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The decay width of the rare decay Z \to \nu\bar{\nu}\gamma\gamma is strictly constrained from the LEP data. Tensor unparticles provide a tree-level contribution to this rare decay. We have calculated the tensor unparticle contribution to the rare decay Z\to \nu\bar{\nu}\gamma\gamma. The current experimental limit have been used to constrain unparticle couplings \nu\bar{\nu}Z {U}^{\mu\nu} and \gamma\gamma {U}^{\mu\nu}.

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