Quark saturation in the QCD phase diagram

We determine the onset of quarkyonic matter corresponding to values of temperature and baryon chemical potential at which the quark phase space density becomes one. At zero temperature for baryon chemical potentials below the mass of the \ensuremath{\Lambda} baryon, only nucleons contribute to the quark density. This is different at finite temperature, where all baryons, mesons and their resonances can be excited and thus add quarks to the phase space. The probability density to find a quark inside a hadron is determined using the Yukawa ansatz of the IdylliQ model of quarkyonic matter. We estimate separately the magnitude of the various contributions of nucleons, \ensuremath{\Delta} baryons, pions as well as further hadrons and resonances. The uncertainty in the parametrization of the probability density to find a quark inside a nucleon is spanned by assuming that at zero temperature the transition density to quarkyonic matter is between one and three times that of nuclear matter. Various predictions for a possible critical point associated with the chiral phase transition are found close to the point at which the line of the deconfinement transition and the curve associated with the transition to quarkyonic mqatter intersect. These considerations provide an estimate for the region in the quantum chromodynamics phase diagram where quarkyonic matter may be found.