Speaker
Description
We aim to construct a unified Equation of State (EOS) capable of describing strongly interacting matter over a wide range of densities and temperatures. As a first step, we validate a Bayesian framework to rigorously incorporate astrophysical constraints into the cold, dense matter sector by considering Relativistic Mean-Field (RMF) models based on the exchange of $\sigma, \omega$, and $\rho$ mesons, including nonlinear nucleon-$\sigma$ couplings and density-dependent $\rho$ coupling. A large set of models is generated using a Markov chain Monte Carlo approach within a Bayesian framework to reproduce nuclear physics knowledge encoded in terms of the nuclear empirical parameters and $\chi$EFT predictions for low-density neutron matter.
These models are then filtered, using astrophysical constraints, such as the tidal deformability obtained from GW170817 parameter estimation and the observational masses deduced from radioastronomy. We obtain a set of selected RMF models compatible with present nuclear and astrophysical constraints, finding that RMF models can produce EOS soft enough to predict low values for neutron star radii compatible with GW170817, and can be made stiff enough at larger densities to be compatible with NICER analyses of massive neutron stars, reaching maximum mass values of up to $2.6M_\odot$.
To extend this description to finite temperatures and deconfinement, we develop a theoretical framework based on an effective Lagrangian where a dilaton field encodes the breaking of scale symmetry in QCD. Starting from the pure gauge $SU(3)_c$ sector, the low-temperature gluon condensate is dominated by the dilaton, evaporating into quasi-free gluons above the critical temperature. To address thermal effects, we study the role of dilaton fluctuations, finding a first-order phase transition, as expected from the results of lattice QCD. We extend this framework by including mesons ($\sigma$, $\pi$, $\omega$, $\rho$) and nucleons along with their thermal fluctuations, at finite temperature and chemical potential. This effective Lagrangian, incorporating both broken-scale symmetry and explicit chiral symmetry breaking, allows us to explore the QCD phase diagram over a wide range of temperatures and densities using a single EOS.
