Fluctuation Diffusion in Quark matter

A unique transition state is a precursor of quark matter formation. We point out the hallmarks of this state and evaluate the quark diffusion coefficient in the vicinity of the QCD critical line. During the last decade the investigation of the quark matter at finite temperature and density became a compelling topic in QCD. Drawn in the (T, μ) plane with μ being the quark chemical potential the QCD phase diagram [1, 2] embodies several domains with quite different and sometimes poorly understood properties. The critical line starts at the point (T = Tc ≃ 170 MeV, μ = 0) and terminates at (T = 0, μ ≃ 300 − 500 MeV). From Tc with μ increasing the critical line presumably corresponds to the analytic crossover which ends at the critical point of the second order from which the first order transition line is perceived to originate supposedly ending at (T = 0, μ ≃ 300 − 500 MeV). The whole critical line spans over the region of strong coupling QCD regime which fails us for the first principle calculations. Lattice simulations have been performed along the T axis at μ = 0 while models like NJL have been used to investigate the transition in the vicinity of the other end point of the critical line. Lattice simulations have been recently extended to nonzero but small values of μ, μ/T < ∼ 1 [4]. At the other end of the critical line at small T and moderate μ model calculations suggest that the system is unstable with respect to the formation of quark-quark Cooper pair condensate [5, 6]. It took quite some time to realize that the nonzero value of the gap obtained within the NJL type calculations for μ ≃ 300−500 MeV does not mean the onset of color superconducting regime similar to the BCS one [7, 8]. Nonzero value of the gap is only a signal of the presence of fermion pairs. Depending on the strength of the interaction, on the fermion density, and on the temperature such pairs may be either stable, or fluctuating in time, may form a BCS condensate, or a dilute Bose gas, or undergo a Bose-Einstein condensation. It was shown [8, 9] that the critical line at small T and moderate μ corresponds to the crossover from strong coupling regime of composite nonoverlapping bosons (diquarks) to the weak coupling regime of macroscopic overlapping Cooper pair condensate (with possible LOFF phase [10] in between the two regimes). The dimensionless crossover parameter is n1/3ξ, where n is the quark density, and ξ is the characteristic length of pair correlation when the system is in the BCS regime and the root of the mean-square radius of the bound state when the system is in the strong coupling regime. The crossover (called BEC-BCS crossover) occurs at n1/3ξ ∼ 1. It can be shown [11] that the same dimensionless parameter defines the Ginzburg-Levanyuk number Gi which characterize the fluctuation contribution to the physical quantities and the width of the fluctuation region