  Lattice measurements provide adequate information to fix the parameters of
long distance effective field theories in Euclidean time. Using such a theory,
we examine the analytic continuation of long distance correlation functions of
composite operators at finite temperature from Euclidean to Minkowski space
time. We show through an explicit computation that the analytic continuation of
the pion correlation function is possible and gives rise to non-trivial
effects. Among them is the possibility, supported by lattice computations of
Euclidean correlators, that long distance excitations can be understood in
terms of (very massive) pions even at temperatures higher than the QCD cross
over temperature.
