Peaks of sound velocity in two color dense QCD: quark saturation effects and semishort range correlations

Abstract: We discuss stiffening of dense matter in two color QCD (QC$_2$D) where hadrons are mesons and diquark baryons. We study two models which describe a transition of matter from the Bose-Einstein-Condensation regime at low density to the Bardeen-Cooper-Schrieffer regime at high density. The first model is based on coherent states of diquarks, and the second is the Nambu-Jona-Lasinio model with diquark pairing terms. We particularly focus on how quark states are occupied as baryon density increases. We find that, due to the occupied quark levels, the ideal gas picture of diquarks breaks down at density significantly less than the density where baryon cores overlap. The saturation of quark states at low momenta stiffens equations of state. We also study the effects of interactions which depend on the quark occupation probability. We argue that equations of state become very stiff when the bulk part of the quark Fermi sea has the effective repulsion but the Fermi surface enjoys the attractive correlations. This disparity for different momentum domains is possible due to the strong channel dependence in gluon exchanges with momentum transfer of $0.2-1$ GeV. These concepts can be transferred from QC$_2$D to QCD in any numbers of colors.