Intermediate distance correlators in hot Yang-Mills theory

TL;DR

This paper investigates the behavior of spatial correlators in hot SU(3) gauge theory at intermediate distances, revealing small but significant differences between channels through a 2-loop computation, with implications for lattice comparisons and quarkonium studies.

Contribution

The study provides a detailed 2-loop analysis of spatial correlators at intermediate distances, highlighting small differences and bridging short and long-distance theoretical predictions.

Findings

Correlators differ slightly at intermediate distances.

Numerical disparity between channels is small.

Results may inform lattice measurements and quarkonium phenomenology.

Abstract

Lattice measurements of spatial correlation functions of the operators FF and FF-dual in thermal SU(3) gauge theory have revealed a clear difference between the two channels at "intermediate" distances, x ~ 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.