Hadron-quark phase transition in neutron star by combining the relativistic Brueckner-Hartree-Fock theory and Dyson-Schwinger equation approach

Abstract: Starting from the relativistic Brueckner-Hartree-Fock theory for nuclear matter and the Dyson-Schwinger equation approach for quark matter, the possible hadron-quark phase transition in the interior of a neutron star is explored. The first-order phase transition and crossover are studied by performing the Maxwell construction and three-window construction respectively. The mass-radius relation and the tidal deformability of the hybrid star are calculated and compared to the joint mass-radius observation of a neutron star and the constraints from gravitational wave detection. For the Maxwell construction, no stable quark core is found in the interior of a neutron star. For the three-window construction, the parameters of the smooth interpolation function are chosen in such a way to keep the thermodynamic stability and lead to a moderate crossover density region. To support a two-solar-mass neutron star under the three-window construction, the effective width of medium screening effects in quark matter should be around $0.35$ GeV.