Hybrid Star Properties with NJL and MFTQCD Model: A Bayesian Approach
Milena Albino, Tuhin Malik, Márcio Ferreira, Constança Providência
TL;DR
This work investigates whether neutron stars can harbor deconfined quark matter by constructing hybrid equations of state (EOS) that couple a hadronic phase described by Relativistic Mean Field theory with two quark-phase models, the Nambu–Jona-Lasinio (NJL) model and Mean Field Theory of QCD (MFTQCD), via a Maxwell construction. A Bayesian framework samples EOS parameters to satisfy NICER X-ray mass–radius constraints and a target phase-transition density around $\rho_{\text{trans}} \approx 0.15$–$0.40\,\mathrm{fm}^{-3}$, with an optional high-density pQCD constraint. The study finds hybrid stars compatible with current observations, but pQCD restrictions lower the maximum mass to about $M_{\max} \sim 2.1$–$2.3\,M_\odot$, with NJL more sensitive to these constraints in the stiff hadronic scenario; MFTQCD can yield smaller radii for moderate-mass stars. Vector interactions are crucial for achieving $M_{\max}>2\,M_\odot$, while multiquark terms can modify indicators of deconfinement, such as the trace anomaly $\Delta$ and conformality-related measures $d_c$; some EOSs even allow a persistently positive renormalized trace anomaly inside the star. Overall, the results support the viability of quark cores under current data and emphasize the role of model details and pQCD guidance in shaping NS properties.
Abstract
The composition of the core of neutron stars (NS) is still under debate. One possibility is that because of the high densities reached in their cores, matter could be deconfined into quark matter. We investigate the existence of hybrid stars, using microscopic models to describe different phases of matter. Within the adopted microscopic models we calculate properties of NS and properties of matter. We want to probe the pQCD calculations influence and analyze properties that identify a transition to deconfined matter. Bayesian approach is applied to generate 8 sets of equations of state (EOS). A Maxwell construction is adopted to describe the deconfinement transition. For the hadron phase, we consider a stiff and a soft EOS obtained from the Relativistic Mean Field model with nonlinear meson terms. For the quark phase, we use 2 different models: the Nambu-Jona-Lasinio model with multiquark interactions and the Mean Field Theory of QCD, a model similar to the vector MIT bag model. Bayesian inference was applied to determine the model parameters that satisfy the X-ray observations from NICER and have phase transition at densities between 0.15 - 0.40 fm$^{-3}$. We also applied restrictions from the pQCD calculations to half of the sets. Hybrid stars are compatible with current observational data. The pQCD restrictions reduce the value of the $M_{max}$. However, even applying this restriction, the models were able to reach values of $2.1 - 2.3 M_\odot$. The conformal limit was still not attained at the center of the most massive stars. The vector interactions are essential to describe hybrid stars with a mass above $2 M_\odot$. The multiquark interactions introduced may affect the limits of some quantities considered as indicators of the presence of a deconfined phase. It is possible to find a set of EOS, that predict that inside NS the renormalized matter trace anomaly is always positive.