  The coupling of unparticles to the Standard Model (SM) Higgs boson leads to a
breaking of conformal symmetry which produces an effective mass term in the
unparticle propagator. Simultaneously, the unparticle couplings to other SM
fields produces an effective unparticle decay width via one-loop self-energy
graphs. The resulting unparticle propagator then leads to a rather unique
appearance for the shape of unparticle resonances that are not of the usual
Breit-Wigner variety when they form in high energy collisions. In this paper we
explore whether or not such resonances, appearing in the Drell-Yan channel at
the LHC, can be differentiated from more conventional $Z'$-like structures
which are representative of the typical Breit-Wigner lineshape. We will
demonstrate that even with the high integrated luminosities available at the
LHC it may be difficult to differentiate these two types of resonance
structures for a substantial range of the unparticle model parameters.
