  We investigate the Pad\'e approximation method for the analytic continuation
of numerical data and its ability to access, from the Euclidean propagator,
both the spectral function and part of the physical information hidden in the
second Riemann sheet. We test this method using various benchmarks at zero
temperature: a simple perturbative approximation as well as the two-loop
Phi-derivable approximation. The analytic continuation method is then applied
to Euclidean data previously obtained in the O(4) symmetric model (within a
given renormalization scheme) to assess the difference between zero-momentum
and pole masses, which is in general a difficult question to answer within
nonperturbative approaches such as the Phi-derivable expansion scheme.
