Decay of Z Boson into Photon and Unparticle

We study the decay of the standard model Z boson into unparticle plus a single photon through a one-loop process. As in the anomaly type decay, only the axial-vector part of the Z coupling matching with the vector unparticle and/or the vector part of the Z coupling matching with the axial-vector unparticle can give a nonzero contribution to the decay. We show that the photon spectrum terminates at the end point in accord with Yang's theorem. Existing data on single photon production at LEP I is used to constrain the unparticle sector.