Lepton flavor violating $\mu\to e\gamma$ and $\mu-e$ conversion in unparticle physics

Abstract

We have studied lepton flavor violation processes $\mu\to e\gamma$ and $\mu-e$ conversion in nuclei induced by unparticle. Both ${\rm Br}(\mu\to e\gamma)$ and $\mu-e$ conversion rate ${\rm CR}(\mu-e,{\rm Nuclei})$ strongly depend on the scale dimension $d_{\cal U}$ and the unparticle coupling $\lambda^{ff'}_{\rm K}$(K=V, A, S, P). Present experimental upper bounds on ${\rm Br}(\mu\to e\gamma)$, ${\rm CR}(\mu-e,{\rm Ti})$ and ${\rm CR}(\mu-e,{\rm Au})$ put stringent constraints on the parameters of unaprticle physics. The scale dimensions $d_{\cal U}$ around 2 are favored for the unparticle scale $\Lambda_{\cal U}$ of ${\cal O}(10 {\rm TeV})$ and the unparticle coupling of ${\cal O}(10^{-3})$. ${\rm CR}(\mu-e,{\rm Nuclei})$ is proportional to $\rm{Z^4_{eff}A^2/Z}$ for the pure vector and scalar couplings between unparticle and SM fermions, this peculiar atomatic number dependence can be used to distinguish unparticle from other theoretical models.