The instanton molecule liquid and 'sticky molasses' above T_c

The main objective of this work is to explore the evolution in the structure of the quark-antiquark bound states in going down in the chirally restored phase from the so-called zero binding points T_zb to the QCD critical temperature T_c at which the Nambu-Goldstone and Wigner-Weyl modes meet. In doing this, we adopt the idea recently introduced by Shuryak and Zahed for charmed c̄c, light-quark qq mesons π, σ, ρ, A ₁ and gluons that at T_zb, the quark-antiquark scattering length goes through ∞ at which conformal invariance is restored, thereby transforming the matter into a near-perfect fluid behaving hydrodynamically, as found at RHIC. We show that the binding of these states is accomplished by the combination of (i) the colour Coulomb interaction, (ii) the relativistic effects and (iii) the interaction induced by the instanton-anti-instanton molecules. The spin-spin forces turned out to be small. While near T_zb all mesons are large-size non-relativistic objects bound by the Coulomb attraction, near T_c they get much more tightly bound, with many-body collective interactions becoming important and making the σ and π masses approach zero (in the chiral limit). The wavefunction at the origin grows strongly with binding, and the near-local four-Fermi interactions induced by the instanton molecules play an increasingly more important role as the temperature moves downward towards T_c.