  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. There are two definitions of mass in each regime; in Euclidean these are
the screening and pole masses. The analytic continuation of these mass
parameters to real time is non-trivial. This is in contrast to the situation at
zero temperature.
