Instantons and Chiral Symmetry in Finite Temperature and Density QCD

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The breakdown of chiral symmetry in the QCD vacuum and its restoration by thermal and/or baryonic density fluctuations are examined in connection with instantons. We adopt the standard formulation based on the dilute instanton gas and a chiral mean-field theory, as adapted to the case of finite temperature T and chemical potential μ for the light u and d quarks. The main result is a non-linear integral equation which defines momentum-dependent, self-consistent quark masses. Two existing formulations are considered: one based on the effective multilinear non-local interaction lagrangian for light quarks, the other based on an expansion in terms of the quark masses. A numerical investigation is made of the self-consistency equations. The procedure of solution involves assumptions common with other instanton applications and, specifically for the present application, the introduction of a single dimensionless parameter corresponding to a definition of renormalization mass. The choice of this parameter is made definite in reference to the T = μ = 0 vacuum case by requiring output dynamical masses of u, d quarks of the order of the constituent quark masses. The critical parameters characterizing the transition to the symmetric phase are then predicted without parameter adjustment.