The hyperfine splitting in QCD mesonic screening masses at asymptotically large temperatures

We determine the hyperfine splitting in the QCD flavour non-singlet mesonic screening masses at asymptotically large temperatures. The analytic calculation is carried out in the dimensionally-reduced effective theory where the first non-zero contribution is of O(g4) in the QCD coupling constant g. Apart for its own theoretical interest, this result provides instrumental information to interpret and to parameterize non-perturbative data that are being produced at very high temperatures by numerical simulations of lattice QCD. Indeed, the comparison with existing non-perturbative results shows that higher order (non-perturbative) contributions in g are needed to explain the data up to the highest temperature explored, which is of the order of the electroweak scale.