Lepton flavor violating processes in unparticle physics

Abstract

We study the virtual effects of unparticle physics in the lepton flavor violating processes ${M}^{0}\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{'}\ensuremath{-}}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{'}\ensuremath{-}}$ scattering, where ${M}^{0}$ denotes the pseudoscalar mesons: ${\ensuremath{\pi}}^{0}$, ${K}_{L}$, ${D}_{0}$, ${B}_{0}$, ${B}_{s}^{0}$ and $l$, ${l}^{\ensuremath{'}}$ denote two different lepton flavors. For the decay of ${B}^{0}\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{'}\ensuremath{-}}$, there is no constraint from the current experimental upper bounds on the vector unparticle coupling with leptons. The constraint on the coupling constant between scalar unparticle field and leptons is sensitive to the scaling dimension of the unparticle ${d}_{\mathcal{U}}$. For the scattering process ${e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}{l}^{\ensuremath{-}}{l}^{\ensuremath{'}+}$, there is only constraint from experiments on the vector unparticle couplings with leptons but no constraint on the scalar unparticle. We study the $\sqrt{s}$ dependence of the cross section $\frac{1}{\ensuremath{\sigma}}\frac{d\ensuremath{\sigma}}{d\sqrt{s}}$ of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{l}^{\ensuremath{-}}{l}^{\ensuremath{'}+}$ with different values of ${d}_{\mathcal{U}}$. If ${d}_{\mathcal{U}}=1.5$, the cross section is independent on the center mass energy. For ${d}_{\mathcal{U}}>1.5$, the cross section increases with $\sqrt{s}$.