Following the idea that a stable sexaquark state with quark content ($uuddss$) would have gone unnoticed by experiments so far and that such a particle would be a good dark matter candidate, we investigate the possible role of a stable sexaquark in the physics of compact stars given the stringent constraints on the equation of state that stem from observations of high mass pulsars and GW170817 bounds on the compactness of intermediate mass stars. We find that there is a “sexaquark dilemma” (analogous to the hyperon dilemma) for which the dissociation of the sexaquark in quark matter is a viable solution fulfilling all present constraints from multimessenger astronomy. The parameters needed to model the hybrid star, including sexaquarks, are in line with parameters of preexisting quark- and hadronic-matter models. We find that current constraints—tidal deformability in accordance with GW170817 and maximum mass above the lower limit from PSR $\mathrm{J}0740+6620$—can be satisfied two ways: with early quark deconfinement such that neither sexaquarks nor hyperons are present in any neutron star interiors, or with later deconfinement such that a neutron-sexaquark shell surrounds the inner quark matter core.

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 nlNJLA) and with density-dependent (model nlNJLB) parameters. We study the model dependence of the phase transition obtained by a Maxwell construction. Our study confirms that also with the present set of equations of state 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 $\mathrm{J}0740+6620$. In this work we provide with model nlNJLB 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 $2.2M_{\odot }$, in accordance with most recent constraints. In model nlNJLA such a phase cannot be realized 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 the GSI Facility for Antiproton and Ion Research, the Nuclotron-based Ion Collider fAcility, and corresponding energy scan programs at the CERN Large Hadron Collider and the BNL Relativistic Heavy Ion Collider.

The presence of dark matter (DM) within neutron stars (NSs) can be introduced by different accumulation scenarios in which DM and baryonic matter (BM) may interact only through the gravitational force. In this work, we consider asymmetric self-interacting bosonic DM, which can reside as a dense core inside the NS or form an extended halo around it. It is seen that depending on the boson mass ($m_{\chi }$), self-coupling constant ($\lambda$) and DM fraction ($F_{\chi }$), the maximum mass, radius and tidal deformability of NSs with DM admixture will be altered significantly. The impact of DM causes some modifications in the observable features induced solely by the BM component. Here, we focus on the widely used nuclear matter equation of state (EoS) called DD2 for describing NS matter. We show that by involving DM in NSs, the corresponding observational parameters will be changed to be consistent with the latest multi-messenger observations of NSs. It is seen that for $m_{\chi }\gtrsim 200$ MeV and $\lambda \lesssim 2\pi$, DM-admixed NSs with $4\%\lesssim F_{\chi }\lesssim 20\%$ are consistent with the maximum mass and tidal deformability constraints.

We provide a systematic study of hybrid neutron star equations of state (EOS) consisting of a relativistic density functional for the hadronic phase and a covariant nonlocal Nambu–Jona-Lasinio (nlNJL) model to describe the color superconducting quark matter phase. Changing the values of the two free parameters, the dimensionless vector and diquark coupling strengths ${\eta }_V$ and ${\eta }_D$ results in a set of EOS with varying stiffness and deconfinement onset. The favorable parameters are obtained from a systematic Bayesian analysis for which the multimessenger constraint on the neutron star radius at $14M_{\odot }$ and the combined mass-radius constraint for PSR $\mathrm{J}0740+6620$ from NICER experiment are used as the constraints. Additionally, the transition from hadronic matter to deconfined quark matter is constrained to occur above nuclear saturation density. Hybrid stars modeled with these favorable parameters are compatible with the NICER results for the radius of the highest known mass neutron star, PSR $\mathrm{J}0740+6620$. Three new observations interesting for neutron star phenomenology are reported: (i) we show that the constant sound speed (CSS) EOS provides an excellent fit to that of the nlNJL model which implies the squared speed of sound at high densities to be about 0.5 for the optimized parameters; (ii) we give a simple functional form for the mapping between the parameter spaces of these two models valid for the whole range of relevant chemical potentials and (iii) we observe that the special point property of hybrid EOS based on CSS quark matter generalizes to a set of lines consisting of special points when two EOS parameters are varied instead of one. A lower limit for the maximum mass of hybrid stars as a function of the vector coupling strength is obtained.

The lowest order constrained variational method is reformulated to find the equation of state of hypernuclear matter. For the nucleon-nucleon interaction we employed the well-known Argonne V18 (AV18) interaction. The equation of state is calculated using two-body central potentials for $\mathrm{\Lambda }N$ and $\mathrm{\Lambda }\mathrm{\Lambda }$ interactions that are determined in order to reproduce the experimental data on single- and double-$\mathrm{\Lambda }$ hypernuclei. For the odd-state part of the $\mathrm{\Lambda }\mathrm{\Lambda }$ interaction, which is not known due to the lack of experimental data, a proposed repulsive and attractive potential is employed to calculate the equation of state. It is shown that the presence of $\mathrm{\Lambda }$ in the hypernuclear matter produces a strong softening of the equation of state. The results are compared with similar calculations with another variational method. The state-dependent energy as well as central and tensor correlation functions are studied up to $J=2$ for each JLSTMT channel where related to total (J), orbital (L) and spin (S) angular momentum and isospin (T) and the third component of isospin (MT) respectively for $\mathrm{\Lambda }N$ and $\mathrm{\Lambda }\mathrm{\Lambda }$ interactions. Furthermore, the effect of baryon density and hyperon density as well as the type of hyperon-hyperon interaction on the two-body correlation functions are investigated.