  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 $\bar c c$, light-quark $\bar q q$ mesons $\pi, \sigma, \rho, A_1$ and
gluons that at $T_{zb}$, the quark-antiquark 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 name this new state of matter as "sticky molasses". 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 $T_c$.
