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The scalar does not decay at finite temperatures

We investigate medium effects on mesonic screening lengths for QCD with 2-flavours of dynamical staggered quarks on lattices with cutoff a=1/6T. Denoting the cross-over temperature by $T_c$, we vary the temperature T from 0.89$T_c$ to 1.92$T_c$, spanning both the hadronic and quark gluon plasma phases. While chiral symmetry restoration in the vector channel appears to take place near $T_c$, it is seen in the scalar channel only above 1.33 $T_c$. Varying spatial lattice sizes, we find very little volume dependence in our results at 0.94 $T_c$. We discuss the stability of the scalar meson at these temperatures.