  If the LHC is able to produce dark matter particles, they would appear at the
end of cascade decay chains, manifesting themselves as missing transverse
energy. However, such "dark matter candidates" may decay invisibly later on. We
propose to test for this possibility by studying the effect of particle widths
on the observable invariant mass distributions of the visible particles seen in
the detector. We consider the simplest non-trivial case of a two-step two-body
cascade decay and derive analytically the shapes of the invariant mass
distributions, for generic values of the widths of the new particles. We
demonstrate that the resulting distortion in the shape of the invariant mass
distribution can be significant enough to measure the width of the dark matter
"candidate", ruling it out as the source of the cosmological dark matter.
