  We propose a spectral decomposition to systematically extract information of
dark matter at hadron colliders. The differential cross section of events with
missing transverse energy (MET) can be expressed by a linear combination of
basis functions. In the case of $s$-channel mediator models for dark matter
particle production, basis functions are identified with the differential cross
sections of sub-processes of virtual mediator and visible particle production
while the coefficients of basis functions correspond to dark matter invariant
mass distribution in the manner of the K\"all\'en-Lehmann spectral
decomposition. For a given MET data set and mediator model, we show that one
can differentiate a certain dark matter-mediator interaction from another
through spectral decomposition.
