We study interactions of unparticles ${cal {U}}$ of dimension $d_{cal {U}}$ due to Georgi with Standard Model (SM) fields through effective operators. The unparticles describe the low energy physics of a non-trivial scale invariant sector. Since unparticles come from beyond the SM physics, it is plausible that they transform as a singlet under the SM gauge group. This helps tremendously in limiting possible interactions. We analyze interactions of scalar ${cal {U}}$, vector ${cal {U}}$$^mu$ and spinor ${cal {U}}$$^s$ unparticles with SM fields and derivatives up to dimension four. Using these operators, we discuss different features of producing unparticles at $e^+ e^-$ collider and other phenomenologies. It is possible to distinguish different unparticles produced at $e^+e^-$ collider by looking at various distributions of production cross sections.
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