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 $\mathrm{Br}(\mu \to e\gamma )$ and $\mu -e$ conversion rate $\mathrm{CR}(\mu -e,\mathrm{Nuclei})$ strongly depend on the scale dimension $d_{\mathcal{U}}$ and the unparticle coupling ${\lambda }_{\mathrm{K}}^{f{f}^{\prime }}$(K=V, A, S, P). Present experimental upper bounds on $\mathrm{Br}(\mu \to e\gamma )$, $\mathrm{CR}(\mu -e,\mathrm{Ti})$ and $\mathrm{CR}(\mu -e,\mathrm{Au})$ put stringent constraints on the parameters of unaprticle physics. The scale dimensions $d_{\mathcal{U}}$ around 2 are favored for the unparticle scale ${\Lambda }_{\mathcal{U}}$ of $\mathcal{O}(10\mathrm{TeV})$ and the unparticle coupling of $\mathcal{O}(10^{-3})$. $\mathrm{CR}(\mu -e,\mathrm{Nuclei})$ is proportional to ${\mathrm{Z}}_{\mathrm{eff}}^4{\mathrm{A}}^2/Z$ 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.

16 pages, 5 figures

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