  The viscoelastic properties of soft jammed solids, such as foams, emulsions,
and soft colloids, have been the subject of experiments, with particular
interest in the anomalous viscous loss. However, a microscopic theory to
explain these experimental results is still lacking. Here, we develop an
effective medium theory that incorporates the effects of contact damping. The
theory explains experimentally observed viscoelastic properties, particularly
attributing the anomalous viscous loss to marginal stability in amorphous
systems. This work establishes a microscopic theory for describing the impact
of damping on soft jammed solids and their viscoelastic behaviors.
