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We discuss a strategy to study non-perturbatively QCD up to very hightemperatures by Monte Carlo simulations on the lattice. It allows not only thethermodynamic properties of the theory but also other interesting thermalfeatures to be investigated. As a first concrete application, we compute theflavour non-singlet mesonic screening masses and we present the results ofMonte Carlo simulations at 12 temperatures covering the range from T $\sim$ 1GeV up to $\sim$ 160 GeV in the theory with three massless quarks. On the oneside, chiral symmetry restoration manifests itself in our results through thedegeneracy of the vector and the axial vector channels and of the scalar andthe pseudoscalar ones, and, on the other side, we observe a clear splittingbetween the vector and the pseudoscalar screening masses up to the highestinvestigated temperature. A comparison with the high-temperature effectivetheory shows that the known one-loop order in the perturbative expansion doesnot provide a satisfactory description of the non-perturbative data up to thehighest temperature considered.

QCD mesonic screening masses up to high temperatures