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We investigate the phase structure of massless three-flavor QCD by extendingthe Nambu-Jona- Lasinio model to include the effects of confinement and theaxial anomaly. We study the interplay between the chiral and diquarkcondensates induced by the axial anomaly, as well as their relationship withthe Polyakov loop, which parameterizes confinement. By minimizing thethermodynamic potential we construct the QCD phase diagram and investigate thepossibility of realizing a recently discovered low temperature critical pointand an associated BEC-BCS crossover. We also perform a Ginzburg-Landauexpansion of the thermodynamic potential, comparing our results to a prioranalysis based purely on symmetry considerations, in order to assess thelowest-order effects of the condensate-confinement couplings.

Axial anomaly and the three-flavor Nambu--Jona-Lasinio model with confinement: Constructing the QCD phase diagram