Thermodynamics and critical behavior in the Nambu-Jona-Lasinio model of QCD

We investigate the phase diagram of strongly interacting matter as a function of temperature and baryonic density/chemical potential, within Nambu--Jona-Lasinio type models. We perform a systematic study concerning the existence, location, and properties of a critical end point/tricritical point, both in SU(2) and SU(3) versions of the model. We verify that, for $m_u=m_d=0$ and up to a critical strange quark mass, there is a tricritical point, which becomes a critical end point in a world with realistic values of the current quark masses. The properties of physical observables, such as the baryon number susceptibility and the specific heat, are analyzed in the vicinity of the critical end point, with special focus on their critical exponents. The behavior of mesons in the $T-\mu_B(\rho_B)$ plane is analyzed in connection with possible signatures of partial and effective restoration of chiral symmetry.