Meson correlation functions at high temperature QCD: $SU(2)_{CS}$ symmetry vs. free quarks

We report on the progress of understanding spatial correlation functions in high temperature QCD. We study isovector meson operators in $n_f=2$ QCD using domain-wall fermions on lattices of $N_s=32$ and different quark masses. It has previously been found that at $\sim 2T_c$ these observables are not only chirally symmetric but in addition approximately $SU(2)_{CS}$ and $SU(4)$ symmetric. In this study we increase the temperature up to $5T_c$ and can identify convergence towards an asymptotically free scenario at very high temperatures.