This diagram is somehow our starting point to set the stage, we will review it in Section 5 feeding in the up to date results. Whether these phases persist to the hadron gas surface of Figure 1 depends on the non-perturbative properties of QCD. A negative isospin chemical potential does instead favor the formation of π − states.
At large and positive μ I we expect to populate the u and d ¯ states with the color interaction inducing the formation of π + states that will eventually condense.
At large μ B we expect that deconfined quarks fill their Fermi spheres and that the color interaction drives the formation of Cooper pairs in a BCS-like color superconducting phase (CSC), see for reviews. The quark-gluon plasma (QGP), realized at large temperature, is asymptotically a gas of quarks and gluons that becomes strongly interacting for the temperature reachable in heavy-ion collisions, see for instance. At large energy scales quarks and gluons should be liberated realizing different phases. The blue region corresponds to a gas of confined hadrons with a chiral broken symmetry. If it were possible we would have added a further axis, μ S, indicating the strangeness content.
The total baryonic density is determined by μ B, while μ I describes the isospin asymmetry, say due to a different number of up and down quarks. To clarify the setting we report in Figure 1 a sketch of the so-called QCD phase diagram: a grand canonical description of the phases of hadronic matter as a function of the hadronic temperature, T, of the isospin chemical potential, μ I, and of the baryonic chemical potentials, μ B.
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