Fermions Obstruct Dimensional Reduction in Hot QCD

We have studied, for the first time, screening masses obtained from glueball-like correlators in quantum chromodynamics with four light dynamical flavors 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 pionlike and sigmalike 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.