  We have studied, for the first time, screening masses obtained from
glueball-like correlators in Quantum Chromodynamics with four light dynamical
flavours of quarks in the temperature range 1.5T_c < T < 3T_c, where T_c is the
temperature at which the chiral transition occurs. We have also studied
pion-like and sigma-like screening masses, and found that they are degenerate
in the entire range of T. These obstruct perturbative dimensional reduction
since the lowest glueball screening mass is heavier than them. Extrapolation of
our results suggests that this obstruction may affect the entire range of
temperature expected to be reached even at the Large Hadron Collider.
