Unparticle decay of neutrinos and its possible signatures at Km2 detector for (3+1) flavour framework

We consider a scenario where ultra high energy neutrinos undergo unparticle decay during its passage from its cosmological source to Earth. The idea of unparticle had been first proposed by Georgi by considering the possible existence of an unknown scale invariant sector at high energies and the unparticles in this sector manifest itself below a dimensional transmutation scale ΛU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Lambda}_{\mathcal{U}} $$\end{document}. We then explore the possible signature of such decaying neutrinos to unparticles at a square kilometer detector such as IceCube.