Neutrino Decays and Neutrino Electron Elastic Scattering in Unparticle Physics

Following Georgi's unparticle scheme, we examine the effective couplings between neutrinos and unparticle operators. As an immediate consequence, neutrinos become unstable and can decay into the unparticle stuff. Assuming the dimension transmutation scale is around $\Lambda^{}_{\cal U} \sim 1 ~{\rm TeV}$, we implement the cosmological limit on the neutrino lifetime to constrain the neutrino-unparticle couplings for different scaling dimensions $d$. In addition, provided that the electron-unparticle coupling is restricted due to the precise measurement of the anomalous magnetic moment of electron, we calculate the unparticle contribution to the neutrino-electron elastic scattering. It is more important to jointly deal with the couplings of the unparticle to the standard model particles rather than separately. Taking into account both electron- and neutrino-unparticle couplings, we find that the scaling dimension of the scalar unparticle should lie in the narrow range $1 < d < 2$ by requiring the observables to be physically meaningful. However, there is no consistent range of $d$ for the vector unparticle operator.