Intermediate distance correlators in hot Yang-Mills theory

Lattice measurements of spatial correlation functions of the operators FF and F (F) over tilde in thermal SU(3) gauge theory have revealed a clear difference between the two channels at intermediate distances, x similar to 1/pi T. This is at odds with the AdS/CFT limit which predicts the results to coincide. On the other hand, an OPE analysis at short distances (x << 1/pi T) as well as effective theory methods at long distances (x >> 1/pi T) suggest differences. Here we study the situation at intermediate distances by determining the time-averaged spatial correlators through a 2-loop computation. We do find unequal results, however the numerical disparity is small. Apart from theoretical issues, a future comparison of our results with time-averaged lattice measurements might also be of phenomenological interest in that understanding the convergence of the weak-coupling series at intermediate distances may bear on studies of the thermal broadening of heavy quarkonium resonances.