Quarkyonic matter with quantum van der Waals theory

We incorporate the empirical low-density properties of isospin symmetric nuclear matter into the excluded -volume model for quarkyonic matter by including attractive mean field in the nucleonic sector and considering variations on the nucleon excluded volume mechanism. This corresponds to the quantum van der Waals equation for nucleons with the interaction parameters fixed to empirical ground state properties of nuclear matter. The resulting equation of state exhibits the nuclear liquid-gas transition at nB p0 and undergoes a transition to quarkyonic matter at densities nB approximate to 1.5 - 2p0 that are reachable in intermediate energy heavy-ion collisions. The transition is accompanied by a peak in the sound velocity. The results depend only mildly on the chosen excluded volume mechanism but do require the introduction of an infrared regulator A to avoid an acausal sound velocity. We also consider the recently proposed baryquark matter scenario for the realization of the Pauli exclusion principle, which yields a similar equation of state and turns out to be energetically favored in all the considered setups.