Topology, fermionic zero modes, and flavor singlet correlators in finite temperature QCD

Abstract

We compute the screening correlators in the $\ensuremath{\sigma}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ flavor singlet channels in finite temperature QCD with 2 light quark flavors. Together with the correlators in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\pi}}$ and $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\delta}}$ channels, these are used to discuss several issues related to symmetry restoration and the nature of the QCD phase transition. Our calculations span a range of temperature extending from approximately 125 MeV to 170 MeV and are carried out in the context of a staggered fermion formulation on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}8$ lattice. In addition to the computation at a fixed quark mass ${(am}_{q}=0.00625)$, we discuss the issue of the chiral limit. After careful consideration of the zero-mode shift lattice artifact, we present rather strong (topological) arguments in favor of the non-restoration of ${U}_{A}(1)$ at ${T}_{c}.$