We present the phenomenology of antisymmetric rank-2 tensor unparticle operator ${\mathcal{O}}_{\mathcal{U},\mathcal{A}}^{\mu \nu }$ with scaling dimension $d_{\mathcal{U}}$. We consider the physical effects of operator $O_{\mathcal{U},\mathcal{A}}^{\mu \nu }$ in $Z^0$ boson invisible decays $Z^0\to \mathcal{U}$, $Z^0\to b\overline{b}$ channel, the electroweak precision observable $S$ parameter, and the muon anomalous magnetic dipole moment. The $Z^0$ boson invisible decay gives a very stringent constraint in the $({\Lambda }_{\mathcal{U}},M_{\mathcal{U}})$ plane, and only small $r\equiv {\Lambda }_{\mathcal{U}}/M_{\mathcal{U}}\lesssim 0.1$ is favored, when ${\Lambda }_{\mathcal{U}}$ is order of several 100 GeV. When the phenomenological parameter $\mu$, which parameterizes the scale invariance breaking, goes to 0, the $S$ parameter and the muon $(g-2)$ diverge for $1<d_{\mathcal{U}}<2$, while for nonzero $\mu$, there will be constraints on $({\Lambda }_{\mathcal{U}},M_{\mathcal{U}})$ which are more stringent than those obtained from collider experiments.

• Received 13 September 2007

DOI:https://doi.org/10.1103/PhysRevD.76.096008