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We explore phenomenological consequences of coupling a non-conformal scale-invariant theory to the standard model. We point out that, under certain circumstances, non-conformal scale-invariant theories have oscillating correlation functions which can dramatically modify standard model processes. We dub this scenario cyclic unparticle physics, or simply cyclunparticle physics. We compute phase spaces and amplitudes associated with final state cyclunparticle and cyclunparticle exchange, respectively. We show detailed formulae in a simple example.
preprint / 2011