The \bar q q Bound States and Instanton Molecule at T >~ T_c

The main objective of this work is to explore the evolution in the structure of the quark-anti-quark bound states in going down in the chirally restored phase from the so-called "zero binding points" $T_{zb}$ to the full (unquenched) 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 $\bar c c$, light-quark $\bar q q$ mesons $\pi, \sigma, \rho, A_1$ and gluons that at $T_{zb}$, the quark-anti-quark scattering length goes through $\infty$ 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 color 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 nonrelativistic objects bound by Coulomb attraction, near $T_c$ they get much more tightly bound, with many-body collective interactions becoming important and making the $\sigma$ and $\pi$ masses approach zero (in the chiral limit). The wave function 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 toward $T_c$.