperatures.

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The method of lowest-order constrained variational, which predicts reasonably the nuclear matter semi-empirical data is used to calculate the equation of state of beta-stable matter at finite temperature. The Reid soft-core with and without the N-∆ interactions which fits the N-N scattering data as well as the U V 14 potential plus the three-nucleon interaction are considered in the nuclear many-body Hamiltonian. The electron and muon are treated relativistically in the total Hamiltonian at given temperature, to make the fluid electrically neutral and stable against beta decay. The calculation is performed for a wide range of baryon density and temperature which are of interest in the astrophysics. The free energy, entropy, proton abundance, etc.of nuclear beta-stable matter are calculated. It is shown that by increasing the temperature, the maximum proton abundance is pushed to the lower density while the maximum itself increases as we increase the temperature.The proton fraction is not enough to see any gas-liquid phase transition. Finally we get an overall agreement with other many-body techniques, which are available only at zero temperature.