  We study supersymmetric QCD in the conformal window as a laboratory for
unparticle physics, and analyze couplings between the unparticle sector and the
Higgs sector. These couplings can lead to the unparticle sector being pushed
away from its scale invariant fixed point. We show that this implies that low
energy experiments will not be able to see unparticle physics, and the best
hope of seeing unparticles is in high energy collider experiments such as the
Tevatron and the LHC. We also demonstrate how the breaking of scale invariance
could be observed at these experiments.
