Stress-stress correlator in φ4 theory: poles or a cut?

We explore the analytical properties of the traceless stress tensor 2-point function at zero momentum and small frequency (relevant for shear viscosity and hydrodynamic response) in hot, weakly coupled lambda phi(4) theory. We show that, rather than one or a small number of poles, the correlator has a cut along the negative imaginary frequency axis. We briefly discuss this result's relevance for constructing 2'nd order hydrodynamic models of hot relativistic field theories.